Upload
phungdan
View
225
Download
0
Embed Size (px)
Citation preview
Modeling and Estimation of Transient CarrierFrequency Offset in Wireless Transceivers
Abstract
Future remote gadgets need to backing numerous applications (eg remote apply autonomy remote computerization and versatile gaming) with amazingly low dormancy and unwavering quality prerequisites over remote associations Upgrading remote handsets while exchanging between remote associations with diverse circuit attributes obliges tending to numerous fittings disabilities that have been neglected at one time Case in point exchanging between transmission and gathering radio capacities to encourage time division duplexing can change the heap on the force supply As the supply voltage changes in light of the sudden change in load the bearer recurrence floats Such a float brings about transient bearer recurrence counterbalance (CFO) that cant be assessed by ordinary CFO estimators and is normally tended to by embeddings alternately broadening watchman interims In this paper we investigate the displaying also estimation of the transient CFO which is displayed as the reaction of an under damped second request framework To adjust for the transient CFO we propose a low unpredictability parametric estimation calculation which utilizes the invalid space of the Hankel-like network built from stage contrast of the two parts of the tedious preparing grouping Moreover to minimize the mean squared mistake of the evaluated parameters in commotion a weighted subspace fitting calculation is inferred with a slight increment in multifaceted nature The Craacutemerndashrao headed for any unprejudiced estimator of the transient CFO parameters is inferred
CHAPTER-1
INTRODUCTION
In order to satisfy the exponential growing demand of wireless multimedia services a high speed
data access is requiredTherefore various techniques have been proposed in recent years to
achieve high system capacities Among them we interest to the multiple-input multiple- output
(MIMO)The MIMO concept has attracted lot of attention in wireless communications due to its
potential to increase the system capacity without extra bandwidth Multipath propagation usually
causes selective frequency channels To combat the effect of frequency selective fading MIMO
is associated with orthogonal frequency-division multiplexing (OFDM) technique OFDM is a
modulation technique which transforms frequency selective channel into a set of parallel flat
fading channelsA cyclic prefix CP is added at the beginning of each OFDM symbol to eliminate
ICI and ISI The inserted cyclic prefix is equal to or longer than to the channel The 3GPP Long
Term Evolution (LTE) is defining the next generation radio access networkLTE Downlink
systems adopt Orthogonal Frequency Division Multiple Access (OFDMA) and MIMO to
provide up to 100 Mbps (assuming a 2x2 MIMO system with 20MHz bandwidth)
11 OFDM
Orthogonal Frequency Division Multiplex the modulation concept being used for many
wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile
Video
Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding
increasing levels of use in todays radio communications scene OFDM has been adopted in the
Wi-Fi arena where the 80211a standard uses it to provide data rates up to 54 Mbps in the 5 GHz
ISM (Industrial Scientific and Medical) band In addition to this the recently ratified 80211g
standard has it in the 24 GHz ISM band In addition to this it is being used for WiMAX and is
also the format of choice for the next generation cellular radio communications systems
including 3G LTE and UMB
If this was not enough it is also being used for digital terrestrial television transmissions as well
as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long
medium and short wave bands is being launched and this has also adopted COFDM Then for the
future it is being proposed as the modulation technique for fourth generation cell phone systems
that are in their early stages of development and OFDM is also being used for many of the
proposed mobile phone video systems
OFDM orthogonal frequency division multiplex is a rather different format for modulation to
that used for more traditional forms of transmission It utilises many carriers together to provide
many advantages over simpler modulation formats
An OFDM signal consists of a number of closely spaced modulated carriers When modulation
of any form - voice data etc is applied to a carrier then sidebands spread out either side It is
necessary for a receiver to be able to receive the whole signal to be able to successfully
demodulate the data As a result when signals are transmitted close to one another they must be
spaced so that the receiver can separate them using a filter and there must be a guard band
between them This is not the case with OFDM Although the sidebands from each carrier
overlap they can still be received without the interference that might be expected because they
are orthogonal to each another This is achieved by having the carrier spacing equal to the
reciprocal of the symbol period
Fig11Traditional view of receiving signals carrying modulation
To see how OFDM works it is necessary to look at the receiver This acts as a bank of
demodulators translating each carrier down to DC The resulting signal is integrated over the
symbol period to regenerate the data from that carrier The same demodulator also demodulates
the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that
they will have a whole number of cycles in the symbol period and their contribution will sum to
zero - in other words there is no interference contribution
Fig12OFDM Spectrum
One requirement of the OFDM transmitting and receiving systems is that they must be linear
Any non-linearity will cause interference between the carriers as a result of inter-modulation
distortion This will introduce unwanted signals that would cause interference and impair the
orthogonality of the transmission
In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such
as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the
peaks whilst the average power is much lower and this leads to inefficiency In some systems the
peaks are limited Although this introduces distortion that results in a higher level of data errors
the system can rely on the error correction to remove them
The data to be transmitted on an OFDM signal is spread across the carriers of the signal each
carrier taking part of the payload This reduces the data rate taken by each carrier The lower data
rate has the advantage that interference from reflections is much less critical This is achieved by
adding a guard band time or guard interval into the system This ensures that the data is only
sampled when the signal is stable and no new delayed signals arrive that would alter the timing
and phase of the signal
The OFDM transmission scheme has the following key advantages __Makes efficient use of the
spectrum by allowing overlap
__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to
frequency selective fading than single carrier systems are
__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and
interleaving one can recover symbols lost due to the frequency selectivity of the channel C
hannel equalization becomes simpler than by using adaptive equalization techniques with single
carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity
as discussed in OFDM is computationally efficient by using FFT techniques to
implement the modulation and demodulation functions
__In conjunction with differential modulation there is no need to implement a channel estimator
__Is less sensitive to sample timing offsets than single carrier systems are
__Provides good protection against cochannel interference and impulsive parasitic noise
In terms of drawbacks OFDM has the following characteristics
__The OFDM signal has a noise like amplitude with a very large dynamic range
therefore it requires RF power amplifiers with a high peak to average power ratio
__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to
leakage of the DFT
12 The Standard IEEE 80211a
The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of
requirements for the physical layer (PHY) and a medium access control (MAC) layer For high
data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE
80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that
require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on
which the 80211 WLANs operate is different from wired media in many ways One of those
differences is the presence of interference in unlicensed frequency bands which can impact
communications between WLAN NICs Interference on the wireless medium can result in packet
loss which causes the network to suffer in terms of throughput performance Current 24-GHz
80211b radios handle interference well because they support a feature in the MAC layer known
as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to
increase the probability of delivering packets without errors induced by the interferer When a
frame is fragmented the sequence control field in the MAC header indicates placement of the
individual fragments and whether the current fragment is the last in the sequence When frames
are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)
control frames are used to manage the data transmission Therefore using fragmentation
esigners can avoid interference problems in their WLAN designs But interference is not the only
problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and
research laboratories all over the
world It has already been accepted for the new wireless local area network standards IEEE
80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access
Communication (MMAC) Systems Also it is expected to be used for wireless broadband
multimedia communications Data rate is really what broadband is about The new standard
specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers
for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-
and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE
80211a following the parameters established for that case OFDM can be seen as either a
modulation technique or a multiplexing technique
One of the main reasons to use OFDM is to increase the robustness against frequency selective
fading or narrowband interference In a single carrier system a single fade or interferer can cause
the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will
be affected Error correction coding can then be used to correct for the few erroneous subcarriers
The concept of using parallel data transmission and frequency division multiplexing was
published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US
patent was filed and issued in January 1970 In a classical parallel data system the total signal
frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is
modulated with a separate symbol and then the N subchannels are frequency-multiplexed It
seems good to avoid spectral overlap of channels to eliminate interchannel interference
However this leads to inefficient use of the available spectrum To cope with the inefficiency
the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid
the use of high-speed equalization and to combat impulsive noise and multipath distortion as
well as to fully use the available bandwidth
Illustrates the difference between the conventional nonoverlapping multicarrier technique and the
overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation
technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique
however we need to reduce crosstalk between subcarriers which means that we want
orthogonality between the different modulated carriers The word orthogonal indicates that there
is a precise mathematical relationship between the frequencies of the carriers in the system In a
normal frequency-division multiplex system many carriers are spaced apart in such a way that
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Abstract
Future remote gadgets need to backing numerous applications (eg remote apply autonomy remote computerization and versatile gaming) with amazingly low dormancy and unwavering quality prerequisites over remote associations Upgrading remote handsets while exchanging between remote associations with diverse circuit attributes obliges tending to numerous fittings disabilities that have been neglected at one time Case in point exchanging between transmission and gathering radio capacities to encourage time division duplexing can change the heap on the force supply As the supply voltage changes in light of the sudden change in load the bearer recurrence floats Such a float brings about transient bearer recurrence counterbalance (CFO) that cant be assessed by ordinary CFO estimators and is normally tended to by embeddings alternately broadening watchman interims In this paper we investigate the displaying also estimation of the transient CFO which is displayed as the reaction of an under damped second request framework To adjust for the transient CFO we propose a low unpredictability parametric estimation calculation which utilizes the invalid space of the Hankel-like network built from stage contrast of the two parts of the tedious preparing grouping Moreover to minimize the mean squared mistake of the evaluated parameters in commotion a weighted subspace fitting calculation is inferred with a slight increment in multifaceted nature The Craacutemerndashrao headed for any unprejudiced estimator of the transient CFO parameters is inferred
CHAPTER-1
INTRODUCTION
In order to satisfy the exponential growing demand of wireless multimedia services a high speed
data access is requiredTherefore various techniques have been proposed in recent years to
achieve high system capacities Among them we interest to the multiple-input multiple- output
(MIMO)The MIMO concept has attracted lot of attention in wireless communications due to its
potential to increase the system capacity without extra bandwidth Multipath propagation usually
causes selective frequency channels To combat the effect of frequency selective fading MIMO
is associated with orthogonal frequency-division multiplexing (OFDM) technique OFDM is a
modulation technique which transforms frequency selective channel into a set of parallel flat
fading channelsA cyclic prefix CP is added at the beginning of each OFDM symbol to eliminate
ICI and ISI The inserted cyclic prefix is equal to or longer than to the channel The 3GPP Long
Term Evolution (LTE) is defining the next generation radio access networkLTE Downlink
systems adopt Orthogonal Frequency Division Multiple Access (OFDMA) and MIMO to
provide up to 100 Mbps (assuming a 2x2 MIMO system with 20MHz bandwidth)
11 OFDM
Orthogonal Frequency Division Multiplex the modulation concept being used for many
wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile
Video
Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding
increasing levels of use in todays radio communications scene OFDM has been adopted in the
Wi-Fi arena where the 80211a standard uses it to provide data rates up to 54 Mbps in the 5 GHz
ISM (Industrial Scientific and Medical) band In addition to this the recently ratified 80211g
standard has it in the 24 GHz ISM band In addition to this it is being used for WiMAX and is
also the format of choice for the next generation cellular radio communications systems
including 3G LTE and UMB
If this was not enough it is also being used for digital terrestrial television transmissions as well
as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long
medium and short wave bands is being launched and this has also adopted COFDM Then for the
future it is being proposed as the modulation technique for fourth generation cell phone systems
that are in their early stages of development and OFDM is also being used for many of the
proposed mobile phone video systems
OFDM orthogonal frequency division multiplex is a rather different format for modulation to
that used for more traditional forms of transmission It utilises many carriers together to provide
many advantages over simpler modulation formats
An OFDM signal consists of a number of closely spaced modulated carriers When modulation
of any form - voice data etc is applied to a carrier then sidebands spread out either side It is
necessary for a receiver to be able to receive the whole signal to be able to successfully
demodulate the data As a result when signals are transmitted close to one another they must be
spaced so that the receiver can separate them using a filter and there must be a guard band
between them This is not the case with OFDM Although the sidebands from each carrier
overlap they can still be received without the interference that might be expected because they
are orthogonal to each another This is achieved by having the carrier spacing equal to the
reciprocal of the symbol period
Fig11Traditional view of receiving signals carrying modulation
To see how OFDM works it is necessary to look at the receiver This acts as a bank of
demodulators translating each carrier down to DC The resulting signal is integrated over the
symbol period to regenerate the data from that carrier The same demodulator also demodulates
the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that
they will have a whole number of cycles in the symbol period and their contribution will sum to
zero - in other words there is no interference contribution
Fig12OFDM Spectrum
One requirement of the OFDM transmitting and receiving systems is that they must be linear
Any non-linearity will cause interference between the carriers as a result of inter-modulation
distortion This will introduce unwanted signals that would cause interference and impair the
orthogonality of the transmission
In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such
as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the
peaks whilst the average power is much lower and this leads to inefficiency In some systems the
peaks are limited Although this introduces distortion that results in a higher level of data errors
the system can rely on the error correction to remove them
The data to be transmitted on an OFDM signal is spread across the carriers of the signal each
carrier taking part of the payload This reduces the data rate taken by each carrier The lower data
rate has the advantage that interference from reflections is much less critical This is achieved by
adding a guard band time or guard interval into the system This ensures that the data is only
sampled when the signal is stable and no new delayed signals arrive that would alter the timing
and phase of the signal
The OFDM transmission scheme has the following key advantages __Makes efficient use of the
spectrum by allowing overlap
__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to
frequency selective fading than single carrier systems are
__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and
interleaving one can recover symbols lost due to the frequency selectivity of the channel C
hannel equalization becomes simpler than by using adaptive equalization techniques with single
carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity
as discussed in OFDM is computationally efficient by using FFT techniques to
implement the modulation and demodulation functions
__In conjunction with differential modulation there is no need to implement a channel estimator
__Is less sensitive to sample timing offsets than single carrier systems are
__Provides good protection against cochannel interference and impulsive parasitic noise
In terms of drawbacks OFDM has the following characteristics
__The OFDM signal has a noise like amplitude with a very large dynamic range
therefore it requires RF power amplifiers with a high peak to average power ratio
__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to
leakage of the DFT
12 The Standard IEEE 80211a
The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of
requirements for the physical layer (PHY) and a medium access control (MAC) layer For high
data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE
80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that
require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on
which the 80211 WLANs operate is different from wired media in many ways One of those
differences is the presence of interference in unlicensed frequency bands which can impact
communications between WLAN NICs Interference on the wireless medium can result in packet
loss which causes the network to suffer in terms of throughput performance Current 24-GHz
80211b radios handle interference well because they support a feature in the MAC layer known
as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to
increase the probability of delivering packets without errors induced by the interferer When a
frame is fragmented the sequence control field in the MAC header indicates placement of the
individual fragments and whether the current fragment is the last in the sequence When frames
are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)
control frames are used to manage the data transmission Therefore using fragmentation
esigners can avoid interference problems in their WLAN designs But interference is not the only
problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and
research laboratories all over the
world It has already been accepted for the new wireless local area network standards IEEE
80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access
Communication (MMAC) Systems Also it is expected to be used for wireless broadband
multimedia communications Data rate is really what broadband is about The new standard
specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers
for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-
and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE
80211a following the parameters established for that case OFDM can be seen as either a
modulation technique or a multiplexing technique
One of the main reasons to use OFDM is to increase the robustness against frequency selective
fading or narrowband interference In a single carrier system a single fade or interferer can cause
the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will
be affected Error correction coding can then be used to correct for the few erroneous subcarriers
The concept of using parallel data transmission and frequency division multiplexing was
published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US
patent was filed and issued in January 1970 In a classical parallel data system the total signal
frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is
modulated with a separate symbol and then the N subchannels are frequency-multiplexed It
seems good to avoid spectral overlap of channels to eliminate interchannel interference
However this leads to inefficient use of the available spectrum To cope with the inefficiency
the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid
the use of high-speed equalization and to combat impulsive noise and multipath distortion as
well as to fully use the available bandwidth
Illustrates the difference between the conventional nonoverlapping multicarrier technique and the
overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation
technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique
however we need to reduce crosstalk between subcarriers which means that we want
orthogonality between the different modulated carriers The word orthogonal indicates that there
is a precise mathematical relationship between the frequencies of the carriers in the system In a
normal frequency-division multiplex system many carriers are spaced apart in such a way that
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
CHAPTER-1
INTRODUCTION
In order to satisfy the exponential growing demand of wireless multimedia services a high speed
data access is requiredTherefore various techniques have been proposed in recent years to
achieve high system capacities Among them we interest to the multiple-input multiple- output
(MIMO)The MIMO concept has attracted lot of attention in wireless communications due to its
potential to increase the system capacity without extra bandwidth Multipath propagation usually
causes selective frequency channels To combat the effect of frequency selective fading MIMO
is associated with orthogonal frequency-division multiplexing (OFDM) technique OFDM is a
modulation technique which transforms frequency selective channel into a set of parallel flat
fading channelsA cyclic prefix CP is added at the beginning of each OFDM symbol to eliminate
ICI and ISI The inserted cyclic prefix is equal to or longer than to the channel The 3GPP Long
Term Evolution (LTE) is defining the next generation radio access networkLTE Downlink
systems adopt Orthogonal Frequency Division Multiple Access (OFDMA) and MIMO to
provide up to 100 Mbps (assuming a 2x2 MIMO system with 20MHz bandwidth)
11 OFDM
Orthogonal Frequency Division Multiplex the modulation concept being used for many
wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile
Video
Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding
increasing levels of use in todays radio communications scene OFDM has been adopted in the
Wi-Fi arena where the 80211a standard uses it to provide data rates up to 54 Mbps in the 5 GHz
ISM (Industrial Scientific and Medical) band In addition to this the recently ratified 80211g
standard has it in the 24 GHz ISM band In addition to this it is being used for WiMAX and is
also the format of choice for the next generation cellular radio communications systems
including 3G LTE and UMB
If this was not enough it is also being used for digital terrestrial television transmissions as well
as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long
medium and short wave bands is being launched and this has also adopted COFDM Then for the
future it is being proposed as the modulation technique for fourth generation cell phone systems
that are in their early stages of development and OFDM is also being used for many of the
proposed mobile phone video systems
OFDM orthogonal frequency division multiplex is a rather different format for modulation to
that used for more traditional forms of transmission It utilises many carriers together to provide
many advantages over simpler modulation formats
An OFDM signal consists of a number of closely spaced modulated carriers When modulation
of any form - voice data etc is applied to a carrier then sidebands spread out either side It is
necessary for a receiver to be able to receive the whole signal to be able to successfully
demodulate the data As a result when signals are transmitted close to one another they must be
spaced so that the receiver can separate them using a filter and there must be a guard band
between them This is not the case with OFDM Although the sidebands from each carrier
overlap they can still be received without the interference that might be expected because they
are orthogonal to each another This is achieved by having the carrier spacing equal to the
reciprocal of the symbol period
Fig11Traditional view of receiving signals carrying modulation
To see how OFDM works it is necessary to look at the receiver This acts as a bank of
demodulators translating each carrier down to DC The resulting signal is integrated over the
symbol period to regenerate the data from that carrier The same demodulator also demodulates
the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that
they will have a whole number of cycles in the symbol period and their contribution will sum to
zero - in other words there is no interference contribution
Fig12OFDM Spectrum
One requirement of the OFDM transmitting and receiving systems is that they must be linear
Any non-linearity will cause interference between the carriers as a result of inter-modulation
distortion This will introduce unwanted signals that would cause interference and impair the
orthogonality of the transmission
In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such
as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the
peaks whilst the average power is much lower and this leads to inefficiency In some systems the
peaks are limited Although this introduces distortion that results in a higher level of data errors
the system can rely on the error correction to remove them
The data to be transmitted on an OFDM signal is spread across the carriers of the signal each
carrier taking part of the payload This reduces the data rate taken by each carrier The lower data
rate has the advantage that interference from reflections is much less critical This is achieved by
adding a guard band time or guard interval into the system This ensures that the data is only
sampled when the signal is stable and no new delayed signals arrive that would alter the timing
and phase of the signal
The OFDM transmission scheme has the following key advantages __Makes efficient use of the
spectrum by allowing overlap
__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to
frequency selective fading than single carrier systems are
__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and
interleaving one can recover symbols lost due to the frequency selectivity of the channel C
hannel equalization becomes simpler than by using adaptive equalization techniques with single
carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity
as discussed in OFDM is computationally efficient by using FFT techniques to
implement the modulation and demodulation functions
__In conjunction with differential modulation there is no need to implement a channel estimator
__Is less sensitive to sample timing offsets than single carrier systems are
__Provides good protection against cochannel interference and impulsive parasitic noise
In terms of drawbacks OFDM has the following characteristics
__The OFDM signal has a noise like amplitude with a very large dynamic range
therefore it requires RF power amplifiers with a high peak to average power ratio
__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to
leakage of the DFT
12 The Standard IEEE 80211a
The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of
requirements for the physical layer (PHY) and a medium access control (MAC) layer For high
data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE
80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that
require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on
which the 80211 WLANs operate is different from wired media in many ways One of those
differences is the presence of interference in unlicensed frequency bands which can impact
communications between WLAN NICs Interference on the wireless medium can result in packet
loss which causes the network to suffer in terms of throughput performance Current 24-GHz
80211b radios handle interference well because they support a feature in the MAC layer known
as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to
increase the probability of delivering packets without errors induced by the interferer When a
frame is fragmented the sequence control field in the MAC header indicates placement of the
individual fragments and whether the current fragment is the last in the sequence When frames
are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)
control frames are used to manage the data transmission Therefore using fragmentation
esigners can avoid interference problems in their WLAN designs But interference is not the only
problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and
research laboratories all over the
world It has already been accepted for the new wireless local area network standards IEEE
80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access
Communication (MMAC) Systems Also it is expected to be used for wireless broadband
multimedia communications Data rate is really what broadband is about The new standard
specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers
for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-
and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE
80211a following the parameters established for that case OFDM can be seen as either a
modulation technique or a multiplexing technique
One of the main reasons to use OFDM is to increase the robustness against frequency selective
fading or narrowband interference In a single carrier system a single fade or interferer can cause
the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will
be affected Error correction coding can then be used to correct for the few erroneous subcarriers
The concept of using parallel data transmission and frequency division multiplexing was
published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US
patent was filed and issued in January 1970 In a classical parallel data system the total signal
frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is
modulated with a separate symbol and then the N subchannels are frequency-multiplexed It
seems good to avoid spectral overlap of channels to eliminate interchannel interference
However this leads to inefficient use of the available spectrum To cope with the inefficiency
the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid
the use of high-speed equalization and to combat impulsive noise and multipath distortion as
well as to fully use the available bandwidth
Illustrates the difference between the conventional nonoverlapping multicarrier technique and the
overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation
technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique
however we need to reduce crosstalk between subcarriers which means that we want
orthogonality between the different modulated carriers The word orthogonal indicates that there
is a precise mathematical relationship between the frequencies of the carriers in the system In a
normal frequency-division multiplex system many carriers are spaced apart in such a way that
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
In order to satisfy the exponential growing demand of wireless multimedia services a high speed
data access is requiredTherefore various techniques have been proposed in recent years to
achieve high system capacities Among them we interest to the multiple-input multiple- output
(MIMO)The MIMO concept has attracted lot of attention in wireless communications due to its
potential to increase the system capacity without extra bandwidth Multipath propagation usually
causes selective frequency channels To combat the effect of frequency selective fading MIMO
is associated with orthogonal frequency-division multiplexing (OFDM) technique OFDM is a
modulation technique which transforms frequency selective channel into a set of parallel flat
fading channelsA cyclic prefix CP is added at the beginning of each OFDM symbol to eliminate
ICI and ISI The inserted cyclic prefix is equal to or longer than to the channel The 3GPP Long
Term Evolution (LTE) is defining the next generation radio access networkLTE Downlink
systems adopt Orthogonal Frequency Division Multiple Access (OFDMA) and MIMO to
provide up to 100 Mbps (assuming a 2x2 MIMO system with 20MHz bandwidth)
11 OFDM
Orthogonal Frequency Division Multiplex the modulation concept being used for many
wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile
Video
Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding
increasing levels of use in todays radio communications scene OFDM has been adopted in the
Wi-Fi arena where the 80211a standard uses it to provide data rates up to 54 Mbps in the 5 GHz
ISM (Industrial Scientific and Medical) band In addition to this the recently ratified 80211g
standard has it in the 24 GHz ISM band In addition to this it is being used for WiMAX and is
also the format of choice for the next generation cellular radio communications systems
including 3G LTE and UMB
If this was not enough it is also being used for digital terrestrial television transmissions as well
as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long
medium and short wave bands is being launched and this has also adopted COFDM Then for the
future it is being proposed as the modulation technique for fourth generation cell phone systems
that are in their early stages of development and OFDM is also being used for many of the
proposed mobile phone video systems
OFDM orthogonal frequency division multiplex is a rather different format for modulation to
that used for more traditional forms of transmission It utilises many carriers together to provide
many advantages over simpler modulation formats
An OFDM signal consists of a number of closely spaced modulated carriers When modulation
of any form - voice data etc is applied to a carrier then sidebands spread out either side It is
necessary for a receiver to be able to receive the whole signal to be able to successfully
demodulate the data As a result when signals are transmitted close to one another they must be
spaced so that the receiver can separate them using a filter and there must be a guard band
between them This is not the case with OFDM Although the sidebands from each carrier
overlap they can still be received without the interference that might be expected because they
are orthogonal to each another This is achieved by having the carrier spacing equal to the
reciprocal of the symbol period
Fig11Traditional view of receiving signals carrying modulation
To see how OFDM works it is necessary to look at the receiver This acts as a bank of
demodulators translating each carrier down to DC The resulting signal is integrated over the
symbol period to regenerate the data from that carrier The same demodulator also demodulates
the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that
they will have a whole number of cycles in the symbol period and their contribution will sum to
zero - in other words there is no interference contribution
Fig12OFDM Spectrum
One requirement of the OFDM transmitting and receiving systems is that they must be linear
Any non-linearity will cause interference between the carriers as a result of inter-modulation
distortion This will introduce unwanted signals that would cause interference and impair the
orthogonality of the transmission
In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such
as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the
peaks whilst the average power is much lower and this leads to inefficiency In some systems the
peaks are limited Although this introduces distortion that results in a higher level of data errors
the system can rely on the error correction to remove them
The data to be transmitted on an OFDM signal is spread across the carriers of the signal each
carrier taking part of the payload This reduces the data rate taken by each carrier The lower data
rate has the advantage that interference from reflections is much less critical This is achieved by
adding a guard band time or guard interval into the system This ensures that the data is only
sampled when the signal is stable and no new delayed signals arrive that would alter the timing
and phase of the signal
The OFDM transmission scheme has the following key advantages __Makes efficient use of the
spectrum by allowing overlap
__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to
frequency selective fading than single carrier systems are
__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and
interleaving one can recover symbols lost due to the frequency selectivity of the channel C
hannel equalization becomes simpler than by using adaptive equalization techniques with single
carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity
as discussed in OFDM is computationally efficient by using FFT techniques to
implement the modulation and demodulation functions
__In conjunction with differential modulation there is no need to implement a channel estimator
__Is less sensitive to sample timing offsets than single carrier systems are
__Provides good protection against cochannel interference and impulsive parasitic noise
In terms of drawbacks OFDM has the following characteristics
__The OFDM signal has a noise like amplitude with a very large dynamic range
therefore it requires RF power amplifiers with a high peak to average power ratio
__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to
leakage of the DFT
12 The Standard IEEE 80211a
The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of
requirements for the physical layer (PHY) and a medium access control (MAC) layer For high
data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE
80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that
require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on
which the 80211 WLANs operate is different from wired media in many ways One of those
differences is the presence of interference in unlicensed frequency bands which can impact
communications between WLAN NICs Interference on the wireless medium can result in packet
loss which causes the network to suffer in terms of throughput performance Current 24-GHz
80211b radios handle interference well because they support a feature in the MAC layer known
as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to
increase the probability of delivering packets without errors induced by the interferer When a
frame is fragmented the sequence control field in the MAC header indicates placement of the
individual fragments and whether the current fragment is the last in the sequence When frames
are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)
control frames are used to manage the data transmission Therefore using fragmentation
esigners can avoid interference problems in their WLAN designs But interference is not the only
problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and
research laboratories all over the
world It has already been accepted for the new wireless local area network standards IEEE
80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access
Communication (MMAC) Systems Also it is expected to be used for wireless broadband
multimedia communications Data rate is really what broadband is about The new standard
specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers
for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-
and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE
80211a following the parameters established for that case OFDM can be seen as either a
modulation technique or a multiplexing technique
One of the main reasons to use OFDM is to increase the robustness against frequency selective
fading or narrowband interference In a single carrier system a single fade or interferer can cause
the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will
be affected Error correction coding can then be used to correct for the few erroneous subcarriers
The concept of using parallel data transmission and frequency division multiplexing was
published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US
patent was filed and issued in January 1970 In a classical parallel data system the total signal
frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is
modulated with a separate symbol and then the N subchannels are frequency-multiplexed It
seems good to avoid spectral overlap of channels to eliminate interchannel interference
However this leads to inefficient use of the available spectrum To cope with the inefficiency
the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid
the use of high-speed equalization and to combat impulsive noise and multipath distortion as
well as to fully use the available bandwidth
Illustrates the difference between the conventional nonoverlapping multicarrier technique and the
overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation
technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique
however we need to reduce crosstalk between subcarriers which means that we want
orthogonality between the different modulated carriers The word orthogonal indicates that there
is a precise mathematical relationship between the frequencies of the carriers in the system In a
normal frequency-division multiplex system many carriers are spaced apart in such a way that
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
If this was not enough it is also being used for digital terrestrial television transmissions as well
as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long
medium and short wave bands is being launched and this has also adopted COFDM Then for the
future it is being proposed as the modulation technique for fourth generation cell phone systems
that are in their early stages of development and OFDM is also being used for many of the
proposed mobile phone video systems
OFDM orthogonal frequency division multiplex is a rather different format for modulation to
that used for more traditional forms of transmission It utilises many carriers together to provide
many advantages over simpler modulation formats
An OFDM signal consists of a number of closely spaced modulated carriers When modulation
of any form - voice data etc is applied to a carrier then sidebands spread out either side It is
necessary for a receiver to be able to receive the whole signal to be able to successfully
demodulate the data As a result when signals are transmitted close to one another they must be
spaced so that the receiver can separate them using a filter and there must be a guard band
between them This is not the case with OFDM Although the sidebands from each carrier
overlap they can still be received without the interference that might be expected because they
are orthogonal to each another This is achieved by having the carrier spacing equal to the
reciprocal of the symbol period
Fig11Traditional view of receiving signals carrying modulation
To see how OFDM works it is necessary to look at the receiver This acts as a bank of
demodulators translating each carrier down to DC The resulting signal is integrated over the
symbol period to regenerate the data from that carrier The same demodulator also demodulates
the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that
they will have a whole number of cycles in the symbol period and their contribution will sum to
zero - in other words there is no interference contribution
Fig12OFDM Spectrum
One requirement of the OFDM transmitting and receiving systems is that they must be linear
Any non-linearity will cause interference between the carriers as a result of inter-modulation
distortion This will introduce unwanted signals that would cause interference and impair the
orthogonality of the transmission
In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such
as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the
peaks whilst the average power is much lower and this leads to inefficiency In some systems the
peaks are limited Although this introduces distortion that results in a higher level of data errors
the system can rely on the error correction to remove them
The data to be transmitted on an OFDM signal is spread across the carriers of the signal each
carrier taking part of the payload This reduces the data rate taken by each carrier The lower data
rate has the advantage that interference from reflections is much less critical This is achieved by
adding a guard band time or guard interval into the system This ensures that the data is only
sampled when the signal is stable and no new delayed signals arrive that would alter the timing
and phase of the signal
The OFDM transmission scheme has the following key advantages __Makes efficient use of the
spectrum by allowing overlap
__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to
frequency selective fading than single carrier systems are
__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and
interleaving one can recover symbols lost due to the frequency selectivity of the channel C
hannel equalization becomes simpler than by using adaptive equalization techniques with single
carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity
as discussed in OFDM is computationally efficient by using FFT techniques to
implement the modulation and demodulation functions
__In conjunction with differential modulation there is no need to implement a channel estimator
__Is less sensitive to sample timing offsets than single carrier systems are
__Provides good protection against cochannel interference and impulsive parasitic noise
In terms of drawbacks OFDM has the following characteristics
__The OFDM signal has a noise like amplitude with a very large dynamic range
therefore it requires RF power amplifiers with a high peak to average power ratio
__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to
leakage of the DFT
12 The Standard IEEE 80211a
The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of
requirements for the physical layer (PHY) and a medium access control (MAC) layer For high
data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE
80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that
require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on
which the 80211 WLANs operate is different from wired media in many ways One of those
differences is the presence of interference in unlicensed frequency bands which can impact
communications between WLAN NICs Interference on the wireless medium can result in packet
loss which causes the network to suffer in terms of throughput performance Current 24-GHz
80211b radios handle interference well because they support a feature in the MAC layer known
as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to
increase the probability of delivering packets without errors induced by the interferer When a
frame is fragmented the sequence control field in the MAC header indicates placement of the
individual fragments and whether the current fragment is the last in the sequence When frames
are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)
control frames are used to manage the data transmission Therefore using fragmentation
esigners can avoid interference problems in their WLAN designs But interference is not the only
problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and
research laboratories all over the
world It has already been accepted for the new wireless local area network standards IEEE
80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access
Communication (MMAC) Systems Also it is expected to be used for wireless broadband
multimedia communications Data rate is really what broadband is about The new standard
specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers
for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-
and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE
80211a following the parameters established for that case OFDM can be seen as either a
modulation technique or a multiplexing technique
One of the main reasons to use OFDM is to increase the robustness against frequency selective
fading or narrowband interference In a single carrier system a single fade or interferer can cause
the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will
be affected Error correction coding can then be used to correct for the few erroneous subcarriers
The concept of using parallel data transmission and frequency division multiplexing was
published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US
patent was filed and issued in January 1970 In a classical parallel data system the total signal
frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is
modulated with a separate symbol and then the N subchannels are frequency-multiplexed It
seems good to avoid spectral overlap of channels to eliminate interchannel interference
However this leads to inefficient use of the available spectrum To cope with the inefficiency
the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid
the use of high-speed equalization and to combat impulsive noise and multipath distortion as
well as to fully use the available bandwidth
Illustrates the difference between the conventional nonoverlapping multicarrier technique and the
overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation
technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique
however we need to reduce crosstalk between subcarriers which means that we want
orthogonality between the different modulated carriers The word orthogonal indicates that there
is a precise mathematical relationship between the frequencies of the carriers in the system In a
normal frequency-division multiplex system many carriers are spaced apart in such a way that
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Fig12OFDM Spectrum
One requirement of the OFDM transmitting and receiving systems is that they must be linear
Any non-linearity will cause interference between the carriers as a result of inter-modulation
distortion This will introduce unwanted signals that would cause interference and impair the
orthogonality of the transmission
In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such
as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the
peaks whilst the average power is much lower and this leads to inefficiency In some systems the
peaks are limited Although this introduces distortion that results in a higher level of data errors
the system can rely on the error correction to remove them
The data to be transmitted on an OFDM signal is spread across the carriers of the signal each
carrier taking part of the payload This reduces the data rate taken by each carrier The lower data
rate has the advantage that interference from reflections is much less critical This is achieved by
adding a guard band time or guard interval into the system This ensures that the data is only
sampled when the signal is stable and no new delayed signals arrive that would alter the timing
and phase of the signal
The OFDM transmission scheme has the following key advantages __Makes efficient use of the
spectrum by allowing overlap
__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to
frequency selective fading than single carrier systems are
__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and
interleaving one can recover symbols lost due to the frequency selectivity of the channel C
hannel equalization becomes simpler than by using adaptive equalization techniques with single
carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity
as discussed in OFDM is computationally efficient by using FFT techniques to
implement the modulation and demodulation functions
__In conjunction with differential modulation there is no need to implement a channel estimator
__Is less sensitive to sample timing offsets than single carrier systems are
__Provides good protection against cochannel interference and impulsive parasitic noise
In terms of drawbacks OFDM has the following characteristics
__The OFDM signal has a noise like amplitude with a very large dynamic range
therefore it requires RF power amplifiers with a high peak to average power ratio
__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to
leakage of the DFT
12 The Standard IEEE 80211a
The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of
requirements for the physical layer (PHY) and a medium access control (MAC) layer For high
data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE
80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that
require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on
which the 80211 WLANs operate is different from wired media in many ways One of those
differences is the presence of interference in unlicensed frequency bands which can impact
communications between WLAN NICs Interference on the wireless medium can result in packet
loss which causes the network to suffer in terms of throughput performance Current 24-GHz
80211b radios handle interference well because they support a feature in the MAC layer known
as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to
increase the probability of delivering packets without errors induced by the interferer When a
frame is fragmented the sequence control field in the MAC header indicates placement of the
individual fragments and whether the current fragment is the last in the sequence When frames
are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)
control frames are used to manage the data transmission Therefore using fragmentation
esigners can avoid interference problems in their WLAN designs But interference is not the only
problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and
research laboratories all over the
world It has already been accepted for the new wireless local area network standards IEEE
80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access
Communication (MMAC) Systems Also it is expected to be used for wireless broadband
multimedia communications Data rate is really what broadband is about The new standard
specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers
for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-
and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE
80211a following the parameters established for that case OFDM can be seen as either a
modulation technique or a multiplexing technique
One of the main reasons to use OFDM is to increase the robustness against frequency selective
fading or narrowband interference In a single carrier system a single fade or interferer can cause
the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will
be affected Error correction coding can then be used to correct for the few erroneous subcarriers
The concept of using parallel data transmission and frequency division multiplexing was
published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US
patent was filed and issued in January 1970 In a classical parallel data system the total signal
frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is
modulated with a separate symbol and then the N subchannels are frequency-multiplexed It
seems good to avoid spectral overlap of channels to eliminate interchannel interference
However this leads to inefficient use of the available spectrum To cope with the inefficiency
the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid
the use of high-speed equalization and to combat impulsive noise and multipath distortion as
well as to fully use the available bandwidth
Illustrates the difference between the conventional nonoverlapping multicarrier technique and the
overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation
technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique
however we need to reduce crosstalk between subcarriers which means that we want
orthogonality between the different modulated carriers The word orthogonal indicates that there
is a precise mathematical relationship between the frequencies of the carriers in the system In a
normal frequency-division multiplex system many carriers are spaced apart in such a way that
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
__In conjunction with differential modulation there is no need to implement a channel estimator
__Is less sensitive to sample timing offsets than single carrier systems are
__Provides good protection against cochannel interference and impulsive parasitic noise
In terms of drawbacks OFDM has the following characteristics
__The OFDM signal has a noise like amplitude with a very large dynamic range
therefore it requires RF power amplifiers with a high peak to average power ratio
__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to
leakage of the DFT
12 The Standard IEEE 80211a
The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of
requirements for the physical layer (PHY) and a medium access control (MAC) layer For high
data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE
80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that
require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on
which the 80211 WLANs operate is different from wired media in many ways One of those
differences is the presence of interference in unlicensed frequency bands which can impact
communications between WLAN NICs Interference on the wireless medium can result in packet
loss which causes the network to suffer in terms of throughput performance Current 24-GHz
80211b radios handle interference well because they support a feature in the MAC layer known
as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to
increase the probability of delivering packets without errors induced by the interferer When a
frame is fragmented the sequence control field in the MAC header indicates placement of the
individual fragments and whether the current fragment is the last in the sequence When frames
are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)
control frames are used to manage the data transmission Therefore using fragmentation
esigners can avoid interference problems in their WLAN designs But interference is not the only
problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and
research laboratories all over the
world It has already been accepted for the new wireless local area network standards IEEE
80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access
Communication (MMAC) Systems Also it is expected to be used for wireless broadband
multimedia communications Data rate is really what broadband is about The new standard
specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers
for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-
and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE
80211a following the parameters established for that case OFDM can be seen as either a
modulation technique or a multiplexing technique
One of the main reasons to use OFDM is to increase the robustness against frequency selective
fading or narrowband interference In a single carrier system a single fade or interferer can cause
the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will
be affected Error correction coding can then be used to correct for the few erroneous subcarriers
The concept of using parallel data transmission and frequency division multiplexing was
published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US
patent was filed and issued in January 1970 In a classical parallel data system the total signal
frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is
modulated with a separate symbol and then the N subchannels are frequency-multiplexed It
seems good to avoid spectral overlap of channels to eliminate interchannel interference
However this leads to inefficient use of the available spectrum To cope with the inefficiency
the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid
the use of high-speed equalization and to combat impulsive noise and multipath distortion as
well as to fully use the available bandwidth
Illustrates the difference between the conventional nonoverlapping multicarrier technique and the
overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation
technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique
however we need to reduce crosstalk between subcarriers which means that we want
orthogonality between the different modulated carriers The word orthogonal indicates that there
is a precise mathematical relationship between the frequencies of the carriers in the system In a
normal frequency-division multiplex system many carriers are spaced apart in such a way that
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Communication (MMAC) Systems Also it is expected to be used for wireless broadband
multimedia communications Data rate is really what broadband is about The new standard
specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers
for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-
and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE
80211a following the parameters established for that case OFDM can be seen as either a
modulation technique or a multiplexing technique
One of the main reasons to use OFDM is to increase the robustness against frequency selective
fading or narrowband interference In a single carrier system a single fade or interferer can cause
the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will
be affected Error correction coding can then be used to correct for the few erroneous subcarriers
The concept of using parallel data transmission and frequency division multiplexing was
published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US
patent was filed and issued in January 1970 In a classical parallel data system the total signal
frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is
modulated with a separate symbol and then the N subchannels are frequency-multiplexed It
seems good to avoid spectral overlap of channels to eliminate interchannel interference
However this leads to inefficient use of the available spectrum To cope with the inefficiency
the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping
subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid
the use of high-speed equalization and to combat impulsive noise and multipath distortion as
well as to fully use the available bandwidth
Illustrates the difference between the conventional nonoverlapping multicarrier technique and the
overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation
technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique
however we need to reduce crosstalk between subcarriers which means that we want
orthogonality between the different modulated carriers The word orthogonal indicates that there
is a precise mathematical relationship between the frequencies of the carriers in the system In a
normal frequency-division multiplex system many carriers are spaced apart in such a way that
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
the signals can be received using conventional filters and demodulators In such receivers guard
bands are introduced between the different carriers and in the frequency domain which results in
a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM
signal so that the sidebands of the individual carriers overlap and the signals are still received
without adjacent carrier interference To do this the carriers must be mathematically orthogonal
The receiver acts as a bank of demodulators translating each carrier down to DC with the
resulting signal integrated over a symbol period to recover the raw data If the other carriers all
beat down the frequencies that in the time domain have a whole number of cycles in the symbol
period T then the integration process results in zero contribution from all these other carriers
Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of
1T
Fig13 Spectra of an OFDM subchannel and and OFDM signal
13 Guard Interval
The distribution of the data across a large number of carriers in the OFDM signal has some
further advantages Nulls caused by multi-path effects or interference on a given frequency only
affect a small number of the carriers the remaining ones being received correctly By using
error-coding techniques which does mean adding further data to the transmitted signal it
enables many or all of the corrupted data to be reconstructed within the receiver This can be
done because the error correction code is transmitted in a different part of the signal
14 OFDM variants
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
There are several other variants of OFDM for which the initials are seen in the technical
literature These follow the basic format for OFDM but have additional attributes or variations
141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error
correction coding is incorporated into the signal
142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast
hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given
spectrum band
143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a
multiple access capability for applications such as cellular telecommunications when using
OFDM technologies
144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It
is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it
uses multiple antennas to transmit and receive the signals so that multi-path effects can be
utilised to enhance the signal reception and improve the transmission speeds that can be
supported
145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree
of spacing between the channels that is large enough that any frequency errors between
transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi
systems
Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal
carriers each carrying low data rate signals During the demodulation phase the data is then
combined to provide the complete signal
OFDM and COFDM have gained a significant presence in the wireless market place The
combination of high data capacity high spectral efficiency and its resilience to interference as a
result of multi-path effects means that it is ideal for the high data applications that are becoming
a common factor in todays communications scene
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
15 OVERVIEW OF LTE DOWNLINK SYSTEM
According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame
is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into
two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM
symbols depending on the length of the CP (normal or extended) In LTE Downlink physical
layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB
has the duration of 1 time slot
Figure 14 LTE radio Frame structure
LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency
division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different
transmission parameters for LTE Downlink systems
16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Figure 15 MIMO-OFDM system
OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a
multiple users radio access technique based on OFDM technique OFDM consists in dividing the
transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is
shared between different users Figure 3 illustrates a baseband OFDM system model The N
complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the
Inverse Discrete Fourier
Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed
independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter
With L tapsTherefore we consider in our system model only a single transmit and a single
receive antenna After removing the CP and performing the DFT the received OFDM symbol at
one receive antenna can be written as
Y represents the received signal vector X is a matrix which contains the transmitted elements on
its diagonal H is a channel frequency response and micro is the noise vector whose entries have the
iid complex Gaussian distribution with zero mean and variance amp We assume that the
noise micro is uncorrelated with the channel H
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Recent works have shown that multiple input multiple output (MIMO) systems can achieve an
increased capacity without the need of increasing the operational bandwidth Also for the fixed
transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by
using spatial diversity In order to obtain these advantages MIMO systems require accurate
channel state information (CSI) at least at the receiver side This information is in the form of
complex channel matrixThe method employing training sequences is a popular and efficient
channel estimation method A number of training- based channel estimation methods for MIMO
systems havebeen proposed However in most of the presented works independent identically
distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice
as spatial channel correlation occurs in most of propagation environments In an MMSE channel
estimator for MIMO-OFDM was developed and its performance was tested under spatial
correlated channelHowever a very simple correlated channel model was used These
investigations neglected the issue of antenna array used at the receiver sideIn practical cases
there is a demand for small spacing of array antenna elements at least at the mobile side of
MIMO system This is required to make the transceiver of compact size However the resulting
tight spacing is responsible for channel correlation Also the received signals are affected by
mutual coupling effects of the array elements
17 Wavelet Based MIMO-OFDM
Wavelet Transform is an important mathematical function because as a tool for multi resolution
disintegration of continuous time signal by different frequencies also different times Now
wavelet transform upper frequencies are superior decided in time as well as lesser frequencies
are better decided in frequency Happening this intellect the signal remains reproduced through
an orthogonal wavelet purpose in addition the transform is calculated independently changed
parts of the time domain signal The wavelet transform can be classified as two categories
continuous ripple transform and discrete ripple transform
The Discrete Ripple Transform could be observed by way of sub-band coding The signal is
analysed and it accepted over a succession of filter banks The splitting the full-band source
signal into altered frequency bands as well as encrypt every band separately established on their
spectrumvitalities is called sub-band coding method
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
The learning of sub-band coding fright starting the digital filter bank scheme it is represented as
a set of filters with has altered centre frequencies Double channel filter bank is mostly used in
addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank
proposal has double steps which are used in signal transmission scheme
The first step is named as analysis stage which agrees toward the decomposition procedure in
which the signal samples remain condensed by double (downsampling) Another step is called
synthesis period which agrees to the exclamation procedure in which the signal samples are
improved by two (up sampling)
The analysis period involves of sub-band filter surveyed by down sampler while the synthesis
period involves of sub-band filter situated next up sampler The sub-band filter period used
through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)
Subsequently there are low pass filter as well as high pass filters at each level the analysis period
takes double output coefficients also they are named as estimate coefficients which contain the
small frequency information of the signal then detail coefficients which comprise the high
frequency data of the signal The analysis period of the multi-level double channels impeccable
restoration filter bank scheme is charity for formative the DWT coefficients The procedure of
restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple
transform (IDRT) Aimed at each level of restoration filter bank the calculation then details
coefficients are up sampled in addition to passed over low pass filter and high pass synthesis
filter
The possessions of wavelets in addition to varieties it by way of a moral excellent for
countless applications identical image synthesis nuclear engineering biomedical engineering
magnetic resonance imaging music fractals turbulence pure mathematics data compression
computer graphics also animation human vision radar optics astronomy acoustics and
seismology
This paper investigates the case of a MIMO wireless system in which the signal is transmitted
from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array
(UCA) antenna The investigations make use of the assumption that the signals arriving at this
array have an angle of arrival (AoA) that follows a Laplacian distribution
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
18 OFDM MODEL
181 Orthogonal frequency-division multiplexing
Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on
multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital
communication whether wireless or over copper wires used in applications such as digital
television and audio broadcasting DSL Internet access wireless networks powerline networks
and 4G mobile communications
OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation
(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier
modulation method The word coded comes from the use of forward error correction (FEC)[1]
A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on
several parallel data streams or channels Each sub-carrier is modulated with a conventional
modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low
symbol rate maintaining total data rates similar to conventional single-carrier modulation
schemes in the same bandwidth
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe
channel conditions (for example attenuation of high frequencies in a long copper wire
narrowband interference and frequency-selective fading due to multipath) without complex
equalization filters Channel equalization is simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather than one rapidly modulated wideband signal
The low symbol rate makes the use of a guard interval between symbols affordable making it
possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on
analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain
ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single
frequency networks (SFNs) where several adjacent transmitters send the same signal
simultaneously at the same frequency as the signals from multiple distant transmitters may be
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
combined constructively rather than interfering as would typically occur in a traditional single-
carrier system
182 Example of applications
The following list is a summary of existing OFDM based standards and products For further
details see the Usage section at the end of the article
1821Cable
ADSL and VDSL broadband access via POTS copper wiring
DVB-C2 an enhanced version of the DVB-C digital cable TV standard
Power line communication (PLC)
ITU-T Ghn a standard which provides high-speed local area networking of existing
home wiring (power lines phone lines and coaxial cables)
TrailBlazer telephone line modems
Multimedia over Coax Alliance (MoCA) home networking
1822 Wireless
The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2
The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD
Radio T-DMB and ISDB-TSB
The terrestrial digital TV systems DVB-T and ISDB-T
The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward
link
The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a
implementation suggested by WiMedia Alliance
The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G
cellular networks and mobile broadband standards
The mobility mode of the wireless MANbroadband wireless access (BWA) standard
IEEE 80216e (or Mobile-WiMAX)
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
The mobile broadband wireless access (MBWA) standard IEEE 80220
the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile
broadband standard The radio interface was formerly named High Speed OFDM Packet
Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
Key features
The advantages and disadvantages listed below are further discussed in the Characteristics and
principles of operation section below
Summary of advantages
High spectral efficiency as compared to other double sideband modulation schemes
spread spectrum etc
Can easily adapt to severe channel conditions without complex time-domain equalization
Robust against narrow-band co-channel interference
Robust against intersymbol interference (ISI) and fading caused by multipath
propagation
Efficient implementation using Fast Fourier Transform (FFT)
Low sensitivity to time synchronization errors
Tuned sub-channel receiver filters are not required (unlike conventional FDM)
Facilitates single frequency networks (SFNs) ie transmitter macrodiversity
Summary of disadvantages
Sensitive to Doppler shift
Sensitive to frequency synchronization problems
High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which
suffers from poor power efficiency
Loss of efficiency caused by cyclic prefixguard interval
19 Characteristics and principles of operation
191 Orthogonality
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals
are orthogonal to each other
In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each
other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard
bands are not required This greatly simplifies the design of both the transmitter and the receiver
unlike conventional FDM a separate filter for each sub-channel is not required
The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the
useful symbol duration (the receiver side window size) and k is a positive integer typically
equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)
The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist
rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band
physical passband signal) Almost the whole available frequency band can be utilized OFDM
generally has a nearly white spectrum giving it benign electromagnetic interference properties
with respect to other co-channel users
A simple example A useful symbol duration TU = 1 ms would require a sub-carrier
spacing of (or an integer multiple of that) for orthogonality N = 1000
sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol
time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie
half of the achieved bandwidth required by our scheme) If a guard interval is applied
(see below) Nyquist bandwidth requirement would be even lower The FFT would result
in N = 1000 samples per symbol If no guard interval was applied this would result in a
base band complex valued signal with a sample rate of 1 MHz which would require a
baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal
is produced by multiplying the baseband signal with a carrier waveform (ie double-
sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz
A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve
almost half that bandwidth for the same symbol rate (ie twice as high spectral
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
efficiency for the same symbol alphabet length) It is however more sensitive to multipath
interference
OFDM requires very accurate frequency synchronization between the receiver and the
transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-
carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are
typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to
movement While Doppler shift alone may be compensated for by the receiver the situation is
worsened when combined with multipath as reflections will appear at various frequency offsets
which is much harder to correct This effect typically worsens as speed increases [2] and is an
important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in
such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a
non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as
WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in
using short filters at the transmitter output in order to perform a potentially non-rectangular pulse
shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other
ICI suppression techniques usually increase drastically the receiver complexity[5]
192 Implementation using the FFT algorithm
The orthogonality allows for efficient modulator and demodulator implementation using the FFT
algorithm on the receiver side and inverse FFT on the sender side Although the principles and
some of the benefits have been known since the 1960s OFDM is popular for wideband
communications today by way of low-cost digital signal processing components that can
efficiently calculate the FFT
The time to compute the inverse-FFT or FFT transform has to take less than the time for each
symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896
micros or less
For an 8192-point FFT this may be approximated to[6][clarification needed]
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
[6]
MIPS = Million instructions per second
The computational demand approximately scales linearly with FFT size so a double size FFT
needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at
1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at
16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]
193 Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (ie where the
symbols are relatively long compared to the channel time characteristics) suffer less from
intersymbol interference caused by multipath propagation it is advantageous to transmit a
number of low-rate streams in parallel instead of a single high-rate stream Since the duration of
each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus
eliminating the intersymbol interference
The guard interval also eliminates the need for a pulse-shaping filter and it reduces the
sensitivity to time synchronization problems
A simple example If one sends a million symbols per second using conventional single-
carrier modulation over a wireless channel then the duration of each symbol would be
one microsecond or less This imposes severe constraints on synchronization and
necessitates the removal of multipath interference If the same million symbols per
second are spread among one thousand sub-channels the duration of each symbol can be
longer by a factor of a thousand (ie one millisecond) for orthogonality with
approximately the same bandwidth Assume that a guard interval of 18 of the symbol
length is inserted between each symbol Intersymbol interference can be avoided if the
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
multipath time-spreading (the time between the reception of the first and the last echo) is
shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum
difference of 375 kilometers between the lengths of the paths
The cyclic prefix which is transmitted during the guard interval consists of the end of the
OFDM symbol copied into the guard interval and the guard interval is transmitted followed by
the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM
symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of
the multipaths when it performs OFDM demodulation with the FFT In some standards such as
Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent
during the guard interval The receiver will then have to mimic the cyclic prefix functionality by
copying the end part of the OFDM symbol and adding it to the beginning portion
194 Simplified equalization
The effects of frequency-selective channel conditions for example fading caused by multipath
propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel
is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This
makes frequency domain equalization possible at the receiver which is far simpler than the time-
domain equalization used in conventional single-carrier modulation In OFDM the equalizer
only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol
by a constant complex number or a rarely changed value
Our example The OFDM equalization in the above numerical example would require
one complex valued multiplication per subcarrier and symbol (ie complex
multiplications per OFDM symbol ie one million multiplications per second at the
receiver) The FFT algorithm requires [this is imprecise over half of
these complex multiplications are trivial ie = to 1 and are not implemented in software
or HW] complex-valued multiplications per OFDM symbol (ie 10 million
multiplications per second) at both the receiver and transmitter side This should be
compared with the corresponding one million symbolssecond single-carrier modulation
case mentioned in the example where the equalization of 125 microseconds time-
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
spreading using a FIR filter would require in a naive implementation 125 multiplications
per symbol (ie 125 million multiplications per second) FFT techniques can be used to
reduce the number of multiplications for an FIR filter based time-domain equalizer to a
number comparable with OFDM at the cost of delay between reception and decoding
which also becomes comparable with OFDM
If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization
can be completely omitted since these non-coherent schemes are insensitive to slowly changing
amplitude and phase distortion
In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically
closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and
the sub-channels can be independently adapted in other ways than varying equalization
coefficients such as switching between different QAM constellation patterns and error-
correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement
of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot
signals and training symbols (preambles) may also be used for time synchronization (to avoid
intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference
ICI caused by Doppler shift)
OFDM was initially used for wired and stationary wireless communications However with an
increasing number of applications operating in highly mobile environments the effect of
dispersive fading caused by a combination of multi-path propagation and doppler shift is more
significant Over the last decade research has been done on how to equalize OFDM transmission
over doubly selective channels[12][13][14]
195 Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction) and
almost always uses frequency andor time interleaving
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading For example when a part of the channel bandwidth fades frequency
interleaving ensures that the bit errors that would result from those subcarriers in the faded part
of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time
interleaving ensures that bits that are originally close together in the bit-stream are transmitted
far apart in time thus mitigating against severe fading as would happen when travelling at high
speed
However time interleaving is of little benefit in slowly fading channels such as for stationary
reception and frequency interleaving offers little to no benefit for narrowband channels that
suffer from flat-fading (where the whole channel bandwidth fades at the same time)
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-
stream that is presented to the error correction decoder because when such decoders are
presented with a high concentration of errors the decoder is unable to correct all the bit errors
and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact
disc (CD) playback robust
A classical type of error correction coding used with OFDM-based systems is convolutional
coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top
of the time and frequency interleaving mentioned above) in between the two layers of coding is
implemented The choice for Reed-Solomon coding as the outer error correction code is based on
the observation that the Viterbi decoder used for inner convolutional decoding produces short
errors bursts when there is a high concentration of errors and Reed-Solomon codes are
inherently well-suited to correcting bursts of errors
Newer systems however usually now adopt near-optimal types of error correction codes that
use the turbo decoding principle where the decoder iterates towards the desired solution
Examples of such error correction coding types include turbo codes and LDPC codes which
perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel
Some systems that have implemented these codes have concatenated them with either Reed-
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to
improve upon an error floor inherent to these codes at high signal-to-noise ratios
196 Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the
channel is sent over a return-channel Based on this feedback information adaptive modulation
channel coding and power allocation may be applied across all sub-carriers or individually to
each sub-carrier In the latter case if a particular range of frequencies suffers from interference
or attenuation the carriers within that range can be disabled or made to run slower by applying
more robust modulation or error coding to those sub-carriers
The term discrete multitone modulation (DMT) denotes OFDM based communication systems
that adapt the transmission to the channel conditions individually for each sub-carrier by means
of so-called bit-loading Examples are ADSL and VDSL
The upstream and downstream speeds can be varied by allocating either more or fewer carriers
for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the
bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever
subscriber needs it most
197 OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique and not a multi-user
channel access method since it is utilized for transferring one bit stream over one
communication channel using one sequence of OFDM symbols However OFDM can be
combined with multiple access using time frequency or coding separation of the users
In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access
is achieved by assigning different OFDM sub-channels to different users OFDMA supports
differentiated quality of service by assigning different number of sub-carriers to different users in
a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control
schemes can be avoided OFDMA is used in
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as
WiMAX
the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA
the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard
downlink The radio interface was formerly named High Speed OFDM Packet Access
(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)
the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as
a successor of CDMA2000 but replaced by LTE
OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area
Networks (WRAN) The project aims at designing the first cognitive radio based standard
operating in the VHF-low UHF spectrum (TV spectrum)
In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA
OFDM is combined with CDMA spread spectrum communication for coding separation of the
users Co-channel interference can be mitigated meaning that manual fixed channel allocation
(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes
are avoided
198 Space diversity
In OFDM based wide area broadcasting receivers can benefit from receiving signals from
several spatially dispersed transmitters simultaneously since transmitters will only destructively
interfere with each other on a limited number of sub-carriers whereas in general they will
actually reinforce coverage over a wide area This is very beneficial in many countries as it
permits the operation of national single-frequency networks (SFN) where many transmitters
send the same signal simultaneously over the same channel frequency SFNs utilise the available
spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where
program content is replicated on different carrier frequencies SFNs also result in a diversity gain
in receivers situated midway between the transmitters The coverage area is increased and the
outage probability decreased in comparison to an MFN due to increased received signal strength
averaged over all sub-carriers
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Although the guard interval only contains redundant data which means that it reduces the
capacity some OFDM-based systems such as some of the broadcasting systems deliberately
use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN
and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum
distance between transmitters in an SFN is equal to the distance a signal travels during the guard
interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be
spaced 60 km apart
A single frequency network is a form of transmitter macrodiversity The concept can be further
utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from
timeslot to timeslot
OFDM may be combined with other forms of space diversity for example antenna arrays and
MIMO channels This is done in the IEEE80211 Wireless LAN standard
199 Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent
phases of the sub-carriers mean that they will often combine constructively Handling this high
PAPR requires
a high-resolution digital-to-analogue converter (DAC) in the transmitter
a high-resolution analogue-to-digital converter (ADC) in the receiver
a linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
raises the noise floor
may cause inter-carrier interference
generates out-of-band spurious radiation
The linearity requirement is demanding especially for transmitter RF output circuitry where
amplifiers are often designed to be non-linear in order to minimise power consumption In
practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
judicious trade-off against the above consequences However the transmitter output filter which
is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that
were clipped so clipping is not an effective way to reduce PAPR
Although the spectral efficiency of OFDM is attractive for both terrestrial and space
communications the high PAPR requirements have so far limited OFDM applications to
terrestrial systems
The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]
CF = 10 log( n ) + CFc
where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves
used for BPSK and QPSK modulation)
For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each
QPSK-modulated giving a crest factor of 3532 dB[15]
Many crest factor reduction techniques have been developed
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB
1991 Efficiency comparison between single carrier and multicarrier
The performance of any communication system can be measured in terms of its power efficiency
and bandwidth efficiency The power efficiency describes the ability of communication system
to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth
efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the
throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used
the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel
is defined as
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Factor 2 is because of two polarization states in the fiber
where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of
OFDM signal
There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency
division multiplexing So the bandwidth for multicarrier system is less in comparison with
single carrier system and hence bandwidth efficiency of multicarrier system is larger than single
carrier system
SNoTransmission
Type
M in
M-
QAM
No of
Subcarriers
Bit
rate
Fiber
length
Power at the
receiver(at BER
of 10minus9)
Bandwidth
efficiency
1 single carrier 64 110
Gbits20 km -373 dBm 60000
2 multicarrier 64 12810
Gbits20 km -363 dBm 106022
There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth
efficiency with using multicarrier transmission technique
1992 Idealized system model
This section describes a simple idealized OFDM system model suitable for a time-invariant
AWGN channel
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data
on each sub-carrier being independently modulated commonly using some type of quadrature
amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is
typically used to modulate a main RF carrier
is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into
parallel streams and each one mapped to a (possibly complex) symbol stream using some
modulation constellation (QAM PSK etc) Note that the constellations may be different so
some streams may carry a higher bit-rate than others
An inverse FFT is computed on each set of symbols giving a set of complex time-domain
samples These samples are then quadrature-mixed to passband in the standard way The real and
imaginary components are first converted to the analogue domain using digital-to-analogue
converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the
carrier frequency respectively These signals are then summed to give the transmission
signal
Receiver
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
The receiver picks up the signal which is then quadrature-mixed down to baseband using
cosine and sine waves at the carrier frequency This also creates signals centered on so low-
pass filters are used to reject these The baseband signals are then sampled and digitised using
analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency
domain
This returns parallel streams each of which is converted to a binary stream using an
appropriate symbol detector These streams are then re-combined into a serial stream which
is an estimate of the original binary stream at the transmitter
1993 Mathematical description
If sub-carriers are used and each sub-carrier is modulated using alternative symbols the
OFDM symbol alphabet consists of combined symbols
The low-pass equivalent OFDM signal is expressed as
where are the data symbols is the number of sub-carriers and is the OFDM symbol
time The sub-carrier spacing of makes them orthogonal over each symbol period this property
is expressed as
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
where denotes the complex conjugate operator and is the Kronecker delta
To avoid intersymbol interference in multipath fading channels a guard interval of length is
inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the
signal in the interval equals the signal in the interval The OFDM signal
with cyclic prefix is thus
The low-pass signal above can be either real or complex-valued Real-valued low-pass
equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use
this approach For wireless applications the low-pass signal is typically complex-valued in
which case the transmitted signal is up-converted to a carrier frequency In general the
transmitted signal can be represented as
Usage
OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)
DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL
(GdmtITU G9921) Mobile phone 4G
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
It is assumed that the cyclic prefix is longer than the maximum propagation delay So the
orthogonality between subcarriers and non intersymbol interference can be preserved
The number ofsubcarriers and multipaths is K and L in the system respectively The received
signal is obtained as
where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y
is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a
vector of independent identically distributed complex Gaussian noise with zero-mean and
variance The noise N is assumed to be uncorrelated with the channel H
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
CHAPTER-2
PROPOSED METHOD
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
21 Impact of Frequency Offset
The spacing between adjacent subcarriers in an OFDM system is typically very small and hence
accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is
introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of
receiver motion Due to the the residual frequency offset the orthogonality between transmit and
receive pulses will be lost and the received symbols will have a time- variant phase rotation We
see the effect of normalized residual frequency
Fig 21Frequency division multiplexing system
This chapter discusses the development of an algorithm to estimate CFO in an OFDM system
and forms the crux of this thesis The first section of the chapter derives the equations for the
received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a
function that provides a measure of the impact of CFO on the average probability of error in the
received symbols The nature of such an error function provides the means to identify the
magnitude of CFO based on observed symbols In the subsequent sections observations are
made about the analytical nature of such an error function and how it improves the performance
of the estimation algorithmWhile that diagram illustrates the components that would make up
the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be
reasonable to eliminate the components that do not necessarily affect the estimation of the CFO
The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the
system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the
impact of CFO on the demodulation of the received bits it may be safely assumed that the
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
received bits are time-synchronised with the receiver clock It is interesting to couple the
performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block
turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond
the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are
separated in frequency space and constellation space While these are practicalconsiderations in
the implementation of the OFDM tranceiver they may be omitted fromthis discussion without
loss of relevance For the purposes of this section and throughoutthis work we will assume that
the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are
ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the
digital domain
22 Expressions for Transmitted and Received Symbols
Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2
aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT
block Using the matrix notation W to denote the inverse Fourier Transform we have
t = Ws
The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft
This operation can be denoted using the vector notation as
u = Ftt
= FtWs
Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM
transmitter
where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the
transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit
DDS In the presence of channel noise the received symbol vector r can be represented as
r = u + z
= FtWs + z
where z denotes the complex circular white Gaussian noise added by the channel At the
receiver demodulation consists of translating the received signal to baseband frequency followed
by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency
The equalizer output y can thus be represented as
y = FFTfFHrrg
= WHFHr(FtWs + z)
= WHFHrFtWs +WHFHrz
where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the
receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer
ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random
vector z denotes a complex circular white Gaussian random vector hence multiplication by the
unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the
uncompensated CFO matrix Thus
y = WHFHrFtWs +WHFHrz
Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector
Let f2I be the covariance matrix of fDenoting WHPW as H
y = Hs + f
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
The demodulated symbol yi at the ith subcarrier is given by
yi = hTi
s + fi
where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D
C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus
en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error
inmapping the decoded symbol ^yn under operating conditions defined by the noise variance
f2 and the frequency offset
23 Carrier Frequency Offset
As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS
frequencies The following relations apply between the digital frequencies in 11
t = t fTs
r = r fTs
f= 1
2_ (t 1048576 r) (211)
= 1
2_(t 1048576 r) _ Ts (212)
As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N
2Ts
24 Time-Domain Estimation Techniques for CFO
For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused
cyclic prefix (CP) based Estimation
Blind CFO Estimation
Training-based CFO Estimation
241 Cyclic Prefix (CP)
The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)
that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol
(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last
samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of
channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not
constitute any information hence the effect of addition of long CP is loss in throughput of
system
Fig24 Inter-carrier interference (ICI) subject to CFO
25 Effect of CFO and STO
The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then
converted down to the baseband by using a local carrier signal of(hopefully) the same carrier
frequency at the receiver In general there are two types of distortion associated with the carrier
signal One is the phase noise due to the instability of carrier signal generators used at the
transmitter and receiver which can be modeled as a zero-mean Wiener random process The
other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the
orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency
domain with shifting of and time domain multiplying with the exponential term and the Doppler
frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX
of the transmitted signal for the OFDM symbol duration In other words a symbol-timing
synchronization must be performed to detect the starting point of each OFDM symbol (with the
CP removed) which facilitates obtaining the exact samples STO of samples affects the received
symbols in the time and frequency domain where the effects of channel and noise are neglected
for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO
All these foure cases
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Case I This is the case when the estimated starting point of OFDM symbol coincides with the
exact timing preserving the orthogonality among subcar- rier frequency components In this
case the OFDM symbol can be perfectly recovered without any type of interference
Case II This is the case when the estimated starting point of OFDM symbol is before the exact
point yet after the end of the (lagged) channel response to the previous OFDM symbol In this
case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring
any ISI by the previous symbol in this case
Case III This is the case when the starting point of the OFDM symbol is estimated to exist
prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the
symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier
components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-
Channel Interference) occurs
26 Frequency-Domain Estimation Techniques for CFO
If two identical training symbols are transmitted consecutively the corresponding signals with
CFO of are related with each other which is a well-known approach by Moose Similar to
SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM
there exists multi-antenna interference (MAI) in the received antennas between the received
signals from different transmit antennas The MAI makes CFO estimation more difficult as
compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for
training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a
few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind
kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they
introduced a random-hopping scheme which robusties the CFO estimator against channel nulls
For training-based CFO estimators the overviews concerning the necessary changes to the
training sequences and thecorresponding CFO estimators when extending SISO-OFDM to
MIMO-OFDM were provided However with the provided training sequences satisfactory CFO
estimation performance cannot be achieved With the training sequences the training period
grows linearly with the number of transmit antennas which results in an increased overhead In
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for
MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require
a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator
only applied to at-fading MIMO channels
OFDM system carries the message data on orthogonal sub-carriers for parallel transmission
combating the distortion caused by the frequency-selective channel or equivalently the inter-
symbol-interference in the multi-path fading channel However the advantage of the OFDM can
be useful only when the orthogonality
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
CHAPTER-3
RESULTS
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
CHAPTER-4
MATLAB
INTRODUCTION TO MATLAB
What Is MATLAB
MATLABreg is a high-performance language for technical computing It integrates
computation visualization and programming in an easy-to-use environment where problems and
solutions are expressed in familiar mathematical notation Typical uses include
Math and computation
Algorithm development
Data acquisition
Modeling simulation and prototyping
Data analysis exploration and visualization
Scientific and engineering graphics
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Application development including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning This allows you to solve many technical computing problems especially
those with matrix and vector formulations in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN
The name MATLAB stands for matrix laboratory MATLAB was originally written to
provide easy access to matrix software developed by the LINPACK and EISPACK projects
Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of
the art in software for matrix computation
MATLAB has evolved over a period of years with input from many users In university
environments it is the standard instructional tool for introductory and advanced courses in
mathematics engineering and science In industry MATLAB is the tool of choice for high-
productivity research development and analysis
MATLAB features a family of add-on application-specific solutions called toolboxes
Very important to most users of MATLAB toolboxes allow you to learn and apply specialized
technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that
extend the MATLAB environment to solve particular classes of problems Areas in which
toolboxes are available include signal processing control systems neural networks fuzzy logic
wavelets simulation and many others
The MATLAB System
The MATLAB system consists of five main parts
Development Environment
This is the set of tools and facilities that help you use MATLAB functions and files Many
of these tools are graphical user interfaces It includes the MATLAB desktop and Command
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Window a command history an editor and debugger and browsers for viewing help the
workspace files and the search path
The MATLAB Mathematical Function
This is a vast collection of computational algorithms ranging from elementary functions
like sum sine cosine and complex arithmetic to more sophisticated functions like matrix
inverse matrix eigen values Bessel functions and fast Fourier transforms
The MATLAB Language
This is a high-level matrixarray language with control flow statements functions data
structures inputoutput and object-oriented programming features It allows both programming
in the small to rapidly create quick and dirty throw-away programs and programming in the
large to create complete large and complex application programs
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as
annotating and printing these graphs It includes high-level functions for two-dimensional and
three-dimensional data visualization image processing animation and presentation graphics It
also includes low-level functions that allow you to fully customize the appearance of graphics as
well as to build complete graphical user interfaces on your MATLAB applications
The MATLAB Application Program Interface (API)
This is a library that allows you to write C and Fortran programs that interact with
MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling
MATLAB as a computational engine and for reading and writing MAT-files
MATLAB WORKING ENVIRONMENT
MATLAB DESKTOP-
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Matlab Desktop is the main Matlab application window The desktop contains five sub
windows the command window the workspace browser the current directory window the
command history window and one or more figure windows which are shown only when the
user displays a graphic
The command window is where the user types MATLAB commands and expressions at the
prompt (gtgt) and where the output of those commands is displayed MATLAB defines the
workspace as the set of variables that the user creates in a work session The workspace browser
shows these variables and some information about them Double clicking on a variable in the
workspace browser launches the Array Editor which can be used to obtain information and
income instances edit certain properties of the variable
The current Directory tab above the workspace tab shows the contents of the current
directory whose path is shown in the current directory window For example in the windows
operating system the path might be as follows CMATLABWork indicating that directory
ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN
DRIVE C clicking on the arrow in the current directory window shows a list of recently used
paths Clicking on the button to the right of the window allows the user to change the current
directory
MATLAB uses a search path to find M-files and other MATLAB related files which are
organize in directories in the computer file system Any file run in MATLAB must reside in the
current directory or in a directory that is on search path By default the files supplied with
MATLAB and math works toolboxes are included in the search path The easiest way to see
which directories are on the search path
The easiest way to see which directories are soon the search path or to add or modify a search
path is to select set path from the File menu the desktop and then use the set path dialog box It
is good practice to add any commonly used directories to the search path to avoid repeatedly
having the change the current directory
The Command History Window contains a record of the commands a user has entered in
the command window including both current and previous MATLAB sessions Previously
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
entered MATLAB commands can be selected and re-executed from the command history
window by right clicking on a command or sequence of commands
This action launches a menu from which to select various options in addition to executing the
commands This is useful to select various options in addition to executing the commands This
is a useful feature when experimenting with various commands in a work session
Using the MATLAB Editor to create M-Files
The MATLAB editor is both a text editor specialized for creating M-files and a graphical
MATLAB debugger The editor can appear in a window by itself or it can be a sub window in
the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor
window has numerous pull-down menus for tasks such as saving viewing and debugging files
Because it performs some simple checks and also uses color to differentiate between various
elements of code this text editor is recommended as the tool of choice for writing and editing M-
functions To open the editor type edit at the prompt opens the M-file filenamem in an editor
window ready for editing As noted earlier the file must be in the current directory or in a
directory in the search path
Getting Help
The principal way to get help online is to use the MATLAB help browser opened as a
separate window either by clicking on the question mark symbol () on the desktop toolbar or by
typing help browser at the prompt in the command window The help Browser is a web browser
integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents The Help Browser consists of two panes the help navigator pane used to find
information and the display pane used to view the information Self-explanatory tabs other than
navigator pane are used to perform a search
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
CHAPTER-5
COMMUNICATION
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Communications System Toolboxtrade provides algorithms and tools for the design simulation
and analysis of communications systems These capabilities are provided as MATLAB reg
functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes
algorithms for source coding channel coding interleaving modulation equalization
synchronization and channel modeling Tools are provided for bit error rate analysis generating
eye and constellation diagrams and visualizing channel characteristics The system toolbox also
provides adaptive algorithms that let you model dynamic communications systems that use
OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C
or HDL code generation
Key Features
Algorithms for designing the physical layer of communications systems including source
coding channel
coding interleaving modulation channel models MIMO equalization and synchronization
GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC
and Viterbi
decoders
Interactive visualization tools including eye diagrams constellations and channel scattering
functions
Graphical tool for comparing the simulated bit error rate of a system with analytical results
Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO
Multipath Fading and
LTE MIMO Multipath Fading
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Basic RF impairments including nonlinearity phase noise thermal noise and phase and
frequency offsets
Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks
Support for fixed-point modeling and C and HDL code generation
System Design Characterization and Visualization
The design and simulation of a communications system requires analyzing its response to the
noise and interference inherent in real-world environments studying its behavior using graphical
and quantitative means and determining whether the resulting performance meets standards of
acceptability Communications System Toolbox implements a variety of tasks for
communications system design and simulation Many of the functions System objectstrade and
blocks in the system toolbox perform computations associated with a particular component of a
communications system such as a demodulator or equalizer Other capabilities are designed for
visualization or analysis
System Characterization
The system toolbox offers several standard methods for quantitatively characterizing system
performance
Bit error rate (BER) computations
Adjacent channel power ratio (ACPR) measurements
Error vector magnitude (EVM) measurements
Modulation error ratio (MER) measurements
Because BER computations are fundamental to the characterization of any communications
system the system
toolbox provides the following tools and capabilities for configuring BER test scenarios and
accelerating BER simulations
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
BER tool mdash A graphical user interface that enables you to analyze BER performance of
communications systems You can analyze performance via a simulation-based semianalytic or
theoretical approach
Error Rate Test Console mdash A MATLAB object that runs simulations for communications
systems to measure error rate performance It supports user-specified test points and generation
of parametric performance plots and surfaces Accelerated performance can be realized when
running on a multicore computing platform
Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade
that enables you to accelerate simulation performance using multicore and GPU hardware within
your computer
Distributed computing and cloud computing support mdash Capabilities provided by Parallel
Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage
the computing power of your server farms and the Amazon EC2 Web service Performance
Visualization The system toolbox provides the following capabilities for visualizing system
performance
Channel visualization tool mdash For visualizing the characteristics of a fading channel
Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding
of system behavior that enables you to make initial design decisions
Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision
points
BER plots mdash For visualizing quantitative BER performance of a design candidate
parameterized by metrics such as SNR and fixed-point word size
Analog and Digital Modulation
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Analog and digital modulation techniques encode the information stream into a signal that is
suitable for transmission Communications System Toolbox provides a number of modulation
and corresponding demodulation capabilities These capabilities are available as MATLAB
functions and objects MATLAB System Modulation types provided by the toolbox are
Analog including AM FM PM SSB and DSBSC
Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM
Source and Channel Coding
Communications System Toolbox provides source and channel coding capabilities that let you
develop and evaluate communications architectures quickly enabling you to explore what-if
scenarios and avoid the need to create coding capabilities from scratch
Source Coding
Source coding also known as quantization or signal formatting is a way of processing data in
order to reduce redundancy or prepare it for later processing The system toolbox provides a
variety of types of algorithms for implementing source coding and decoding including
Quantizing
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Companding (micro-law and A-law)
Differential pulse code modulation (DPCM)
Huffman coding
Arithmetic coding
Channel Coding
Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)
Turbo encoder and decoder examples
The system toolbox provides utility functions for creating your own channel coding You can
create generator polynomials and coefficients and syndrome decoding tables as well as product
parity-check and generator matrices
The system toolbox also provides block and convolutional interleaving and deinterleaving
functions to reduce data errors caused by burst errors in a communication system
Block including General block interleaver algebraic interleaver helical scan interleaver matrix
interleaver and random interleaver
Convolutional including General multiplexed interleaver convolutional interleaver and helical
interleaver
Channel Modeling and RF Impairments
Channel Modeling
Communications System Toolbox provides algorithms and tools for modeling noise fading
interference and other distortions that are typically found in communications channels The
system toolbox supports the following types of channels
Additive white Gaussian noise (AWGN)
Multiple-input multiple-output (MIMO) fading
Single-input single-output (SISO) Rayleigh and Rician fading
Binary symmetric
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
A MATLAB channel object provides a concise configurable implementation of channel models
enabling you to
specify parameters such as
Path delays
Average path gains
Maximum Doppler shifts
K-Factor for Rician fading channels
Doppler spectrum parameters
For MIMO systems the MATLAB MIMO channel object expands these parameters to also
include
Number of transmit antennas (up to 8)
Number of receive antennas (up to 8)
Transmit correlation matrix
Receive correlation matrix
To combat the effects noise and channel corruption the system toolbox provides block and
convolutional coding and decoding techniques to implement error detection and correction For
simple error detection with no inherent correction a cyclic redundancy check capability is also
available Channel coding capabilities provided by the system toolbox include
BCH encoder and decoder
Reed-Solomon encoder and decoder
LDPC encoder and decoder
Convolutional encoder and Viterbi decoder
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
RF Impairments
To model the effects of a nonideal RF front end you can introduce the following impairments
into your communications system enabling you to explore and characterize performance with
real-world effects
Memoryless nonlinearity
Phase and frequency offset
Phase noise
Thermal noise
You can include more complex RF impairments and RF circuit models in your design using
SimRFtrade
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Equalization and Synchronization
Communications System Toolbox lets you explore equalization and synchronization techniques
These techniques are generally adaptive in nature and challenging to design and characterize
The system toolbox provides algorithms and tools that let you rapidly select the appropriate
technique in your communications system Equalization To evaluate different approaches to
equalization the system toolbox provides you with adaptive algorithms such as
LMS
Normalized LMS
Variable step LMS
Signed LMS
MLSE (Viterbi)
RLS
CMA
These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)
implementations and as
linear (symbol or fractionally spaced) equalizer implementations
Synchronization
The system toolbox provides algorithms for both carrier phase synchronization and timing phase
synchronization For timing phase synchronization the system toolbox provides a MATLAB
Timing Phase Synchronizer object that offers the following implementation methods
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Early-late gate timing method
Gardnerrsquos method
Fourth-order nonlinearity method
Stream Processing in MATLAB and Simulink
Most communication systems handle streaming and frame-based data using a combination of
temporal processing and simultaneous multi frequency and multichannel processing This type of
streaming multidimensional processing can be seen in advanced communication architectures
such as OFDM and MIMO Communications System Toolbox enables the simulation of
advanced communications systems by supporting stream processing and frame-based simulation
in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade
which use MATLAB objects to represent time-based and data-driven algorithms sources and
sinks System objects implicitly manage many details of stream processing such as data
indexing buffering and management of algorithm state You can mix System objects with
standard MATLAB functions and operators Most System objects have a corresponding
Simulink block with the same capabilities Simulink handles stream processing implicitly by
managing the flow of data through the blocks that make up a Simulink model Simulink is an
interactive graphical environment for modeling and simulating dynamic systems that uses
hierarchical diagrams to represent a system model It includes a library of general-purpose
predefined blocks to represent algorithms sources sinks and system hierarchy
Implementing a Communications System
Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point
representation of your design
Communications System Toolbox supports fixed-point modeling in all relevant blocks and
System objectstrade with tools that help you configure fixed-point attributes
Fixed-point support in the system toolbox includes
Word sizes from 1 to 128 bits
Arbitrary binary-point placement
Overflow handling methods (wrap or saturation)
Rounding methods ceiling convergent floor nearest round simplest and zero
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data
types to fixed point For configuration of fixed-point properties the tool tracks overflows and
maxima and minima
Code Generation
Once you have developed your algorithm or communications system you can automatically
generate C code from it for verification rapid prototyping and implementation Most System
objects functions and blocks in Communications System Toolbox can generate ANSIISO C
code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System
objects and Simulink blocks can also generate HDL code To leverage existing intellectual
property you can select optimizations for specific processor architectures and integrate legacy C
code with the generated code
You can also generate C code for both floating-point andfixed-point data types
DSP Prototyping DSPs are used in communication system implementation for verification rapid
prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation
capability found in Embedded Coder you can verify generated source code and compiled code
by running your algorithmrsquos implementation code on a target processor FPGA Prototyping
FPGAs are used in communication systems for implementing high-speed signal processing
algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test
RTL code in real hardware for any
existing HDL code either manually written or automatically generated HDL code
CHAPTER-6
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
CONCLUSION
In this paper we examine an one of a kind issue in minimal remote handsets transient bearer
recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks
that oblige time division duplex (TDD) operation We showed that the transient CFO can be
demonstrated as the step reaction of an under damped second request framework To digitally
adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-
like grid A weighted subspace fitting calculation is additionally proposed to progress the
estimation precision The execution examination is confirmed in light of both numerical
recreations and exploratory results from the test bed gathered specimens The transient
hindrances emerge in gadgets that need to switch between different radio works and debase the
framework execution through the bended sign
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
CHAPTER-7
REFERENCES
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO
communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb
2004
[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or
zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12
pp 2136ndash2148 Dec2002
[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with
transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3
pp461ndash471March 1999
[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for
broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and
Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003
[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and
modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008
[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel
estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul
1995 pp 815-819
[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel
estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology
Conference Atlanta GA USAApr 1996 pp 923-927
[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for
MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007
[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo
IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008
[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in
Proc International Conference on Computer and Information Technology pp 545-549 December
2010
[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel
Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April
2011
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552
[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-
board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power
Electron vol 11 no 2 pp 328ndash337 Mar 1996
[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in
Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344
[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset
correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994
[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency
offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997
[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo
Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011
[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped
sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol
ASSP-30 no 6 pp 833ndash840 Dec 1982
[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal
signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no
2 pp 481ndash486 Feb 1997
[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially
dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no
5 pp 814ndash824 May 1990
[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE
Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965
[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd
ed Hoboken NJ USA Wiley-IEEE Press 2012
[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo
IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995
[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of
state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf
Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552