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Degree Project
Haris Majeed, Rahim Umar, Arslan Ali Basit
2011-06-10
Subject: Master Thesis
Level: Second
Course code: 5ED06E
SMART ANTENNAS – MIMO, OFDM & SINGLE
CARRIER FDMA FOR LTE
Supervisor: Sven Nordebo
School of Computer Sciences, Physics and Mathematics
Submitted for the degree of Master in Electrical Engineering Specialized in Signal Processing and Wave Propagation
ACKNOWLEDGEMENT
All praises to Almighty Allah, Whose enormous blessings give us strength and make us able to
complete this thesis.
We thank our honourable supervisor Prof. Sven Nordebo for his kind support, assistance and
guidance throughout our thesis. His motivation brought source of inspiration to our thesis.
We are grateful to Swedish government for such a wonderful education system, who welcomed
us to complete our master education in Sweden.
Finally, all blessings upon our beloved parents and families whose prayers and moral support
always motivated us to complete our studies.
To our Parents, Teachers and Family.
Contents
Abstract 1
1 Introduction 2
2 3GPP Long Term Evolution 42.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Performance Targets . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 LTE Physical Layer . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Smart Antenna Beamforming and Direction of Arrival 103.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Smart Antenna Beamforming . . . . . . . . . . . . . . . . . . . . 103.3 Implementation of Beamforming Techniques . . . . . . . . . . . . 153.4 Advantages and Disadvantages of RLS and LMS Algorithm . . . 183.5 Direction of Arrival . . . . . . . . . . . . . . . . . . . . . . . . . . 183.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Multiple Input Multiple Output-MIMO 214.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Why MIMO system . . . . . . . . . . . . . . . . . . . . . . . . . 214.3 Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.4 Space diversity types . . . . . . . . . . . . . . . . . . . . . . . . . 234.5 Discrete Time MIMO Model . . . . . . . . . . . . . . . . . . . . . 244.6 Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.7 Space time coding . . . . . . . . . . . . . . . . . . . . . . . . . . 324.8 Alamouti Encoding Transmitting and decoding . . . . . . . . . . 344.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5 Orthogonal Frequency Division Multiplexing - OFDM 375.1 DIGITAL MODULATION . . . . . . . . . . . . . . . . . . . . . . 375.2 Phase Shift keying (PSK) modulations . . . . . . . . . . . . . . . 385.3 Quadrature Amplitude modulation (QAM) . . . . . . . . . . . . 425.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.5 OFDM Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.6 OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.7 Advantages of OFDM . . . . . . . . . . . . . . . . . . . . . . . . 485.8 Disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.9 OFDM Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
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5.10 MIMO OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.11 Challenges in MIMO OFDM . . . . . . . . . . . . . . . . . . . . 505.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6 Single Carrier- FDMA 526.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.2 Why SC-FDMA? . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.3 Single Carrier FDE . . . . . . . . . . . . . . . . . . . . . . . . . . 536.4 Single Carrier - FDMA . . . . . . . . . . . . . . . . . . . . . . . . 546.5 Subcarrier Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 556.6 SC-FDMA and OFDMA (PAPR Comparison) . . . . . . . . . . . 586.7 MIMO SC-FDMA . . . . . . . . . . . . . . . . . . . . . . . . . . 606.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7 Simulation and Results 637.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637.2 MIMO Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637.3 OFDM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.4 SC-FDMA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.5 PAPR Comparison between OFDM and SC-FDMA . . . . . . . . 74
8 Summary 76
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Abstract
With the evolution in the telecommunication generations, more and more re-search is going on in the eld of wireless communications. The purpose of theseresearches has always been to provide good network coverage across the regionwith higher data rates, accuracy and better performance. Control on coverageand performance has always been in focus and is achieved using better and betterantennas. Research has brought us with a sophisticated approach on the controlof the properties of the antennas - introduction to Smart Antennas. Smart an-tennas can be used to support any radio based telecommunication system in anyband, with the same level of performance. Several techniques are used to getgood performance out of the antennas system. One impressive way is the usageof multiple antennas techniques. The approach is to transmit and receive 2 ormore unique data on a single radio channel. To increase the diversity gain withthe use of multiple input multiple output (MIMO), OFDM is a good technologyused at the physical layer. It provides robustness to frequency selective fading,high spectral eciency and low computational complexity. So MIMO-OFDMgenerates a good basis for 3GPP (3rd Generation Partnership Project) and 4Gtelecommunication technologies as well as other wireless communications sys-tems. With MIMO-OFDM as basis, dierent standards like WiMAX (WirelessInteroperability for Microwave Access) and LTE (Long Term Evolution) havebeen implemented now. The use of OFDM has some limitations when it isconsidered for uplink like high peak to average power ratio (PAPR), for whicha new technique of using Single Carrier is considered for uplink. Single Car-rier FDMA has same advantages as of OFDM with low PAPR. In this thesis,we investigate the smart antennas with its application as LTE with the studyof MIMO-OFDM and Single Carrier FDMA Systems. Performance of MIMOOFDM and SC-FDMA is evaluated by using simulations on MATLAB.
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Chapter 1
Introduction
There was a time when kids used to connect two empty ice-cream cups togetherby a thread and enjoy saying we have made a telephone. Communication, to-day, has gone so beyond that there is no way of communication today that istotally wired-ly. Today, every telecommunication system must have a wirelesspath/hop to get connected between users. The evolution of this telecommuni-cation is happening in dierent generation phases. The early experiments ofice-cream cups are, technically speaking, zero generation (0G) of telecommuni-cation, with which have people lived in some 18xx's and early 19xx's. Evolutiongraph increased exponentially in late 80's when analogue wireless communica-tion started that we call First Generation (1G). It was 198x's and was sendingdata in the form of analogue signal, only the voice. Data rates were very smallbut enough to transmit/receive voice clearly. This was the beginning of thecellular network.World was in a time when looking at things digitally was innovative and promot-ing, providing us with a new way of communication and we entered into SecondGeneration (2G). Turning things digitally was so successful that 2G networkslike GSM/CDMA were highly populated network. Telecommunication becamepopular in a real sense in 2G. Initial purpose of 2G is to provide voice onlydigitally. But then it upgraded itself with higher data rates to provide not onlyvoice but packet data also. We call those eras as 2.5G and 2.75G, in whichhigher data rates for internet usage, picture messaging, video messaging wasachieved. Data rates upto 478kbps was the target of 2.75G, which removed thespeed-related-drawbacks in 2G network. 2G-2.75G are in use in many of thecountries across the globe.Till now, the concept of broadband was limited to wired network, when ThirdGeneration (3G) widens our minds and provided us wireless broadband mo-bile technologies. It supports voice, data and multimedia communication overwireless networks. The famous standards in 3G are CDMA2000, UMTS andWCDMA etc. Video calling become possible in 3G. An upgrade in 3G networktakes it to 3.5G or High Speed Downlink Packet Access (HSDPA) by whichdownloading has become fast enough (up to 2Mbps) that small software andaudio songs can be downloaded in some seconds instead of minutes previously.The road has no end, dreams have no limits, and researchers are now able toget a speed of at least 100Mbps on wireless, still planning to go higher. This isthe 4th Generation (4G) in which world has recently entered and many of the
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bigger operators and vendors have started deploying 4G networks in dierentcountries. 4G includes higher releases of following two standards: Wireless In-teroperability Microwave Access (WiMAX) and Long Term Evolution (LTE).In this thesis, we shall study the technologies used to implement wireless inter-face of LTE. LTE uses Orthogonal Frequency Division Multiplexing (OFDM) asdownlink access scheme and Single Carrier Frequency Division Multiple Access(SC-FDMA) as uplink access scheme. To improve diversity it uses multi antennatechniques called Multiple Input Multiple Output (MIMO) antenna systems onboth sides of communications, introducing the concepts of Smart Antennas. Wehave divided the whole thesis as:Chapter 2 describes the LTE standard briey. Chapter 3 gives details on SmartAntennas and its characteristics of beam forming and controlling direction ofarrival. Chapter 4 details on MIMO systems, emphasizing classical AlamoutiScheme. Chapter 5 describes OFDM technology in detail. Chapter 6 details onSC-FDMA and gives comparison between OFDMA and SC-FDMA. In chapter7 are the results of the simulations that we performed using MATLAB. Finallychapter 8 gives the summary of our work and what can be done in future.
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Chapter 2
3GPP Long Term Evolution
2.1 Introduction
As a result of increased demands of mobile data usage with the applications suchas Mobile TV, Multimedia Online Gaming and Streaming contents, the 3rd Gen-eration Partnership Project (3GPP) started putting their eorts to work on theLong Term Evolution (LTE) [2]. 3GPP is a collaborative group of internationalstandards organizations and mobile technology companies.3GPP-LTE is the latest standard in the mobile network technology that pro-duced the GSM/EDGE and UMTS/HSxPA network technologies. It oers asuperior user experience and simplied technology for next generation mobilebroadband. It was developed to provide higher data rates, lower latencies,wider spectrum and packet optimized radio technology. It uses spectrum up to20MHz to provide compatibility with already existing technologies like UMTSand HSPA, i.e, LTE is backward compatible. It supports scalable bandwidthwhich makes it possible to be deployed in any bandwidth combination and thosecombinations can be used together to make one bigger band when it gets moreusers with the passage of time. Paired and unpaired spectrum is supported inoriginal LTE requirements [1][2][3].To accommodate all types of spectrum resources, LTE uses Frequency DivisionDuplex (FDD) as well as Time Division Duplex (TDD) as duplex techniques.LTE also supports for inter-working with existing 3G systems and non-3GPPspecied systems [1][4][5].
2.2 Performance Targets
The performance goals achieved by LTE standard are following [1][2][3]:
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Parameter RequirementPeak Data Transmission Rate DL: >100 Mbps UL: >50 MbpsMobility Support Up to 500km/h but optimized for low speeds from 0 - 30 km/h.Control Plane Latency <100ms (from idle to active)User Plane Latency <5msControl Plane Capacity >200 users per cell (for 5MHz spectrum)Coverage (Cell sizes) 5 100km with slight degradation after 30kmSpectrum exibility 1.25, 2.5, 5, 10, 15, and 20MHz
2.3 Architecture
The basic architecture of LTE system is demonstrated in gure 2.1. The maincomponents shown are eNB, MME serving GW, PDN Gateway. All of thesecomponents are connected via dierent interfaces which are all IP based. Thissystem contains two networks: Core Network and Radio Access Network.
Figure 2.1: Basic Architecture
.
2.3.1 Core Network
In LTE, core network is an IP based network. All of the interfaces in thisnetwork use internet protocol (IP), that's why it is also called Evolved PacketCore (EPC). EPC architecture has a at structure. Entities in EPC are [40][9]:
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Mobility Management Entity (MME)
This entity is for signalling. It belongs to the control plane function of EPC.Main controls of MME are the UE's paging, location update functions and thesession establishment.
Serving Gateway (S-GW)
This entity is for switching and routing. Its purpose is to route user data fromUE to PDN via Node B's and vice versa.
2.3.2 Packet Data Network Gateway (PDN-GW)
It is the connectivity point between EPC and the external internet serviceprovider.
2.3.3 Policy and Charging Rules Function (PCRF)
This entity functions Policy and Charging Control (PCC). Tari and Quality ofService (QoS) control are managed, dened in P-GW and S-GW.A detailed LTE/SAE(System Architecture Evolution) at architecture is shownin gure 2.2.
2.3.4 Radio Access Network
LTE Radio Access Network is called Evolved Universal Terrestrial Radio AccessNetwork (E-UTRAN). Evolved Node B (eNB) is the only element of this part.It is the radio station that connects with UE through air interface. It actsas a gateway for UE to connect it to EPC. All the radio resource management,protocols, admission control and resource scheduling are handled by eNB [10][2].
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Figure 2.2: Flat Architecture of LTE and SAE
In next, we shall discuss Physical Layer of Radio Access network.
2.4 LTE Physical Layer
The LTE physical layer is based on Orthogonal Frequency Division Multiplex-ing scheme OFDM to meet the targets of high data rate and improved spectraleciency. The spectral resources are used as a combination of both time andfrequency units. MIMO options with 2 or more antennas are supported. Multi-user MIMO is supported in both uplink and downlink. The modulation schemessupported in the downlink and uplink are QPSK, 16PSK, 16QAM and 64QAM.
2.4.1 Downlink (DL) Physical Channel
The downlink transmission uses the OFDM with cyclic prex. Some of theadvantages of using OFDM are given below [6][8]:
- Fading: Multiple carrier modulation (MCM) helps in countering the fre-quency selective fading as the channel appears to have nearly at frequency
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response for the narrow band subcarrier.
- Flexible Spectrum Allocation: The frequency range of the resourceblock and the number of resource blocks can be adapted to the channelcondition, allowing exible spectrum allocation.
- Higher peak data rates can be achieved by using multiple resource blocksand not by reducing the symbol duration or using still higher order mod-ulation thereby reducing the receiver complexity.
- Orthogonality: The multiple orthogonal subcarriers inherently providehigher spectral eciency.
- ISI and Equalization: The cyclic prex (CP) is the partial repetitionof the symbol sequence from the end to the beginning. This makes thetime domain input sequence to appear periodic over the duration so thatthe DFT representation is possible for any frequency domain processingmaking it possible to perform simplest equalization. Also the duration ischosen larger than the channel delay spread which helps in reducing theinter-symbol interference.
Pilot Signals:
The following pilot signals are dened for the downlink physical layer[7][8]:
1 Reference signal: At a dened position of OFDM symbol a referencesignal consisting of known symbols is transmitted in the slot. This as-sists the receiver at the user terminal in estimating the channel impulseresponse so that channel distortion in the received signal can be compen-sated for. There is one reference signal transmitted per downlink antennaport and an exclusive symbol position is assigned for an antenna port suchthat when one antenna port transmits a reference signal other ports aresilent.
2 Synchronization Signal: Primary and secondary synchronization sig-nals are transmitted at a xed sub frames (rst and sixth) position in aframe and assists in the cell search and synchronization process at the userterminal. Each cell is assigned unique Primary sync signal.
2.4.2 Uplink (UL) Physical Channel
The uplink transmission uses the SC-FDMA (Single Carrier FDMA) scheme.The SC-FDMA scheme is realized as a two stage process where the rst stagetransforms the input signal to frequency domain (represented by DFT coef-cients) and the second stage converts these DFT coecients to an OFDMsignal using the OFDM scheme. Because of this association with OFDM, theSC-FDMA is also called as DFT-Spread OFDM [8]. The reasons (in additionto those applicable for OFDM for downlink) for this choice are given below:
- The two stage process allows selection of appropriate frequency range forthe subcarriers while mapping the set of DFT coecients to the ResourceBlocks. Unique frequency can be allocated to dierent users at any given
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time so that there is no co-channel interference between users in the samecell. Also channels with signicant co-channel interference can be avoided.
- The transformation is equivalent to shift in the centre frequency of thesingle carrier input signal. The subcarriers do not combine in randomphases to cause large variation in the instantaneous power of the modu-lated signal. This means lower PAPR (Peak to Average Power Ratio).
- The PAPR (Peak to Average Power Ratio) of SC-FDMA is lesser thanthat of the conventional OFDMA, so the RF power amplier (PA) canbe operated at a point nearer to recommended operating point. Thisincreases the eciency of a PA thereby reducing the power consumptionat the user terminal.
Pilot Signals
The following pilot signals are dened for the uplink physical layerlayer [7][8]:
- Demodulation Reference signal: This signal send by the user termi-nal along with the uplink transmission, assists the network in estimatingthe channel impulse response for the uplink bursts so as to eectively de-modulate the uplink channel.
- Sounding Reference Signal: This signal is sent by the user terminalassists the network in estimating the overall channel conditions and toallocate appropriate frequency resources for uplink transmission.
In chapter 5 and 6, we shall discuss both of these multiple access techniques indetail and then compare PAPR for both of these cases.
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Chapter 3
Smart Antenna Beamforming
and Direction of Arrival
3.1 Introduction
In the age of telecommunication, antenna plays a vital role to transmit or receiveelectromagnetic waves. In order to achieve peak data rates as well as the increasein the demand of both voice and data, the use of smart antenna is inevitable as itcomplements 3G technologies. An increase in performance can also be achievedby means of alleviation and reduction of the degradation factors as well as theimprovement in SNR which can easily be achieved by the smart antennas. Tounderstand the function of smart antenna it is important to know about theAdaptive Beamforming and the Direction of Arrival [11].
3.2 Smart Antenna Beamforming
The technique of Beamforming in smart antenna has a wide range of solutionsto over when it comes to reducing the interference level as well as the improve-ment of system capacity and bandwidth. This system makes use of a techniqueto transmit or receive signal only in the direction of the particular user from thebase station. This will help to reduce interference and will also increase the ca-pacity and bandwidth. Whereas one Base station can support one or more userson the same frequency with the dierent directions, by directing the individualbeam of antenna to each user. In order to estimate the capacity of the telephonesystem, spatial domain multiple access (SDMA) is used. In beamforming tech-nique both phase and amplitude of each antenna array can be controlled. Toachieve better steer nulls and adjust side lobe levels it is important to combineboth phase and amplitude at a time, while the sum of amplitudes can be de-noted by ak and phase shift control by xk which are called complex weight wkfor the kth antenna element. To get the required nulls and desired peaks in theradiation pattern the complex weight wk must be chosen carefully, these weightswk give one central beam which let the beam move towards some direction. Theweight wk is then changed in such a way that it continuously steer the beamuntil the direction of the signal source is found and maximum strength of the
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signal occurs. The weight wk provides the radiation pattern which increases thestrength of the signal and maximizes the quality of the received signal. Nor-mally, in beamforming there are two things while transmitting the signal, one isinterfering source and other is desired signal, due to this nulls are created in thedirection of interfering source and a peak in a pattern is pointed to the signalsource [12].
Figure 3.1: Beamforming using Smart Antennas
3.2.1 Switched Beam and Adaptive Beamforming
Smart Antenna can be classied into two categories in general, one is adaptivearray system and other is switched beam technique.Using Antenna arrays backed by strong signal process capabilities, adaptivebeamforming changes the beam pattern in accordance with the changing signalenvironment. It not only introduces the nulls at the interfering directions dur-ing the tracking of desired mobile users, it also directs the maximum amount ofradiations in the desired mobile user. In Adaptive Beamforming technique, thedesired radiation pattern can be achieved by multiplying the complex weightswith incoming signals and combine them together, these weights can be com-puted adaptively by adapting the environmental eects on signal, while thecomplex weight computations can be achieved by using the software algorithms[13].
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Figure 3.2: Block Diagram of Adaptive Array Beamforming
In Adaptive Array beamforming the incoming signals are brought down to theintermediate frequencies IF's according to the gure 3.2, then the incoming sig-nal is weighted by the adaptive array systems using DSP. In order to digitize thedown converted signal the Analog to Digital Converters (ADCs) are used beforethey are processed by Digital Signal Processor. Then the incoming data infor-mation is being interpreted by the processor to determine the complex weightsto each element output to optimize the array pattern. This optimization is doneby minimizing the interference and noise while producing the maximum beamgain at the desired direction. Hence adaptive array beamforming is a techniquewhich is used to achieve the maximum reception in the desired direction whichcan only be done by adjusting the weights of each antenna used in an array. Thesignals coming from dierent directions and dierent transmitters use the samefrequency channels, then the desired signal is separated from the interfering sig-nal. Phase is an important element for the signal to be transmitted or receivedin a desired direction which can be achieved by using the array factor. Thearray factor AF of N elements which is equally spaced linear array are shownbelow,
AF (φ) =
k−1∑k=0
Ak exp(jk 2πdλ cos(φ)+α), (3.1)
where α is the interelement phase shift,
α =−2πd
λ0cos(φ0), (3.2)
where φ0 is the desired beam direction, and λ the wavelength [13].
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Figure 3.3: An adaptive array system
The gure 3.3 shows the complete structure and function of adaptive arraysystem, where Sm(t) are the input signals of the array element while ni(t) isthe noise. Therefore each array element encounter noise thats why each inputsignal is connected with noise factor n(t). While Ω(t) are weights, which arecalculated repeatedly by depending upon the output y(t).Here, y(t) is an array output which is shown below with
y(t) = ΩHx(t), (3.3)
where ΩH denotes the complex conjugate transpose of the weight vector. Theoptimum weights can only be calculated if the steering vector from the sampledata of y(t) is already known. By the summation of the attenuated originalsignal Si(t) and phase shift signal, the Baseband received signal at the N th
antenna is obtained as,
xN (t) =
N∑k=1
pN (θk)Sk(t) exp−j2π(fc)lNθk , (3.4)
where Sk(t) contains both interferer and received signals while fc is the carrierfrequency and lN θk is the delay of the signal.Let,
PN (θk) = [p1(θk) exp−j2π(fc)l1θk , p2(θk) exp−j2π(fc)l2θk .....pN (θk) exp−j2π(fc)lNθk ]T ,(3.5)
where PN (θk) is the steering vector with delay lN θk,
P (θ) = [p(θ1) p(θ2) · · · p(θm)], (3.6)
S(t) = [S1(t) S2(t) · · ·Sm(t)]T , (3.7)
x(t) = P (θ)S(t), (3.8)
with the addition of noise factor we get,
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x(t) = P (θ)S(t) + n(t), (3.9)
Beamformer response can be shown in vector form while p(θ) is possible depen-dent on Ω,
r(θ,Ω) = ΩHp(θ,Ω), (3.10)
by separating the interfering signal Ui(t) and the desired signal S(t), we get thefollowing response,
x(t) = S(t)p(θ0) +
Nu∑i=1
Ui(t)p(θi) + n(t). (3.11)
In the above equation x(t), the desired signal and the interferer signal is sepa-rated. Let S(t) be the desired signal arriving at the antenna array at an angleof incidence θ0, while Ui(t) is an undesired signal which is arriving at an angleof incidence θi, where p(θ0) is the array vector of desired signal while p(θi) isthe array vector of undesired signal at ith value.Error can be estimating by subtracting the complex conjugate transpose weightwith the closely correlated desired signal d?(t),
ε(t) = [d?(t)− ΩHx(t)], (3.12)
by taking the expectation and squaring the error signal ε(t) we get,
E[ε2(t)] = E[d?(t)− ΩHx(t)]2, (3.13)
E[ε2(t)] = E[d2(t)]− 2ΩHE[d?(t)x(t)] + E[ΩHx(t)], (3.14)
γ = E[d?(t)x(t)], (3.15)
where γ is the cross correlation matrix between the received and desired signal.
R = E[x(t)xH(t)], (3.16)
where R is the autocorrelation of the received signal which is also known ascovariance.
E[ε2(t)] = E[d2(t)]− 2ΩHγ + ΩHRΩ, (3.17)
by taking the gradient of the expectation of the error signal Minimum squareerror (MSE) is achieved as,
OΩ(E[ε?(t)]) = −2γ + 2RΩ = 0. (3.18)
The optimum solution is shown below while ω?opt is also called as Wiener weightvector,
ω?opt = R−1γ. (3.19)
Generally Adaptive Array beamforming is capable of performing the followingfunction:- Estimating the Direction of Arrival (DOA) of all incoming signals which also
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includes interfering and multipath signals using the dierent DOA algorithmslike Capon DOA or Music DOA [13].- Desired signal is identied and undesired/interfering signal is ltered from theincoming signals.- Beam is steered only in the direction of desired signal, while when the usermoves from one direction to the other it keep track the user by placing the nullsat the interfering signal direction and also by updating the complex weightsconstantly.In a switched beam system array of xed beam antennas in predetermineddirections are used to serve the users. This technique gives the best performanceas the mobile user moves from the one cell to other, because the base stationsswitches between several xed beams [13].
Figure 3.4: Phase Diagram of Switch Beam System
Switched beam system is typically consisting of multiple array antennas, whileeach array covers a certain section in the cell for Base Station. The phaseshifting network is used to shift the number of beams in certain directions, asshown in the gure 3.4. While the control logic is controlled by an algorithm,which scans all the incoming beams and selects the one of the strongest signal.The above mentioned technique is simple in implementation and operation butnot suitable for high interference areas, due to which the performance of switchbeam system is limited as compared to other techniques.However, Adaptive Array beamforming provides better performance because ituse various advanced signal processing techniques for processing the informationarrived by the antenna arrays. Adaptive array system is smart because it adaptsitself according to the changing RF environment, while antenna array system isdynamically controlled by advanced signal processing techniques [13].
3.3 Implementation of Beamforming Techniques
The two main types to implement the Beamforming techniques are explainedbelow:
3.3.1 Least Mean Square method (LMS)
- Use gradient based method of steepest decent.
- Estimate gradient vector from the available data.
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- Simple and Easy Computations.
- This algorithm deals with iterative procedure to minimize the error.
- It computs the weight which is based on Mean Square Error.
Figure 3.5: Block diagram of LMS Algorithm
By separating the interfering signal Ui(t) and the desired signal S(t), we get thefollowing response,
x(t) = S(t)p(θ0) +
Nu∑i=1
Ui(t)p(θi) + n(t). (3.20)
Weights Ω are calculated seperately then the individual elements are linearlycombined and antenna pattern is optimized in such a way that they producemaximum gain in the desired direction and placing the nulls in the undesireddirection.The update equation of the weight vector is shown below:
Ω(n+1) = Ωn + ρx(n)[d?n − xHΩn], (3.21)
Ω(n+1) = Ωn + ρx(n)ε?(n), (3.22)
where ρ controls the convergence of the LMS algorithm,
y(n) = ΩHx(n), (3.23)
where y(n) is the output, and
ε(n) = d?(n)− y(n), (3.24)
where ε(n) indicates the error term. The update equation becomes,
Ω(n+1) = Ωn + ρx(n)ε?(n), (3.25)
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where Ω(n+1) is the weight vector. The LMS algorithm must be initiated withan arbitrary value of weight Ω(0) at n = 0. With the successive iteration of theweight vector it will leads to the mean square error.Where the convergence of the weight vector can be achieved by adapting the inequation shown below,
0 < ρ <1
ζmax. (3.26)
The equation (3.26) explains the convergence of algorithm, where ζ is the largesteigenvalue of the correlation matrix. If theρ is large, then there will be very fastconvergence even it will lose the stability around the minimum value, but if theconvergence is small then the algorithm work more proper and coverges slowly[13].
3.3.2 Recursive Least Square Algorithm
When LMS algorithm fail to converge the desired values then RLS algorithm isused. It computes the values recursively. In LMS algorithm the ρ is responsiblefor the convergence, in an evironment where ρ is having large values then theconvergence will occur fast and will produce unstable output. This problem canbe resolved by replacing the gradient parameter ρ to gain matrix z−1. Theweight update equation is shown as,
Ωn = Ω(n−1) −z−1(n)x(n)ε?(Ω(n−1)), (3.27)
where gain matrix can be shown as,
z(n) = δ0z(n− 1) + x(n)xH(n), (3.28)
z(n) =
n∑k=0
δn−k0 x(k)xH(k), (3.29)
where δ0 is the real scalar number close to 1 which deals with the forgettingfactor and update the old information when the new information comes in, and
11−δ0 deals with the memory factor if δ0 = 0.99 then the algorithm is having amemory close to 100 samples.The inverse of the gain matrix is shown below:
1
z(n)=
1
δ0z0(n− 1) + x(n)xH(n), (3.30)
z−1(n) =1
δ0[
z−1(n− 1)δ0δ0 + xH(n)z−1(n− 1)x(n)
], (3.31)
z−1(n) = 1δ0
[z−1(n−1)δ0+z−1(n−1)xH(n)z−1(n−1)x(n)−z−1(n−1)x(n)xH(n)z−1(n−1)
δ0+xH(n)z−1(n−1)x(n)], (3.32)
z−1(n) =1
δ0[z−1(n− 1)− z−1x(n)xH(n)z−1(n− 1)
δ0 + xH(n)z−1x(n)]. (3.33)
17
The matrix is initialized as,
z(0) =1
ε0I. (3.34)
The comulative square error of the RLS algorithm can be minimized by thefollowing equation:
ψ(n) =
n∑p=0
δn−k0 |ε(p)|2. (3.35)
The convergence speed of RLS Algorithm is independent on the eigenvalues ofarray correlation matrix [13].
3.4 Advantages and Disadvantages of RLS andLMS Algorithm
There are several advantages as well as disadvantages involved in both methods.In RLS algorithm the complexity, computational cost and processing is increasedbecause it calculates the values recursively, on the other hand LMS is simpleand easily applied algorithm. The error rate in RLS algorithm is also veryless because its computation is high and it also oers fast convergence whileerror rate in LMS algorithm is high because it deals with current values only.Another advantage of RLS algorithm is that it treats with the past data too tominimize the errors which means it has an innite memory, while LMS containsthe current values only. Under certain limits both of the algorithms can be usedin a same way but we prefer to use LMS algorithms, because it is simple toimplement and also it reduces complexity.
3.5 Direction of Arrival
As we are using MIMO system, it is necessary for the antenna to judge whichsignal is useful and which one useless for it. This is due to the fact that therelots of signals in air. Therefore to locate the approximate direction of arrivalabout the useful signal MUSIC DOA or Capon DOA algorithms can be used.Normally in densely populated cities or less populated cities the average mea-sured angular spread goes up to 15, due to which the quality of high resolutionDOA estimation gets lower [14].
3.5.1 MUSIC DOA
MUSIC stands for MUltiple SIgnal Classication, this techique is based on ex-ploiting the eigenstructure of the input covariance matrix. It is a high resolutiontechnique which is based upon the assumption that the noise in each channelis uncorrelated from the other channel which can be done by diagonalizing thecorrelation matrix, but the incident signal arriving on the antenna is correlatedwhich can be done by nondiagonalizing the signal correlation matrix [15].The N number of signal elements arriving at the M antenna array elements,where N is the number of signal eigenvectors and eigenvalues, and the number
18
Figure 3.6: M antenna element array with N arriving signals using DOA esti-mation Algorithm.
of noise eigenvectors and eigenvalues is M-N. The covarriance matrix of thearray signal is,
Rxx = PRssPH + σ2
nI, (3.36)
where H is the Hermitian transpose of the matrix and σ2nI is the autocorellation
noise and,
P = [p(θ1) p(θ2) p(θ3) p(θ4) · · · p(θN )], (3.37)
where P is the steering matrix of M ×N array elements. And,
Rss = [s1(k) s2(k) s3(k) s4(k) · · · sN (k)]T , (3.38)
where Rss is the N ×N source correlation matrix. We can denote the subspacespanned by noise eigenvector by noise subspace,
vN = [v1 v2 v3 v4 · · · vM−N ], (3.39)
where vN is the subspace spanned by the noise eigenvectors.The steering vector which arrives at the angles of θ1, θ2, θ3, θ4, ......, θN are or-thogonal to the noise subspace eigenvectors.The pseudo spectrum of MUSIC algorithm is given by,
PMUSIC(θ) =1
abs((p(θ)HVNV HN p(θ)). (3.40)
The resolution of the MUSIC decreases if the signal source is either coherent orthe noise variance varies. This problem can be eliminated by collecting sometime samples of recieved signal with noise. Then estimate the correlation matrixusing the equation below [15],
Rxx =1
k
K∑k=1
x(k)x(k)H , (3.41)
19
and,
Rxx = PRssPH + PRsn +RnsP
H + σ2nI. (3.42)
By taking the time sample of recieved signal with noise and averaging the cor-relation matrix the MUSIC pseudospectrum will provide the high angular res-olution.
3.5.2 Capon Method
Capon is a DOA estimation technique [17] which is also called as MinimumVariance Distortionless Response (MVDR). This method uses a technique for abeam to be looked in a desired direction, by maintaining the gain of total outputpower along the desired direction as a constant and reducing the undesiredDOA's by minimizing the total output power [16].
minΩ(ΩHzsΩ) subject to|ΩHp(θ)| = 1. (3.43)
The weight vector of Capon algorithm is shown as,
Ωc =z−1s p(θ)
pH(θ)z−s 1p(θ). (3.44)
The output power spectrum of Capon algorithm is shown as,
Pc(θ) =1
pH(θ)z−1s p(θ)
. (3.45)
This method provides the better performance but it also depends on the SNRand also on the number of antenna array elements. This algorithm fails whenthe incident signals arriving on the source antenna array element is correlated[16].
3.6 Summary
In this chapter we studied the two main types of beamforming one is Switchedbeamforming and other is Adaptive beamforming, then we discussed the im-plementation of beamforming techniques using Least Mean Square (LMS) andRecursive Least Square(RLS) algorithm. As there are so many signals in theair so it is important for the antenna to know that which signal is desired andwhich signal is undesired, for this Direction of Arrival (DOA) is to be used likeMUSIC DOA and Capon DOA.
20
Chapter 4
Multiple Input Multiple
Output-MIMO
4.1 Introduction
As the wireless communication is rapidly developing technology in present timeswith new product and service emerging almost on daily basis. These develop-ments present enormous challenges for communication engineers as the demandsfor increased capacity growing explosively. The biggest challenge in wirelesscommunication is the phenomena called multipath induced fading, namely ran-dom uctuation in the channel gain that arises due to multi path scattering.Previously multipath scattering was seen as biggest impairment in wireless com-munication but today now by employing multiple antennas in the transmitterand receiver called MIMO, rich scattering environment can be exploited to cre-ate multiplicity of parallel links to increase the data rate without the expenseof extra bandwidth.
4.2 Why MIMO system
There is unprecedented growth in demand for providing high speed wirelesscommunication link in order to support wide range of applications such as voice,video email web browsing to name few. The biggest challenge in this scenariois the scarcity of the available bandwidth which is the real price to pay. Nowwith MIMO system the following benets without the expansion of the availablebandwidth or increase of transmitted power can be achieved.
4.2.1 Array gain
By using multiple antennas at the transmitter and antennas, the signal to noiseratio is increased by coherently combining eect of wireless signals at the re-ceiver which improves resistance to noise which results in larger coverage areaof wireless system [18].
21
4.2.2 Spatial Multiplexing
MIMO systems oer tremendous linear increase in data rate by transmittingindependent data streams with available bandwidth enhancing the capacity ofwireless system. The spatial multiplexing increases the capacity of wirelesschannel [19].
4.2.3 Interference suppression
By exploiting the special dimension provided by multiple antennas interferencecan be mitigated in that a way that it was not possible with single antenna.Hence the system is turned into less susceptible to interference.
4.2.4 Spatial diversity gain
Multiple antennas can be used to counter act the fading due to multipath prop-agation. By increases the number of multiple copies of signal at receiver, theprobability that all the signals are in deep fade simultaneously is very low whichcauses diversity gain results in robustness of the wireless link [20].
4.3 Diversity
Diversity scheme is a technique which is used to improve the performance of thecommunication system by eectively transmitting the same information multipletimes to improve the signal to noise ratio such that transmitted signal is detectedcorrectly.
4.3.1 Types of Diversity
There are several types of diversities which are explained below.
Time diversity
It is the type of diversity in which same information bearing signal is transmittedin dierent intervals.
Frequency diversity
It is the type of diversity in which information bearing signals are transmittedby means of several carriers suciently apart from each other to provide inde-pendent fading version of signal. OFDM modulation is the example of frequencydiversity.
Space diversity
It is type of diversity in which signal is sent over dierent propagation paths byusing multiple antennas at the transmitter and at the receiver. The spacing iscarefully chosen to ensure the independence of possible fading events occurringin the channel [21].
22
4.4 Space diversity types
The types of space diversity are explained below:
4.4.1 SISO
SISO stands for single input and signal output. It uses one antenna at thetransmitter and one antenna at the receiver as shown in gure 4.1. SISO channelis more susceptible to problem caused by multipath eect however it is cheapto implement.
Figure 4.1: SISO Systems
4.4.2 SIMO
SIMO stands for single input and multiple output. It uses single antennas attransmitter and multiple antennas at the receiver as shown in gure 4.2. SIMOsystem is preferably used in uplink scenarios.
Figure 4.2: SIMO Systems
4.4.3 MISO
MISO stands for multiple input and single output. It uses multiple antennasat transmitter and single antennas at the receiver as shown in the gure 4.3.MISO system is preferable used in downlink scenarios.
23
Figure 4.3: MISO Systems
4.4.4 MIMO
As mentioned earlier MIMO stands for multiple input and multiple output.It employs multiple antennas at the transmitter and multiple antennas at thereceiver as shown in gure 4.4. It is mostly used for both uplink and downlinkscenarios [22].
Figure 4.4: MIMO Systems
4.5 Discrete Time MIMO Model
Consider a communication link with MT transmit antennas and MR receiveantennas as shown in gure 4.4. The discrete time MIMO model is given by thesystem of linear equation in matrix form,
y1
y2
...yn
=
h11 h12 · · · h1mt
h21 h22 · · · h2mt
......
...hm1 hm2 . . . hmrmt
x1
x2
...xmt
+
n1
n2
...nr
y = Hx+ n, (4.1)
where y is received signal vector H represents complex channel gain which in-corporates fading inuence of channel. And x is a transmitting vector and n is
24
assumed to be uncorrelated Gaussian noise with zero mean and covariance σ2nI.
Channel H is assumed to be zero mean spatially white in which entries of H areIdentical Independent distribution(iid) zero mean unit variance complex circu-larly symmetric Gaussian random variable [32]. Receive antenna "i" receives asuperposition of every sent signal form the transmitter weighted by the channelresponse and some AWGN are added.The channel is Mr ×Mt transition matrix is made up of elements is given asfollows,
H=
h11 · · · h1Mt
.... . .
...hM1 · · · hMrMt
,where hij represents complex channel coecient between jth transmitter anten-nas and ith receiver antenna.
4.5.1 Parallel Decomposition of MIMO channel
Consider a MIMO channel model (4.1) where channel matrix gain H is knownto transmitter and receiver both. Let RH be rank of channel matrix H. BySingular Value Decomposition [23],
H = U∑
V H , (4.2)
where U is Mr ×Mr Orthogonal matrix V is Mt ×Mt orthogonal mtarix∑
isMr ×Mt diagonal matrix such that,
∑=
σ1 0 0 0 0 00 σ2 0 0 0 0
0 0. . . 0 0 0
0 0 · · · σr 0 00 0 0 0 0 0
0 0 0 0 0. . .
,
with r singular values σi, i = 1, 2, ......, r on main diagonal values. The singularvalues are strictly positive and usually organized in decreasing order,
σ1 ≥ σ2 ≥ σ2...... ≥ σr > 0.The parallel decomposition is obtained by dening signal processing techniquecalled transmit pre coding and receiver shaping. In transmit pre coding, theinput antenna x is generated by operating V H on the input signal. Receivershaping perform similar operation by operating output vector y with UH insuch a way that the system model (4.1) becomes,
y = U∑
V H x+ n, (4.3)
UH y = UH(U∑
V H x+ n), (4.4)
y = UHU∑
V HV x+ n, (4.5)
y =∑
x+ n. (4.6)
25
Figure 4.5: Equivalent MIMO Communication System
The corresponding modied communication model is depicted in gure 4.5where x is input vector signal, n is noise vector and y is received output vector.The equation (4.6) consists of diagonal matrix sigma can be interpreted as rindependent parallel uncoupled systems written as follows:
y1 = σ1x1 + n1, (4.7)
y2 = σ2x2 + n2, (4.8)
yr = σrxr + nr, (4.9)
where r is the rank of the channel matrix, RH = min(Mr × Mt), thus bytransmit pre coding and receiver shaping MIMO channel is decomposed in RHindependent SISO channel [32] as shown as gure 4.6.
Figure 4.6: Parallel Decomposition of MIMO Channel
4.6 Capacity
Capacity is dened as the number of bits per channel per Hz.
26
4.6.1 Capacity for SISO
For SISO system the capacity is given by Shannon formula [24],
C = B log2(1 + SNR). (4.10)
4.6.2 Capacity of MIMO
For MIMO system, the capacity is given by Shannon formula [24],
C = log2 det(I +1
σ2n
HRxHH), (4.11)
where Rx is the covariance matrix of input signal x(t) and σ2n is the variance of
uncorrelated Gaussian noise. The Shannon Capacity is the fundamental limitfor error free communication. As by the property of determinant [23],
det(I +AB) = det(I +BA). (4.12)
The equation (4.11) becomes,
C = log2 det(I +1
σ2n
RxHHH), (4.13)
where HHH is a positive denite matrix [23], with eigen values σ1,σ2,....,σr.It is diagonalized using the unitary matrix such as HHH = W
∑WH where
W is unitary matrix whose columns are associated eigenvectors, such that theequation (4.11) becomes,
C = log2det[I +1
σ2n
RxW∑
WH ], (4.14)
by applying the property of determinant (4.12),
C = log2det[I +1
σ2n
∑WHRxW ], (4.15)
now,
Rs = WHRxW, (4.16)
equation (4.16) is transformed covariance matrix,
Rs =
P1 0 0 00 P2 0 0
0 0. . . 0
0 0 · · · Pk
,the equation (4.14) becomes,
C = log2det[I +1
σ2n
∑Rs], (4.17)
where Rs is non nagative denite matrix [23]. The non negative denite matrixA satises the Hadamard inequality [29],
detA ≤ Πkakk, (4.18)
27
where akk are diagonal elements of matrix A, so applying this inequality to(4.17), we get
det[I +1
σ2n
∑Rs] ≤ ΠN
k=1(1 +1
σ2n
σ2krs,kk), (4.19)
where σ2k is the k
th eigen value of matrix product HHH and rs,kk is kth diagonalelement of transformed matrix Rs. By using the equality sign to proceed furtherfor capacity calculation (4.17) yields,
C = log2ΠNk=1(1 +
1
σ2n
σ2krs,kk), (4.20)
C =
N∑k=1
log2(1 +1
σ2n
σ2krs,kk), (4.21)
p =
r∑k=1
Pk, (4.22)
n∑k=1
rs,kk = Ptotal, (4.23)
C =
N∑k=1
log2(1 +1
σ2n
σ2kPk), (4.24)
This is the capacity of equivalent parallel uncoupled MIMO system.
4.6.3 Comparison between SISO and MIMO
In this section we compared SISO channel and MIMO channel in terms of ca-pacity. Transmitted Power is nite, for example 1 watt and gain is assumed tobe unity with noise variance σ2
n as shown in gure 4.7. the capacity if SISO(4.10) becomes,
Figure 4.7: Capacity of SISO
C = log2(1 +1
σ2n
). (4.25)
For MIMO we have N channels having channel gain unity we divide same power1 watt on N channels equally such that Ptotal =
∑Ni=1 Pi = 1 with same noise
variance σ2n as shown in gure 4.8.
28
Figure 4.8: Capacity of MIMO
The capacity for MIMO in equation (4.24) becomes,
C =
N∑k=1
log21 +1
σ2n
1
N, (4.26)
C = N log21 +1
σ2nN. (4.27)
By comparing (4.25) with (4.27) the capacity of MIMO system is much greaterthan the SISO system.
4.6.4 Optimum Capacity
When the channel site information (CSI) is known to transmitter, the methodfor optimum capacity uses water lling Algorithm for nding the best channelsto utilize the available power in smart way. When transmitter knows the eigen-values and eigenvectors corresponding to H channel matrix and noise power σ2
n
it uses this information in a smart way. See [27] for complete description ofwater lling Algorithm. The water lling technique is used to determine thepowers transmitted in each channel to achieve the greatest possible capacity.There is no general proof of water lling technique but the idea will be shownfor a 2× 2 MIMO system. In Shannon Capacity formula (4.24), σ2
k and σ2n are
constants. For optimum power distribution we have to maximize the shannoncapacity (4.24) with respect to variable Pk (Power) but power is limited. Sowe have a constraint as
∑Ni=1 Pi = Ptotal. This give rise to optimization prob-
lem which is solved by using Langrange multiplier method [28]. We formedLangrange multiplier function L, which depends upon variable Pi as,
L(Pi, λ) =
r∑i=1
log(1 +1
σn2
σ2i pi) + λ(
∑i
Pi − Ptotal), (4.28)
29
subjected to constraints,∑Ni=1 Pi = Ptotal and Pi ≥ 0, where λ is Langrange
multiplier. For optimum capacity we dierentiate the principle function of (4.28)with respect to Pi,
dLdPi
= (1
1 +σ2iPiσ2n
)σ2i
σ2n
+ λ = 0, (4.29)
σ2i
σ2n + σ2
i Pi+ λ = 0, (4.30)
σ2n + σ2
i Piσ2i
= − 1
λ, (4.31)
σ2n
σ2i
+ Pi = − 1
λ, (4.32)
Pi = −σ2n
σ2i
− 1
λ, (4.33)
− 1λ is termed as γ,
Pi = γ − σ2n
σ2i
. (4.34)
The optimization criterion, there is number γ such that,
Pi =
γ − σ2n
σ2i, if γ − σ2
n
σ2i> 0
0, if γ − σ2n
σ2i≤ 0
(4.35)
and total power to be transmitted can be written as,
n∑i=1
Pi =
Nact∑i=1
(γ − σ2n
σ2i
) = Ptotal, (4.36)
where Nact is the number of active channels for channel Pi > 0. The completevisualization of waterlling algorithm is given in the gure 4.9.
30
Figure 4.9: Waterlling Algorithm
31
4.6.5 Power distribution
There are two dierent types of strategy optimum power distribution:- Uniform input power distribution- Non Uniform power distributionIf the channel site information (CSI) at unknown to transmitter then it is sen-sible to use uniform power distribution across each channel. On other hand ifchannel site information (CSI) is available to transmitter it is better to increasethe capacity by sending more power to channel with larger gains in correspon-dence with Water lling algorithm.
4.7 Space time coding
There are number of space time block code but in this thesis we are focusingon Alamouti time space block code invented by Sivash M.Alamouti in 1998. Ituses two by two orthogonal space time code for two transmit antennas and tworeceive antennas as shown in gure 4.10. The space time code will not achieveoptimal capacity for MIMO system but still gives the promising approach. See[26] for complete description.
4.7.1 Alamouti space time block code
The Alamouti block code is described by the following transmission matrix asfollows:
S=
[S1 S2
−S∗2 −S∗1
]In this matrix row represents spatial dimension and column
represents time dimension. The gure 4.10 shows a block diagram of Alamoutiencoding in the transmitter. The Alamouti code works with a pair of symbolsin time. It takes two time instants to transmit the two symbols [25].
32
Figure 4.10: Alamouti Encoding
4.7.2 Orthogonality of Alamouti code
The Alamouti code is simple orthogonal matrix[23] as it satises the conditionof orthogonality on both special and temporal sense. By multiplying the codematrix with Hermitian transpose we get,
SSH =
[S1 S2
−S?2 S?1
] [S?1 −S2
S?2 S1
],
SSH =
[|S1|2 + |S2|2 −S2S1 + S1S2
−S?1S?2 + S?1S?2 |S1|2 + |S2|2
],
SSH =[|S1|2 + |S2|2
] [1 00 1
],
SSH = [|S1|2 + |S2|]2I, (4.37)
where I is the Identity matrix. By multipying the Hermitian transpose of S onLeft hand side of Alamouti code matrix,
SHS =
[S?1 −S2
S?2 S1
] [S1 S2
−S?2 S?1
],
SHS =
[|S1|2 + |S2|2 S?1S2 − S?1S2
S?2S1 |S1|2 + |S2|2],
SHS =
[|S1|2 + |S2|2 0
0 |S1|2 + |S2|2],
SHS =[|S1|2 + |S2|2
] [1 00 1
],
SHS = [|S1|2 + |S2|2]I, (4.38)
which clearly shows complex orthogonailty of Alamouti code matrix. AlamoutiCode is orthogonal space time code in that product of its transmission matrixwith its Hermitian transpose is equal to two by two identity matrix scaled by
33
sum of squared amplitudes of the transmitted symbols as discussed in equa-tion (4.37), (4.38).
4.8 Alamouti Encoding Transmitting and decod-ing
In this section we describe simple space time encoding, transmitting and de-coding by Alamouti coding. The channel is assumed to be slowly varying suchthat complex distortion caused by two consecutive instants are essentially same.There are two transmit antennas and two receive antennas. The transmitter hasno knowledge about channel site information (CSI). On other hand receiver hasfull knowledge channel site information.
4.8.1 Alamouti Channel Model
By inserting Alamouti Code [25], the channel model (4.1) at time instant n-1and n becomes,
y(n− 1) = HC(n− 1) + V (n− 1), (4.39)
y(n) = HC(n) + V (n), (4.40)
where y(n − 1) and y(n) are the output vectors at time instant n-1 and nrespectively. V (n) and V (n− 1) are zero mean uncorrelated additive noise withvariance σ2
V . The two code words in Alamouti code is given by the followingvectors:
C(n− 1) =
[s1
s2
], C(n) =
[−s∗2s∗1
].
4.8.2 Alamouti Encoding
By putting these code words in signal mode (4.39) and (4.40), we get thefollowing signal model in explicit component form.At instant n-1,
y1(n− 1) = h11s1 + h12s2 + v1(n− 1). (4.41)
y2(n− 1) = h12s1 + h22s2 + v2(n− 1). (4.42)
At instant n,
y1(n) = −h11s∗2(n) + h12s
∗1 + v1(n). (4.43)
y2(n) = −h21s∗1(n) + h22s
∗1 + v2(n). (4.44)
34
4.8.3 Alamouti Decoding
Now the Alamouti Decoding [25] is given by,
s1 = −h∗11y1(n− 1) + h12y∗1(n) + h∗21y2(n− 1) + h22y
∗2(n). (4.45)
s2 = h∗12y1(n− 1)− h11y∗1(n) + h∗22y2(n− 1)− h21y
∗2(n). (4.46)
By inserting signal model (4.41), (4.42), (4.43) and (4.44) in Alamouti decodingwe nally obtained,
s1 = [|h11|2 + |h12|2 + |h21|2 + |h22|2]s1 + V (n− 1). (4.47)
s2 = [|h11|2 + |h12|2 + |h21|2 + |h22|2]s2(n) + V (n). (4.48)
Due to complex orthogonality of Alamouti code, the unwanted signal s2 is can-celled out in equation (4.47) and unwanted signal s1 is cancelled out for equa-tion (4.48). The cancellation are responsible for simplication in the receiver.The two decoupled signal s1(n − 1) and s2(n) are sent to maximum likelihooddecoder as shown in gure 4.11 which estimates s2(n) and s1(n − 1) and foreach signal, decision rule is applied given in [25].
35
Figure 4.11: Alamouti Space time block code with 2X2 Transmitter
4.9 Summary
In this chapter we studied MIMO, its benets and need for meeting currentcapacity demands. We investigated the capacity relationships between MIMOand SISO to show, how MIMO gains superiority over SISO. We discussed Spacetime coding such as SVD and Alamouti space time coding for 2× 2 system.
36
Chapter 5
Orthogonal Frequency
Division Multiplexing -
OFDM
5.1 DIGITAL MODULATION
Modulation of a signal changes the amplitude, phase or frequency of carrier,however in OFDM only phase or amplitude or both at same time is varied butthe frequency is kept constant to ensure the orthogonality among the subcar-riers. The type of modulation scheme is chosen according to application. Indigital modulation scheme, symbols are converted into bits, a complex numberrepresents the number of bits to transmit according to modulation scheme em-ployed for example binary phase shift keying (BPSK) one bit corresponds toone symbol, in quardrature phase shift keying (QPSK) two bits corresponds toone symbol, in eight phase shift keying three bits corresponds to one symbol,in 16-QAM four bits represents one symbol and in 64-QAM six bits representper symbol. In short the following parameters [30] are to be considered whenchoosing the appropriate scheme.
1. Maximum data rate.
2. Minimum probability of symbol errors.
3. Minimum transmitted power.
4. Maximum channel band width.
5. Maximum resistance to interfering signals.
6. Minimum circuit complexity.
A few modulation techniques used in OFDM are as follows:
37
5.2 Phase Shift keying (PSK) modulations
In PSK modulation scheme, the data is transferred by varying the phase of thereference signal usually called carrier. A nite number of angles represent digitaldata. Each of the angle is given a specic collection of binary digits usually eachphase encodes equal number of bits. Each collection of bits is termed as symbolthat corresponds to particular phase. An elegant way of representing any digitalmodulation scheme is its constellation diagram.
Figure 5.1: PSK Constellation
In PSK, constellation points are usually placed in uniform angular spacingaround a circle as shown in gure 5.1. This arrangement provides better phaseseparation between the adjacent points and this gives better noise immunity.All of the points are placed on circle such that all the transmitted symbols havesame amplitude and power. Since data is transferred in binary digits the PSKscheme is designed with the number of constellation points being the power of2. There are many types of Phase shift keying. Some of them used in OFDMsimulation are as follows, -BPSK,-QPSK,-8PSK,-16PSK
5.2.1 Binary phase shift keying
As the name indicates, it uses two phases to code the binary digits of infor-mation. There are two results 0 and 1. They are separated by phase shift of180. BPSK signal lies on x axis. Constellation diagram of BPSK is shown ingure 5.2.
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Figure 5.2: 1Q Diagram for BPSK Constellation
When the data is transmitted through the noisy channel. The points on theconstellation diagram will not remain on same place where it was initially placedthere at the time of transmission. The dierence between the exact location andthe place where data is actually received is termed as error vector. The receiverdecodes the data that which bit was sent after seeing the data in which part ofthe real axis the data is received which is supposed to 0 or 1.
5.2.2 Quardrature phase shift keying
In QPSK there are four points in constellation diagram. Each point is has twocomponents that is real part and imaginary part makes it as complex number.This means that beside points in either side of zero line in real dimension usu-ally called in phase component it also has points on either side of zero line ofimaginary dimension usually called as quadrature component as shown in gure5.3.The data is placed in four quadrant each symbols represents two bits. The areawhere data points is being eected after passing thought the noisy channel lie inquarter of the constellation map if it has to decode correctly at the receiver side.And if the data point lies in dierent quadrant as compared to quadrant whenit was transmitted initially the receiver will interpret as dierent data point anderror will occur.
39
Figure 5.3: 1Q diagram for QPSK Constellation
5.2.3 8PSK
In 8PSK there are eight points in constellation diagram. Each points is complexnumber carrying three bits. Each phase shift is separated by 45 which meansit has eight phase levels as shown in gure 5.4.
40
Figure 5.4: 8-PSK Constellation
The date is placed in those eight levels. The area where data points is beingeected after passing through noisy channel lie in one of eight phase levels if ithas to decode correctly at the receiver side.
5.2.4 16-PSK
In 16-PSK there are 16 points in constellation diagram. Each point is complexnumber carrying four bits of data. Here each point which is complex number isnow 22.5 apart which means it has 16 phase levels as shown in gure 5.5.
41
Figure 5.5: 16-PSK Constellation
The area where data points is being eected after passing through noisy channelis one of 16 phases level if it has to decode correctly at the receiver side. Bitrate is now four times that of BPSK for the same symbol rate.
5.3 Quadrature Amplitude modulation (QAM)
It is the type of digital modulation scheme where both phase and amplitude ofthe reference signal is changed simultaneously. Each point is a complex number,placed in rectangular constellation diagram. Unlike PSK, two aspects of signalsuch as phase and amplitude need to be corrected to ensure that correct datais received. The SNR of signal has to be greater in order to decode the signalcorrectly. There are many types of QAM some of commonly used in OFDMsimulation are listed below:
5.3.1 16 QAM
In 16-QAM there are 16 points on the constellation diagram each point is com-plex symbol carrying four bits to represent each QAM complex symbol. Thephase dierence is of 45. The constellation map is shown in gure 5.6 whereeach symbol is dierentiated on both phase and amplitude.
42
Figure 5.6: 16-QAM Constellation
5.3.2 64-QAM
In this modulation scheme there are 64 points on the constellation map. EachQAM is complex symbol carrying ve bits in each symbol. The phase dierenceis 22.5 as shown in the gure 5.7.
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Figure 5.7: 64-QAM constellation
There are four levels of amplitude. The signal need a higher SNR to ensure thatdata is correctly extracted from the signal [31].
5.4 Conclusion
The Bit error rate (BER) increases for same signal to noise ratio level as bitsper symbol mapping criteria increase. As the level of the signal increases, SNRneed to higher for ecient bit error transmission. This is due to smaller phasedierence and amplitude dierence when the number of points in the constel-lation map is increased. The number of points increases so does the bit rateincreases as a result the average power also increases.
5.5 OFDM Evolution
5.5.1 Single carrier modulation
Since last decade there has been increasingly demand for wireless communicationnetwork with high speed data rates, which means that the symbol width oftransmitted pulse has to decrease as it occupies more bandwidth. Now if symbolwidth of transmitted pulse is decreased, the channel which was a narrow bandchannel initially it will start behaving a wide band channel resulting in severeinter symbol interference (ISI). Thus there is a limitation as far as data rates isconcerned on single carrier modulation scheme demanding need for some otherecient scheme.
44
5.5.2 Need for multi carrier Modulation
The idea of multi carrier modulation is to divide bandwidth of single carrier intoseveral narrow bands so to increase the overall throughput of the communicationsystem. The date rate on each sub channel is much less the total data rateand corresponding sub channel bandwidth is less then coherence bandwidthof channel such that each sub channel experience at fading and frequencyselectivity of the wide band channel experienced by single carrier modulation iscompletely overcome by the use of multiple carriers for high data rates [32].
5.5.3 Basic structure of Multi carrier Transmission scheme
The basic structure of multicarrier carrier transmission scheme is depicted asfollows,
Figure 5.8: Multicarrier modulation scheme
This type of multi carrier transmission can be regarded as type frequency di-vision multiple access (FDMA). In FDMA transmission scheme no matter howintelligently transmitted pulses such as root raised cosine pulses are used, still itoccupies more bandwidth which results in inecient transmission system whichreduces the spectral eciency. More over by employing band pass lters andcrystal oscillators eectively results in costly system. So there has been alwaysroom for intelligent and smart way of multiplexing [32].
5.6 OFDM
OFDM stands for orthogonal frequency division multiplexing. It is the specictype of multicarrier modulation scheme. The basic idea of OFDM is same as todivide available spectrum into several sub channels by doing so each sub channelacts as narrow band channel experiencing at fading [33]. OFDM is based onDFT to generate orthogonal carriers, hence the name OFDM. In this way the
45
frequency response of sub channels are overlapped, eectively results in highspectral eciency of transmission system.
5.6.1 The principle of OFDM
A basic OFDM transmission system is described in gure 5.9. Input data is infrequency domain where sample is supplied in channel encoder that is mappedinto QPSK or QAM constellations. The symbol stream is passed through serialto parallel converter, whose output is a set of N parallel digital modulated sym-bols. These symbols are transformed into time domain by performing IFFT onN symbols and is usually be called as parallel to serial conversion. Now in timedomain signal cyclic prex is added. Cyclic prex is a copy of last part of OFDMsymbol which is appended to the transmitted symbol. After adding cyclic prexthe transmitted symbols are passed through channel. At the receiver cyclic pre-x is removed than data is converted in frequency domain taking FFT. Finallyeach symbol is decoded by corresponding digital demodulation scheme to getback the original transmitted input data.
Figure 5.9: A basic OFDM block diagram
The main idea of OFDM is to turn the channel convolution eect of the equation[35] as r(t) =
∫∞−∞ h(τ)x(t− τ)dτ into multiplicative one in order to simply the
equalization task in the receiver. To accomplish this task OFDM scheme addsredundancy called cyclic prex in a smart way in order to circularize the channeleect [32]. The length of cyclic prex has to be greater the length of delay spreadof the channel such that circular convolution employed by FFT frame becomeslinear convolution in that particular OFDM frame of interest as depicted ingure 5.10. Based on the fact that circular convolution can be diagonalized inFFT basis [35], the multiplepath time domain channel is transformed into set ofparallel frequency at channel, is the key principle of channel equalization [34].
46
Linear Convolution:r(t) = s(t) ∗ h(t) =
τ=∞∑τ−∞
s(τ)h(t− τ). (5.1)
Circular Convolution:r(t) = s(t)⊗ h(t) =
NDFT−1∑τ=0
s(τ)h(t− τ). (5.2)
CP>DS→ r(t) = r(t) for t ∈ [0, NDFT − 1]. (5.3)
Provided thath(t) = h(t) for t ∈ [0, NDFT − 1]. (5.4)
R(k) = H(k)S(k). (5.5)
Orthogonal matrix,
Reciever equalization: S(k) = R(k)/H(k), (5.6)R(k)
R(1)
R(2)...
R(N − 1)
=
H(0) 0 0 · · · 0
0 H(1) 0 · · · 0
0 0 H(2) 0 · · · 0...
......
. . ....
H(N − 1)
S(0)
S(1)
S(2)...
S(N − 1)
where R(k) is a recieved symbol vector, H(k) is channel matrix and S(k) isinput symbol vector.
47
Figure 5.10: Linear and Circular Convolution
OFDM is extremely simple and smart way of achieving orthonalization in thechannel.
5.7 Advantages of OFDM
1. OFDM is computationally ecient as it is FFT [35] based modulation anddemodulation technique.
2. OFDM is highly robust against multi path propagation in wireless channel.
3. Due to orthogonal property of OFDM it is easy design an ecient channelestimators and equalizers in receiver.
4. OFDM is more resistant to frequency selective fading than single carriersystems.
5. High band width ecient for large number of subcarriers.
6. Channel equalization is extremely simple.
7. OFDM provides good protection against co channel interference and im-pulsive parasitic noise.
8. Mitigates inter symbol interference (ISI) and inter carrier interference(ICI) through use of cyclic prex [34].
5.8 Disadvantages
1. Low band width eciency for small number of sub carriers.
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2. It is more sensitive to carrier frequency oset due to jitter of the carrierwave then to a single carrier system due to leakage of DFT and the Dopplereect caused by the relative motion of receiver or transmitter.
3. The OFDM signal suers high peak to average power ratios of transmittedsignal and high demand for linear ampliers [33].
4. Synchronization is extremely necessary when subcarriers are shared amongdierent transmitters.
5. As there might be spectral nulls in channels there is an intensive need foradaptive or coded scheme to recover the data of the subcarriers which wasaected by spectral nulls.
6. There has to be complete synchronization between the transmitter andreceiver as the receiver has to know when the OFDM symbol starts andends to correctly remove the cyclic prex [36].
5.9 OFDM Capacity
In OFDM the main cause of signal degradation is other cell interference andbackground noise due to smart way of one tap equalization by the addition ofcyclic prex. The signal to noise plus interference is given by following formula[37],
ρOFDM =P
fP +No, (5.7)
where P is power, f represents the ratio of other cells and own cell signal. There-for the Shannon Capacity formula (4.10) becomes,
C = log2(1 +P
fP +No), (5.8)
COFDM = log2(1 +ρ
ρf + 1), (5.9)
where,
ρ =P
Nois signal to Noise plus interference ratio. (5.10)
In OFDM, we need to take cyclic prex factor into an account. So OFDMcapacity (5.9) is scaled down by the factor, as given below
COFDM = (1− 4Ts
) log2(1 +ρ
ρf + 1), (5.11)
where 4 is a cyclic prex duration and Ts is the OFDM symbol duration.
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5.10 MIMO OFDM
Consider the MIMO OFDM system with N subcarriers used over MIMO fre-quency selective channel as shown in gure 5.11. The fading coecients arespatially uncorrelated over frequency and they remain constant in time. Inputdata is in frequency domain, it is digitally modulated using any modulationscheme for instance QPSK or 16-QAM. The data is fed into Alamoti time spaceencoder which creates the code words according to Alamouti coding scheme [38].The data is converted in time domain by taking IFFT of code words generatedby Alamouti encoder. Then the transmitter appends the cyclic prex. Afteradding cyclic prexes the Alamouti coded symbol are transmitted by the twoantennas in the rst instant. In second instant, other Alamouti coded symbolare transmitted. At the receiver cyclic prex are removed from OFDM Alamouticode symbols, then they are converted in frequency domain by taking FFT. Theoutput of FFT block is fed into Alamouti docorder which decouples the desiredsymbol form unwanted symbols according to Alamouti decoding [38]. Finallythe data is digitally demodulated to detect the correct symbol which was sentinitially to get the output symbol.
Figure 5.11: MIMO OFDM block diagram
5.11 Challenges in MIMO OFDM
MIMO OFDM oers simplicity in decoding, besides so many advantages it alsooers some challenges. MIMO OFDM symbol is typically long as compared tosingle carrier. So in practical system even there is small channel variation overOFDM symbol, the orthogonality of subcarriers is aected which may resultin inter symbol interference (ISI) which will result in degradation of systemperformance. Secondly there is a big problem of large peak to average powerratios (PAPR) in the transmitted signal due to addition of so many sinusoidalsignals with dierent frequencies. So non linear Ampliers are needed whichmay introduce signicant distortion into the transmitted signal [39].
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5.12 Summary
In this chapter we studied dierent modulation schemes that are mostly used inOFDM. We studied OFDM, a multiple access technique used in 3GPP LTE, fordown link transmission. We investigated its key principle of One tap frequencyequalization which results in orthogonality of channel. We highlighted its prosand corns in communication system. Then in the last section we studied MIMOimplementation of OFDM with reference to Alamouti's 2× 2 transmit diversityscheme.
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Chapter 6
Single Carrier- FDMA
6.1 Introduction
In communication systems, when it comes to uplink, it is more complex to designan ecient multiplexing and multiple access schemes because of many-mobiles-to-one base station nature of uplink transmission. Another important aspectto keep in mind is that as mobile system (UE) has limited transmission power,so low peak to average power ratio supported technique needs to be imple-mented on uplink [40]. Mobile systems (UE's) have limited power transmittingability compared to eNode B (eNB) and so they use a better technique withlow power requirements i.e. Single Carrier Frequency Division Multiple Access(SC-FDMA). It is a multiple access technique like TDMA, FDMA, CDMA, andOFDMA which assigns multiple user access to a shared communication resource.
6.2 Why SC-FDMA?
In current 3G systems, downlink and uplink both are implemented by WCDMA(Wideband Code Division Multiple Access) scheme using Walsh codes [40]. Indownlink (Node B to UE), since Node B transmits at the same time from axed location towards all of the UE's so the transmission by using these codesis orthogonal when they are received on the UE's, even when they are at dierentdistances from the Node B (which is a typical scenario), if multipath propagationis ignored. But in the presence of multipath propagation, which is the practicalscenario, these Walsh codes are no longer orthogonal and they cause inter symbolinterference (ISI). Now take the case of uplink (i.e. UE to Node B), situationhere is such that UE's are at dierent distances from Node B and each UEis transmitting independently at dierent times. So when these symbols arereceived on the Node B, they are not synchronised and there is no assuranceof orthogonality. So they cause ISI even when no multipath propagation isconsidered. And when there is multipath propagation in uplink, situation iseven worse [40]. The purpose of using SC-FDMA as multiple access schemes foruplink is to provide low PAPR as well as orthogonal transmission to get rid ofISI.
52
6.3 Single Carrier FDE
Before going into details of SC-FDMA, rst we shall discuss Single Carrier -Frequency Domain Equalization (SC-FDE). Consider the following two blockdiagrams:
Figure 6.1: Signle Carrier Frequency Domain Equalization
Figure 6.2: Orthogonal Frequency Division Multiple Acces
In gure 6.1, the time-domain input signal is transmitted on channel afteradding just cyclic prex to make it look like a periodic signal to get circularconvolution of the channel impulse response look like linear convolution andto prevent inter block interference(IBI) [43] [44]. On the receiving side, cyclicprex is removed and then signal is converted to frequency domain by DFT.Frequency domain makes it possible to perform an easy equalization comparedto time domain equalization, for multipath propagation. In other words, singlecarrier with frequency domain equalization is a way to tackle frequency selectivefading channel. After equalization, signal is converted to time domain by IDFToperation and then detection is performed accordingly.The performance of SC-FDE is same as for OFDM with the same overall com-plexity even for longer channel delay [41][42]. If we observe the two system blockdiagrams of SC-FDE and OFDM system, there are a lot of similarities: all ofcommunication component blocks are same; the only dierence is the locationof IDFT block. So the two systems are expected to have similar link level per-formance and spectral eciency. But there are some certain dierences betweenthe two systems. In the receiver, OFDM performs data detection in frequencydomain on per subcarrier basis, but SC-FDE performs detection in time domainafter performing an additional operation IDFT. This dierence makes OFDMmore sensitive to a null in the channel spectrum to require channel coding as amust. Also, the complexity of the transmitter is reduced in SC-FDE [44].Single Carrier FDMA is an extension of SC-FDE, which is discussed in nextsection.
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6.4 Single Carrier - FDMA
Single carrier FDMA is a technique that has the same performance and com-plexity as those of OFDMA system. It utilizes single carrier modulation andfrequency domain equalization to accommodate multiple user access [45].
Figure 6.3: Single Carrier Frequency Division Multiple Acces
Figure 6.3 shows the block diagram of the SC-FDMA technique. Informa-tion signal is digitally modulated with dierent modulation schemes like BPSK,QPSK, 16-QAM, 64-QAM. The modulated symbols xn are then grouped intoblocks of M symbols. The rst step in modulating the SC-FDMA subcarrieris to perform an M point DFT to take the signal in frequency domain Xk ofthe input signal. Then it maps each of the M-DFT outputs Xk to one of theN orthogonal subcarriers that can be transmitted. N is kept greater than Mwith a relation between them is N = Q×M , where Q is bandwidth expansionfactor of the symbol sequence. If all the terminals transmit M symbols perblock, Q is the total number of simultaneous transmissions that are received atthe base station without co-channel interference [45]. Details of subcarrier map-ping are given in the next section where we study dierent types of subcarriermapping and their characteristics. After subcarrier mapping we get signal Xl
(where l = 0, 1, 2..., N − 1), which are the complex amplitudes of subcarriers Mnumber of which are non zero. Now IDFT modulates complex amplitudes Xl
and transforms into time domain signal xl. A cyclic prex is added then to getSC-FDMA symbol. In cyclic prex a last part of the block is appended in thebeginning of the block for following two reasons:
1. CP behaves as a guard interval between consecutive blocks. The length ofCP is kept larger than maximum delay spread of the channel or at leastequal to it to avoid Inter Block Interference (IBI).
54
2. CP converts discrete time linear convolution to discrete time circular con-volution, due to which the transmission of signal through channel can beconsidered as a circular convolution between the signal and the channel.For frequency domain, it means that there is a point wise multiplicationof the DFT frequency samples. Equalization becomes simplied by per-forming a point wise division operation in frequency domain. Also, otherequalization techniques can be implemented more easily.
After adding cyclic prex, SC-FDMA symbol is ready to be transmitted withpulse shaping and up-conversion. Comparing with OFDMA, since there is onlydierence of a DFT in transmitter and an IDFT in receiver, SC-FDMA is some-times referred to as DFT spread OFDMA [45].
6.5 Subcarrier Mapping
DFT output of the data symbols is mapped to a subset of subcarriers. Thesubcarrier mapping assigns DFT output complex values as the amplitudes ofsome of the selected subcarriers. Subcarrier mapping can be classied into twotypes:
1. Localized Mapping (LFDMA)
2. Distributed Mapping (DFDMA)
Figure 6.4 show both types of mapping techniques. In localized mapping, theDFT amplitudes are assigned to a subset of consecutive subcarriers of IDFTblock, thereby conning them to only a fraction of the system bandwidth. Indistributed mapping, the DFT outputs of the input data are assigned to sub-carriers over the entire bandwidth non-continuously, resulting in zero amplitudefor the remaining subcarriers. A special case of distributed SC-FDMA, wherethe occupied subcarriers are equally spaced over the entire bandwidth, is calledinterleaved SC-FDMA (IFDMA).
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Figure 6.4: IFDMA AND LFDMA
Figure 6.5 shows an example of LFDMA and DFDMA with M = 4, N = 8 andQ = 2.
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Figure 6.5: Example Mapping
The mathematical description of time domain LFDMA and IFDMA symbols isas follows [45] [40]:
6.5.1 LFDMA
Frequency samples after subcarrier mapping Xl can be described as:
Xl =
Xl, 0 ≤ l ≤M − 10, M ≤ l ≤ N − 1
(6.1)
where 0 ≤ l ≤ N − 1 and N = QM .
Let n = Qm+ q, where 0 ≤ n ≤ N − 1 and 0 ≤ q ≤ Q− 1. Then,
xl =1
N
N−1∑l=0
(Xl exp(j2πln)N ) =
1
QM
M−1∑l=0
(Xl exp(j2πl(Qm+q))
QM ), (6.2)
57
If q = 0, then
xl =1
Q
1
M
M−1∑l=0
Xl expj2πlmM , (6.3)
xl =1
Qxm, (6.4)
which shows that the resulting time domain symbols of N-IDFT xl are just arepetition of the input symbols with a scaling factor of 1
Q . For q 6= 0, the timedomain sample at the output of N-IDFT is the sum of time domain samples atthe input of size M-DFT with dierent complex weighting.
6.5.2 IFDMA
Frequency samples after subcarrier mapping Xl can be described as:
Xl =
Xl/Q, l = Qk, 0 ≤M − 1
0, otherwise(6.5)
where 0 ≤ l ≤ N − 1 and N = QM . Let n = M.q + m, where 0 ≤ q ≤ Q − 1and 0 ≤ m ≤M − 1. Then,
xl =1
N
N−1∑l=0
(Xl exp(j2πln/N)) =1
QM
M−1∑k=0
(Xk exp(j2πkn/M)), (6.6)
xl =1
Q
1
M
M−1∑k=0
(Xk exp(j2πk(Mq+m)/M)) =1
Q(
1
M
M−1∑k=0
(Xk exp(j2πkm/M))),
(6.7)
xl =1
Qxm, (6.8)
which shows that the resulting time domain symbols of N-IDFT xl are just arepetition of the input symbols with a scaling factor of 1
Q .
6.6 SC-FDMA and OFDMA (PAPR Compari-son)
Peak to average power ratio is dened as the ratio of peak signal power and av-erage signal power. Although the performance and complexity of OFDMA andSC-FDMA are similar, SCFDMA has a major advantage of having low PAPRcompared to that of OFDMA. Low PAPR is quite valuable for user terminalsso does SC-FDMA as an access scheme for uplink.It can be formulated as:
PAPR =|s(t)|2
E[|s(t)|2]. (6.9)
58
In general, a low PAPR is required for improved power amplier eciency andmaximum power eciency is achieved when the amplier operates at the satu-ration point. With high PAPR, the power amplier operating point has to bebacked o to lower the signal distortion, thus lowering the amplier eciency.Since SC-FDMA modulated signal can be viewed as a single carrier signal, apulse shaping lter can be applied to transmit signal to further improve PAPR.In OFDM, a large number of tones are used to transmit to single or dierentUE's (downlink). High PAPR is resulted from the superposition of parallel tones(sub channels) transmission[40]. Figure 6.6 illustrates this scenario of simple sinewave, where 4 OFDM tones at frequencies f, 2f, 3f and 4f are shown separatelyand their superposition is also shown in gure 6.7. Left plot is simple additionof four tones modulated by +1 and in right plot f1 and f3 are modulated by +1but 2f and 4f are modulated with -1.
Figure 6.6: Superposition a
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Figure 6.7: Superposition b
We can observe that average is quite smaller than the peak level. When tonesare increased to 64, 256 and so on (a practical scenario), this dierence is evenworse, reasoning for high PAPR. It is observed that PAPR in the case of IFDMAis lower than that of LFDMA [46]. The reason for this is that, in case of IFDMAwith "u" users the SC-FDMA symbols which are coming out of the IFFT moduleare simply u repetitions of shorter versions of the original SC-FDMA symbols.It means the output is again a classical single carrier signal with a low PAPR[47].
6.7 MIMO SC-FDMA
Although when SC-FDMA was introduced for uplink communication in LTEinitially because of its low PAPR compared to OFDMA, it was SISO (singleinput single output) implementation, but then SIMO (single input multipleoutput) and MIMO (multiple input multiple output) implementation with SC-FDMA are introduced to get the spatial diversity gain and spatial multiplexinggain [48]. In this section we shall describe the MIMO implementation of SC-FDMA. Spatial Diversity gives reliability of communication in fading channelsby having number of copies of the transmitted signal go through fading pathsindependently. Alamouti transmit diversity scheme [49], Smart antenna tech-niques [50] and space-time coding [51] are some of well known spatial diversitytechniques. Spatial Multiplexing increases the capacity of data by sending mul-tiple streams in parallel through multiple spatial channels BLAST (Bell LabsSpace-time Architecture) is a typical spatial multiplexing technique [52]. Weshall use Alamouti Scheme in our work. Alamouti scheme has been describedin detail in chapter 4. Consider the following block diagram of 2× 2 Alamoutiimplementation of SC-FDMA Symbols.
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Figure 6.8: Block Diagram of MIMO SC-FDMA WITH ALAMOUTI
Input data, after digital modulation, is converted to frequency domain by M-DFT. Then Alamouti scheme is applied to get two parallel data signals. Alam-outi codes are generated in frequency domain. Subcarrier mapping is performedon these code words independently. After that, N point IDFT, where N > M,is taken to convert the signal in time domain. Adding cyclic prex in the nalstep to get SC-FDMA symbol, after which signal is transmitted in air. It isassumed that channel information does not change for two symbol durations.Also, transmitter does not know the channel information according to Alamouti.The Code word matrix is made in frequency domain like this:
C=
[Xik −X(i+1)∗
k
X(i+1)k Xi∗
k
],
where Xik and Xi+1
k are two consecutive outputs of M-DFT. These X ′k aremapped onto subcarriers with one of the subcarrier mapping schemes and thenafter the operation of N-IDFT and cyclic prex addition xk are sent throughRayleigh fading channel. The output y can be written as:
y = h ∗ c+ n, (6.10)
where,
y=
[y11 y12
y21 y22
], h=
[h11 h12
h21 h22
], c=
[xlk −x(l+1)∗
k
x(l+1)k xl∗k
],
yij : output at each antenna at instant 1 and 2,hij : time domain channel,cij :SC-FDMA symbol after CP addition.
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On the receiver side, after CP removal, N-DFT and sub-carrier de-mapping, weget "y" on which Alamouti decoding scheme is implemented. Point to be notedthat at transmitter Alamouti scheme was implemented in frequency domain andat receiver, the decoding is also performed in frequency domain. This is becauseSC-FDMA inherits OFDM, which converts a frequency selective channel intofrequency at channel making it possible to perform simple one tap equalization.Alamoutis decoding is given as:
X lk = H∗k11Yk11 +Hk12Y
∗k12 +H∗k21Yk21 +Hk22Y
∗k22 , (6.11)
X l+1k = H∗k12Yk11 −Hk11Y
∗k12 +H∗k22Yk21 −Hk21Y
∗k22 . (6.12)
Finally, the estimated symbols Xks are converted to time-domain by M-IDFT,converted to serial data, to perform detection process.
6.8 Summary
In this chapter we studied single carrier FDMA, another multiple access tech-nique used in 3GPP LTE, for uplink transmission. The reason for choosing SC-FDMA over OFDMA for uplink is its low PAPR even the complexity, robustnessand performance are same for both. We studied dierent ways of sub-carriermapping i.e, LFDMA, DFDMA and IFDMA which is a special case of DFDMA.Then in the last section we studied MIMO implementation of SC-FDMA withreference to Alamouti's 2× 2 transmit diversity scheme.
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Chapter 7
Simulation and Results
7.1 Introduction
In this chapter we shall present the results of the simulations performed onMATLAB. First, MIMO, OFDM and SC-FDMA are investigated independently.Then a combination of MIMO-OFDM and MIMO-SCFDMA will be investi-gated. We shall check percentage error and capacity comparison by using dier-ent digital modulation schemes like: BPSK, QPSK, 16PSK, 4QAM and 8QAM,in the presence of AWGN and Rayleigh Noise. Channel environment is takenas Rayleigh Fading. In our thesis, we have always taken Alamouti 2× 2 MIMOscheme.We shall investigate following cases:1. MIMO.2. OFDM - SISO.3. OFDM - MIMO Single Tap Channel.4. OFDM - MIMO Multi Tap Channel.5. SC-FDMA - SISO.6. SC-FDMA - MIMO Single Tap Channel.We start perform simulations according to list mentioned above: from Alamouti2× 2 scheme.
7.2 MIMO Model
In this section, we consider Alamouti's 2 × 2 MIMO systems to see simulationbetween Signal to Noise Ratio (SNR) and Symbol Error Rate (SER) for QPSKand 16PSK modulation. Then we compare the results with Shannon CapacityLimit for 2× 2 MIMO systems.
7.2.1 Results
gure 7.1 and gure 7.2 show that capacity can be increased with higher SNRfor error free transmission. Shannon Capacity for multi antennas are given inchapter 5 is:
C = log2 |I +1
σ2HHH | (7.1)
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Figure 7.1: SER vs SNR with Alamouti 2x2 Scheme
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Figure 7.2: Shannon Capacity for 2x2 MIMO System
7.3 OFDM Model
In this section, we investigate symbol error and capacity performance of anOFDM system for SISO and MIMO Systems.
Results
1. Simulation results for following Specications are plotted in gure 7.3 andgure 7.4:
Parameter RequirementAntenna System SISOConstellation QPSK, 16PSK, 4QAMFFT Size 64Cyclic Prex Size 15 % of FFT SizeDelay Spread CP Size-1Channel Model Rayleigh Fading Multi taps (9 taps)Noise Model AWGN
65
Figure 7.3: SER vs SNR for SISO-OFDM
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Figure 7.4: Shannon Capacity for OFDM
Capacity formula used here is:
(1− ∆
Ts) log2(1 + SNR), (7.2)
where ∆ = CP Size and Ts=OFDM symbol duration.
C = log2(1 + SNR). (7.3)
One can see dierent capacity comparisons between dierent modulation schemes.2. Simulation results for following Specications are plotted in gure 7.5 andgure 7.6:
Parameter RequirementAntenna System MIMO AlamoutiConstellation QPSK, 16PSK, 4QAMFFT Size 64Cyclic Prex Size 15 % of FFT SizeDelay Spread CP Size-1Channel Model Rayleigh Fading Single tapNoise Model Rayleigh Noise
67
Figure 7.5: SER vs SNR for MIMO-OFDM (Single tap channel)
68
Figure 7.6: Shannon Capacity for MIMO-OFDM
(1− ∆
Ts) log2 |I +
1
σ2HHH |. (7.4)
Capacity in gure 7.6 is calculated using equation (7.1) mentioned above.3. Simulation results for following Specications are plotted in gure 7.7:
Parameter RequirementAntenna System MIMO AlamoutiConstellation QPSK, 16PSK, 4QAMFFT Size 64Cyclic Prex Size 15 % of FFT SizeDelay Spread CP Size-1Channel Model Rayleigh Fading Multi tapsNoise Model Rayleigh Noise
69
Figure 7.7: MIMO-OFDM (Alamout i2x2)
7.4 SC-FDMA Model
In this section, we investigate symbol error rate and capacity performance ofan SC-FDMA system for SISO and MIMO Systems. Recommended subcarriermapping for 3GPP LTE is Localized SC-FDMA, so is used in simulations.
Results:
1. Simulation results for following Specications are plotted in gure 7.8 andgure 7.9:
Parameter RequirementAntenna System SISOConstellation QPSK, 16PSK, 4QAMFFT Size 64Cyclic Prex Size 15 % of FFT SizeDelay Spread CP Size-1Channel Model Rayleigh Fading Multi taps (9 taps)Noise Model AWGNSub-carrier mapping Localized FDMA (LFDMA)Bandwidth Spread(Q) 4
70
Figure 7.8: SER vs SNR for SISO SC-FDMA
71
Figure 7.9: Shannon Capacity for SC-FDMA
(1− ∆
Ts) log2(I + SNR). (7.5)
2. Simulation results for following Specications are plotted in gure 7.10 andgure 7.11:
Parameter RequirementAntenna System MIMO AlamoutiConstellation QPSK, 16PSK, 4QAMFFT Size 64Cyclic Prex Size 15 % of FFT SizeDelay Spread CP Size-1Channel Model Rayleigh Fading Single TapNoise Model Rayleigh NoiseSub-carrier mapping Localized MappingBandwidth Spread(Q) 4
72
Figure 7.10: SER vs SNR for MIMO-SCFDMA
73
Figure 7.11: Shannon Capacity for MIMO-SCFDMA
(1− ∆
Ts) log2 |I +
1
σ2HHH |. (7.6)
7.5 PAPR Comparison between OFDM and SC-FDMA
Finally, we compare the PAPR for OFDM and SC-FDMA system. We haveconsidered Localized SC-FDMA as subcarrier mapping. Figure 7.12 shows CDF(commulative distribution function) plots for OFDM and SC-FDMA, whichclearly tells that PAPR for SC-FDMA is less than that of OFDM.Mathematically,
PAPR =|s(t)|2
E[|s(t)|2]. (7.7)
74
Figure 7.12: CDF plots of PAPR for OFDM and SC-FDMA
75
Chapter 8
Summary
In this thesis we studied smart antenna properties of beamforming and direc-tion of arrival to optimize the spectral power distribution. Then we studiedthe multi antenna techniques MIMO as a spatial diversity technique. SVD andAlamouti coding techniques were analysed separately. We studied OFDM andSC-FDMA as multiple access techniques for downlink and uplink transmission,respectively. OFDM and SC-FDMA are closely related to each other with somedierences like DFT spread and subcarrier mapping in SC-FDMA and highPAPR for OFDM system.Capacity for SISO, MIMO, OFDM and SC-FDMA were studied and simu-lated independently and then as a combination of MIMO-OFDM and MIMO-SCFDMA on MATLAB. We investigated symbol error rate (SER) for all above,and observed the trade-o between better capacities and higher transmit power,in our simulations. We evaluated peak power performance (PAPR comparison)between OFDM and SC-FDMA system.These techniques (MIMO-OFDM, MIMO-SCFDMA) are the candidates for3GPP Long Term Evolution (LTE) standard. We took an overview on LTEstandard as well.
76
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