Design of Spreading Permutations Based on Stbc

7/29/2019 Design of Spreading Permutations Based on Stbc

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1.1 Introduction

Code Division Multiple Access (CDMA) and multiple input multiple output- (MIMO)

CDMA systems suffer from multiple access interference (MAI) which limits the spectral

efficiency of these systems. By making these systems more power efficient, we can increase the

overall spectral efficiency. This can be achieved through the use of improved modulation and

coding techniques. Conventional MIMO-CDMA systems use fixed spreading code assignments.

By strategically selecting the spreading codes as a function of the data to be transmitted, we can

achieve coding gain and introduce additional degrees of freedom in the decision variables at the

output of the matched filters. In this paper, we examine the bit error rate performance of parity

bit-selected spreading and permutation spreading under different wireless channel conditions. A

suboptimal detection technique based on maximum likelihood detection is proposed for these

systems operating in frequency selective channels. Simulation results demonstrate that these

code assignment techniques provide an improvement in performance in terms of bit error rate

(BER) while providing increased spectral efficiency compared to the conventional system.

Moreover, the proposed strategies are more robust to channel estimation errors as well as spatial

correlation.

In wireless communication system, Multiple Input Multiple Output (MIMO) refers to links

for which the transmitting as well as the receiving end is equipped with multiple antenna

elements. The transmit antennas on one end and the receive antenna on the other end are jointly

combined in such a way that can the quality (bit error rate) or the rate (Bit/sec) of the

communication is improved. This project is important because a new technique can be produced

which is MIMO-CDMA system that can improve the performance of wireless links.

This project analyzes the performance of MIMO-CDMA with comparison to conventional

Code Division Multiple Access (CDMA) system.MIMO refers to wireless link with multiple

antennas at the transmitter and receiver side. Given multiple antennas, the spatial dimension can

be exploited to improve the performance of the wireless link. The performance is often measured

as the average bit rate (bit/s) the wireless link can provide or the average bit error rate (BER).

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1.2 Problem Statement

Today, communication system requires high capacity and faster data transmission with

minimum error and losses. The capacity will become congested in future. Therefore, the system

needs new technique so that can accommodate this insufficiency.MIMO is one of the techniques

that can provide promising approaches.

1.3Objective of Project

The objective of the project is to develop the simulation model for conventional CDMA and

MIMO-CDMA by using MATLAB 7.1 software with Simulink and Communications Block set.

Besides that, the project also analyzes the performance of conventional Code Division Multiple

Access (CDMA) system and MIMO-CDMA system. Finally, this project compares the

performance of MIMO-CDMA system with conventional CDMA system.

1.4 Scope of Work

The scope of this project are to analyze the performance of conventional CDMA and

MIMO-CDMA system measured in average bit error rate (BER) and capacity. The simulation

models are simulated with different number of antennas which are two transmit-two

receive(2Tx2Rx) and four transmit-four receive(4Tx4Rx).The simulation model will be done by

using MATLAB software. The comparision between conventional CDMA system and MIMO-

CDMA are done.

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2.1 Introduction

Code division Multiple Access, a digital cellular technology that uses spread-spectrum

techniques. Unlike competing systems, such as GSM, that use TDMA, CDMA does not assign aspecific frequency to each user. Instead, every channel uses the full available spectrum.

Individual conversations are encoded with a pseudo-random digital sequence. CDMA

consistently provides better capacity for voice and data communications than other commercial

mobile technologies, allowing more subscribers to connect at any given time, and it is the

common platform on which 3G technologies are built.

CDMA is a military technology first used during World War II by English allies to foil

German attempts at jamming transmissions. The allies decided to transmit over several

frequencies, instead of one, making it difficult for the Germans to pick up the complete signal.

Because Qualcomm created communications chips for CDMA technology, it was privy to the

classified information. Once the information became public, Qualcomm claimed patents on the

technology and became the first to commercialize it.

For radio systems there are two resources, frequency and time. Division by frequency, so

that each pair of communicators is allocated part of the spectrum for all of the time, results in

Frequency Division Multiple Access (FDMA). Division by time, so that each pair of

communicators is allocated all (or at least a large part) of the spectrum for part of the time results

in Time Division Multiple Access (TDMA). In Code Division Multiple Access (CDMA), every

communicator will be allocated the entire spectrum all of the time. CDMA uses codes to identify

connections.

2.1.1 Coding

CDMA uses unique spreading codes to spread the baseband data before transmission.

The signal is transmitted in a channel, which is below noise level. The receiver then uses a

correlator to dispread the wanted signal, which is passed through a narrow bandpass filter.

Unwanted signals will not be dispread and will not pass through the filter. Codes take the form of

a carefully designed one/zero sequence produced at a much higher rate than that of the baseband

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data. The rate of a spreading code is referred to as chip rate rather than bit rate.

See coding process page for more details.

Figure 2.1 Multiple Access Schemes

Multiple access schemes are used to allow many mobile users to share simultaneously a common

bandwidth. There are three main types of multiple access system, each of which has its own way

of sharing the bandwidth such as Frequency Division Multiple Access(FDMA),Time Division

Multiple Access (TDMA) and Code Division Multiple Access(CDMA).FDMA and TDMA are

narrowband technologies while CDMA is wideband.

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2.1.2 Codes

CDMA codes are not required to provide call security, but create a uniqueness to enable

call identification. Codes should not correlate to other codes or time shifted version of itself.

Spreading codes are noise like pseudo-random codes, channel codes are designed for maximum

separation from each other and cell identification codes are balanced not to correlate to other

codes of itself.

Figure 2.2 CDMA spreading

With CDMA, unique digital codes, rather than separate RF frequencies or channels, are

used to differentiate subscribers. The codes are shared by both the mobile station (cellular phone)

and the base station, and are called pseudo Random Code Sequences. All users share the same

range of radio spectrum. For cellular telephony, CDMA is a digital multiple access technique

specified by the Telecommunications Industry Association (TIA) as IS-95.

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Figure 2.3 Example OVSF codes, used in channel coding

2.2 The Spreading Process

WCDMA uses Direct Sequence spreading, where spreading process is done by directly

combining the baseband information to high chip rate binary code. The Spreading Factor is the

ratio of the chips (UMTS = 3.84Mchips/s) to baseband information rate. Spreading factors vary

from 4 to 512 in FDD UMTS. Spreading process gain can in expressed in dBs (Spreading factor

128 = 21dB gain).

Figure 2.4 CDMA spreading

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2.2.1 Power Control

CDMA is interference limited multiple access system. Because all users transmit on the

same frequency, internal interference generated by the system is the most significant factor in

determining system capacity and call quality. The transmit power for each user must be reduced

to limit interference, however, the power should be enough to maintain the required Eb/No

(signal to noise ratio) for a satisfactory call quality. Maximum capacity is achieved when Eb/No

of every user is at the minimum level needed for the acceptable channel performance. As the MS

moves around, the RF environment continuously changes due to fast and slow fading, external

interference, shadowing, and other factors. The aim of the dynamic power control is to limit

transmitted power on both the links while maintaining link quality under all conditions.

Additional advantages are longer mobile battery life and longer life span of BTS power

amplifiers.

2.2.2 Handover

Handover occurs when a call has to be passed from one cell to another as the user moves

between cells. In a traditional "hard" handover, the connection to the current cell is broken, and

then the connection to the new cell is made. This is known as a "break-before-make" handover.Since all cells in CDMA use the same frequency, it is possible to make the connection to the new

cell before leaving the current cell. This is known as a "make-before-break" or "soft" handover.

Soft handovers require less power, which reduces interference and increases capacity. Mobile

can be connected to more that two BTS the handover. "Softer" handover is a special case of soft

handover where the radio links that are added and removed belong to the same Node B.

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Figure 2.5 CDMA soft handover

2.3 Multipath and Rake Receivers

One of the main advantages of CDMA systems is the capability of using signals that

arrive in the receivers with different time delays. This phenomenon is called multipath. FDMA

and TDMA, which are narrow band systems, cannot discriminate between the multipath arrivals,

and resort to equalization to mitigate the negative effects of multipath. Due to its wide bandwidth

and rake receivers, CDMA uses the multipath signals and combines them to make an even

stronger signal at the receivers. CDMA subscriber units use rake receivers. This is essentially a

set of several receivers. One of the receivers (fingers) constantly searches for different multipaths

and feeds the information to the other three fingers. Each finger then demodulates the signal

corresponding to a strong multipath. The results are then combined together to make the signal

stronger.

The receiver performs the following steps to extract the Information:

Demodulation

Code acquisition and lock

Correlation of code with signal Decoding of Information data

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2.3.1 Multiple-Input/Multiple-Output (MIMO)

Multiple Input, Multiple Output (MIMO) technology is a wireless technology that uses

multiple transmitters and receivers to transfer more data at the same time (Figure 2.3.1). MIMOtechnology takes advantage of a radio-wave phenomenon called multipath where transmitted

information bounces off walls, ceilings, and other objects, reaching the receiving antenna

multiple times via different angles and at slightly different times.

Figure 2.6 MIMO Technology Uses Multiple Radios to Transfer More Data at the Same Time

MIMO technology leverages multipath behavior by using multiple, smart transmitters

and receivers with an added spatial dimension to dramatically increase performance and range.

MIMO allows multiple antennas to send and receive multiple spatial streams at the same time.

This allows antennas to transmit and receive simultaneously.

MIMO makes antennas work smarter by enabling them to combine data streams arriving

from different paths and at different times to effectively increase receiver signal-capturing

power. Smart antennas use spatial diversity technology, which puts surplus antennas to good use.

If there are more antennas than spatial streams, as in a 2x3 (two transmitting, three

receiving) antenna configuration, then the third antenna can add receiver diversity and increase

range.

In order to implement MIMO, either the station (mobile device) or the access point (AP)

need to support MIMO. Optimal performance and range can only be obtained when both the

station and the AP support MIMO.

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Legacy wireless devices cant take advantage of multipath because they use a Single

Input, Single Output (SISO) technology. Systems that use SISO can only send or receive a single

spatial stream at one time.

MIMO (multiple input, multiple output) is an antenna technology for wireless

communications in which multiple antennas are used at both the source (transmitter) and the

destination (receiver). The antennas at each end of the communications circuit are combined to

minimize errors and optimize data speed. MIMO is one of several forms of smart antenna

technology, the others being MISO (multiple input, single output) and SIMO.

In conventional wireless communications, a single antenna is used at the source, and

another single antenna is used at the destination. In some cases, this gives rise to problems with

multipath effects. When an electromagnetic field (EM field) is met with obstructions such as

hills, canyons, buildings, and utility wires, the wavefronts are scattered, and thus they take many

paths to reach the destination. The late arrival of scattered portions of the signal causes problems

such as fading, cut-out (cliff effect), and intermittent reception (picket fencing). In digital

communications systems such as wireless Internet, it can cause a reduction in data speed and an

increase in the number of errors. The use of two or more antennas, along with the transmission of

multiple signals (one for each antenna) at the source and the destination, eliminates the trouble

caused by multipath wave propagation, and can even take advantage of this effect.

MIMO technology has aroused interest because of its possible applications in digital

television (DTV), wireless local area networks (WLANs), metropolitan area networks (MANs),

and mobile communications.

2.3.2 Forms of MIMO

Multi-antenna MIMO (or Single user MIMO) technology has been mainly developed and is

implemented in some standards, e.g. 802.11n products.

SISO/SIMO/MISO are degenerate cases of MIMO

o Multiple-input and single-output (MISO) is a degenerate case when the receiver

has a single antenna.

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o Single-input and multiple-output (SIMO) is a degenerate case when the

transmitter has a single antenna.

o Single input single output(SISO) is a radio system where neither the transmitter

nor receiver have multiple antenna.

Principal single-user MIMO techniques

o Bell laboratories layered space time(BLLST) Gerard. J. Foschini (1996)

o Per Antenna Rate Control (PARC), Varanasi, Guess (1998), Chung, Huang,

Lozano (2001)

o Selective Per Antenna Rate Control (SPARC), Ericsson (2004)

Some limitations

o The physical antenna spacing are selected to be large; multiple wavelengths at the

base station. The antenna separation at the receiver is heavily space constrained in

hand sets, though advanced antenna design and algorithm techniques are under

discussion.

2.4 Functions of MIMO

Precoding is multi-stream beam forming, in the narrowest definition. In more general

terms, it is considered to be all spatial processing that occurs at the transmitter. In (single-layer)

beam forming, the same signal is emitted from each of the transmit antennas with appropriate

phase (and sometimes gain) weighting such that the signal power is maximized at the receiver

input. The benefits of beam forming are to increase the received signal gain, by making signals

emitted from different antennas add up constructively, and to reduce the multipath fading effect.

In the absence of scattering, beam forming results in a well defined directional pattern, but in

typical cellular conventional beams are not a good analogy. When the receiver has multipleantennas, the transmit beam forming cannot simultaneously maximize the signal level at all of

the receive antennas, and precoding with multiple streams is used. Note that precoding requires

knowledge of channel state information (CSI) at the transmitter.

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Spatial multiplexing requires MIMO antenna configuration. In spatial multiplexing, a

high rate signal is split into multiple lower rate streams and each stream is transmitted from a

different transmit antenna in the same frequency channel. If these signals arrive at the receiver

antenna array with sufficiently different spatial signatures, the receiver can separate these

streams into (almost) parallel channels. Spatial multiplexing is a very powerful technique for

increasing channel capacity at higher signal-to-noise ratios (SNR). The maximum number of

spatial streams is limited by the lesser in the number of antennas at the transmitter or receiver.

Spatial multiplexing can be used with or without transmit channel knowledge. Spatial

multiplexing can also be used for simultaneous transmission to multiple receivers, known as

space-division multiple access. By scheduling receivers with different spatial signatures, good

separability can be assured.

Diversity Coding techniques are used when there is no channel knowledge at the

transmitter. In diversity methods, a single stream (unlike multiple streams in spatial

multiplexing) is transmitted, but the signal is coded using techniques called space-time coding.

The signal is emitted from each of the transmit antennas with full or near orthogonal coding.

Diversity coding exploits the independent fading in the multiple antenna links to enhance signal

diversity. Because there is no channel knowledge, there is no beam forming or array gain from

diversity coding.

Spatial multiplexing can also be combined with precoding when the channel is known at

the transmitter or combined with diversity coding when decoding reliability is in trade-off.

2.5 MIMO-CDMA

Consider theKuser MIMO-CDMA uplink system model, employing Binary Phase Shift

Keying (BPSK) modulation. The data of each user is spatially multiplexed into Nttransmitting

antennas. The substream to be transmitted on antenna iof user kon time interval nis spread by a

spreading code vector wki(n). The spreading code vector is of dimension Nc x 1:

( ) [ ]TNnik

nik

nik

nik

w )0

()(

,),......2(

)(,

),1()(

,, =

(2.1)

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where Ncis the spreading factor and the subscript Trepresents the transpose operator.Nc = Ts/ Tc

is an integer number where Tsis the symbol period and Tcis the chip period. The spreading code

vector is selected from a set ofNspreading vectors

kC

Nkc

kc

kc

,,.........

2,,

,,1, (2.2)

The wireless media is considered to be a slowly-varying discrete-time baseband channel

model with chip-spaced channel taps. Thus, assuming the same channel order L for all single

input single output (SISO) channels, the sampled channel response from the transmit antenna i to

the receive antenna j of user kis given by theL1 vector:

( ) ( ) ( )[ ]TLkij

hkij

hkij

hkij

h1,,

,.......1

,,,

0,,,,

=(2.3)

To keep the model simple, we assume that the maximum channel delay is smaller than

the signaling interval. In case of frequency selective channels, MIMO-CDMA systems suffer

from intersymbol interference (ISI) and multiple access interference (MAI). Since, we are

interested in single user detection; the received signal at antenna jcan be written as:

( ) ( ) ( ) ( )= +=tN

injnnikbkijhnikSnjr 1 ,,,, (2.4)

bk,i(n) is the transmitted data by antenna i of user k at instant nj

(n) encompasses the complex

Gaussian noise with variance 2 , the ISI and MAI,for the conventional, the parity bit selected

spreading and permutation spreading MIMO-CDMA systems will rely on correlators matched to

the differentNspreading codes used by the transmitter.

In conventional MIMO-CDMA, each user can use the same spreading code for all

transmitting antennas or a different spreading code for each transmitting antenna. In our case, we

use the latter. Hence, wk,i(n) =ck,i. For each transmit antenna, we apply a correlator matched to the

signature used by the transmitting antenna. The output of the correlator matched to the transmit

antenna iof user kusing the received signal at receiving antenna jis anL1 vector:

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( ) ( )( ) ( )njrHn

ikS

nkij

y,,,

=(2.5)

The subscriptHrepresents the conjugate transpose of a matrix. The receiver than estimates bi,k(n)

from the decision variable of the previous equation as follows:

( ) ( ) ( )

=

= nkij

y

HrN

j kijh

nki

b,,1 ,,

sgn,

(2.6)

2.5.1 Parity Bit-Selected Spreading System

In parity bit selected spreading, the data on different antennas is spread by a single

spreading waveform that is selected based on the parity bits that are generated when a message is

encoded using a systematic linear block code . For each user with Nttransmit antennas, the set Mof all possible message vectors has 2Ntdifferent elements. The different messages that produce

the all zero parity vector form subset of M that is closed under modulo-2 addition. We denote

this subset as M1. If we select an element e M such that e M1 and add modulo-2 to all

elements in M1, the resulting set is called a coset of M1. Messages from distinct cosets of M1

produce unique parity bit vectors when being input to the parity bit calculator. In parity bit-

selected spreading, each of the cosets is assigned one of the Nspreading codes. For example, if

userkhas 4 transmitting antennas, the set Mhas 16 elements. If each user is assigned N = 8

spreading codes, then we can partition M into 8 cosets as follows:M1 = {0000, 1111}, M2 =

{0001, 1110}, . . ., and M8 = {0111, 1000}. Each of these cosets is assigned one of the N

spreading waveforms; therefore if the word to be transmitted is m(m) Mm, then all transmitting

antennas will use the spreading code assigned to coset Mm. The same spreading code is used on

each transmit antenna. Hence mkcn

tNkw

nk

w,

)(,

.......)(1,

=== .

In this paper, we consider a MIMO-CDMA system employing Nt = 4 transmit antennas.

In each case, we choose N = 2Nt1; therefore all cosets are made up of 2 message vectors. Thisis not necessarily the optimum choice for N.

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For each mkcn

tNkw

nk

w,

)(,

.......)(1,

=== we construct),(

,

mn

ikS . Since all transmit antennas from

the same user use the same code at instant n, all),(

,

mn

ikS are the same. In this case, we can use

),(),(

,...............

),(

1,

mn

kS

mn

tNk

Smn

kS === (2.7)

We will then be able to compute the corresponding correlator outputs:

)(),(),(,

n

jr

Hmn

kS

mn

kjy

= (2.8)

The detection strategy in case of parity bit-selected spreading is different from the

conventional MIMO system. Indeed, for each userk, we must detect theNt 1

[ ]T

n

tNkb

n

kb

n

kb

n

kb

)(

,,......

)(

2,,

)(

1,

)(

= (2.9)

vector of bits transmitted by all its antennas at instant n since the choice of spreading code

depends upon the value of this vector.

Using the same development in previous section, we can rewrite (2.8) as

( ) =

+=t

N

i

n

jn

n

ikb

kijh

n

kS

Hmn

kS

mn

kjy

1

)(")(

,,,)(),(),(

,(2.10)

where

)(" n

jn

represents the despread noise, the MAI, and part of SI. Indeed,

),(

,

mn

kjy

gathers partof the SI since we need the information from all transmitting antennas of the user of interest.

Equation (10) can be rewritten as

=

+=t

N

i

nj

nn

ikb

ijh

mn

kR

mn

kjy

1

)(")(,,

),(),(

,(2.11)

Where

)(),(),( n

kS

Hmn

kS

mn

kR = (2.12)

is the correlation matrix between the codes used by user k. It is worth noting here that when

)(),( nk

Smn

ks = the correlation matrix has important diagonal elements. However, it will not

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be diagonal because of cross-correlation due to the multipath effect. This is true even with

perfectly orthogonal codes. When)(),( n

kS

mn

ks , the diagonal elements are zeros (case of

orthogonal codes) while off-diagonal elements are nonzero.

2.5.2 Permutation Spreading System

In contrast to the parity bit-selected spreading technique, the permutation spreading

technique allocates different spreading codes to each transmit antenna. When permutation

spreading is used, depending on which coset the message comes from, a unique permutation of

the spreading codes assigned to the user is employed. Each permutation employs Ntof the N

spreading waveforms and we attempt to minimize the number of spreading codes that each

permutation has in common. Furthermore, if a spreading waveform is used by antenna iof user k

in one permutation, it cannot be used by antenna i in any other permutation for this same user.

The design of the different spreading permutations is based on t-designs which are used in

permutation modulation schemes. From the detectors perspective, as for the case of parity bit-

selected spreading, we do not have prior knowledge of which codes have been used by each user.

However, we know that we have to pick Ntdifferent codes from the set CkofNdifferent codes

for user k. Hence, we need to apply a bank of correlators for each possible code assignment:

( )=

+=t

N

i

n

jnn

ikbijhn

ikS

Hmn

ikSmn

kjy

1

)(")(

,,

)(

,

),(

,),(

,(2.13)

( ) )(,

),(

,),(

,

n

ikS

Hmn

ikSmn

ikR = (2.14)

is the correlation matrix of the code employed to spread the message sent by antenna i of user k

and one of the Npossible codes available for user k. In case of orthogonal normalized spreading

codes, the correlation matrix is an identity matrix when)(

,

),(

,

n

ikS

mn

ikS = .Otherwise, the correlation

matrix is a nonzero matrix with zeros in its diagonal.

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For the same reasons as the parity bit-selected spreading system, a suboptimal detector is

proposed. The estimated data is determined using the following decision rule:

=

+

=

=r

N

j

n

k

yn

ik

b

kij

htN

i

mn

ik

Rmn

jk

y

Bmb

n

k

b

1

2)(

2

)(

,,,1

),(

,

),(

,)(

min)( (2.15)

Where)(n

ky is a vector containing a concatenation of all )

',(

,

mn

jky with 'm =1N,

'm m and

j = 1Nr.B is the set of 2N

tpossible values of b(m),where

Tm

tNb

m

ib

mb

mb ]

)(.......

)(.....

)(

1[

)( = .

2.5.3 MIMO testing

MIMO signal testing focuses first on the transmitter/receiver system. The random phases

of the sub-carrier signals can produce instantaneous power levels that cause the amplifier to

compress, momentarily causing distortion and ultimately symbol errors. Signals with a high PAR

(peak to average ratio) ratio can cause amplifiers to compress unpredictably during transmission.

OFDM signals are very dynamic and compression problems can be hard to detect because of

their noise-like nature.

Knowing the quality of the signal channel is also critical. A channel emulator can

simulate how a device performs at the cell edge, can add noise or can simulate what the channel

looks like at speed. To fully qualify the performance of a receiver, a calibrated transmitter, such

as a vector signal generator (VSG), and channel emulator can be used to test the receiver under a

variety of different conditions. Conversely, the transmitter's performance under a number of

different conditions can be verified using a channel emulator and a calibrated receiver, such as a

vector signal analyzer (VSA).

Understanding the channel allows for manipulation of the phase and amplitude of each

transmitter in order to form a beam. To correctly form a beam, the transmitter needs to

understand the characteristics of the channel. This process is called channel sounding or channel

estimation. A known signal is sent to the mobile device that enables it to build a picture of the

channel environment. The phone then sends back the channel characteristics to the transmitter.

The transmitter then can apply the correct phase and amplitude adjustments to form a beam

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directed at the mobile device. This is called a closed-loop MIMO system. For beam forming, it is

required to adjust the phases and amplitude of each transmitter.

2.6 Applications of MIMO

Spatial multiplexing techniques makes the receivers very complex, and therefore it is

typically combined with Orthogonal frequency-division multiplexing (OFDM) or with

Orthogonal Frequency Division Multiple Access (OFDMA) modulation, where the problems

created by multi-path channel are handled efficiently. The IEEE 802.16e standard incorporates

MIMO-OFDMA. The IEEE 802.11n standard, released in October 2009, recommends MIMO-

OFDM.

MIMO is also planned to be used in Mobile radio telephone standards such as recent

3GPP and 3GPP2 standards. In 3GPP, High-Speed Packet Access plus (HSPA+) and Long Term

Evolution (LTE) standards take MIMO into account. Moreover, to fully support cellular

environments MIMO research consortia including IST-MASCOT propose to develop advanced

MIMO techniques, i.e., multi-user MIMO (MU-MIMO).

2.6.1 Other applications

Given the nature of MIMO, it is not limited to wireless communication. It can be used for

wire line communication as well. For example, a new type of DSL technology (Gigabit DSL) has

been proposed based on Binder MIMO Channels.

2.7 Wireless standards

In the commercial arena, Iospan Wireless Inc. developed the first commercial system in

2001 that used MIMO with Orthogonal frequency-division multiple access technology (MIMO-

OFDMA). Iospan technology supported both diversity coding and spatial multiplexing. In 2005,

Airgo Networks had developed an IEEE 802.11n precursor implementation based on their

patents on MIMO. Following that in 2006, several companies (including at least Broadco, Intel,

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and Marvell) have fielded a MIMO-OFDM solution based on a pre-standard for 802.11n WiFi

standard. Also in 2006, several companies (Beceem Communications, Samsung, Runcom

Technologies, etc.) have developed MIMO-OFDMA based solutions for IEEE 802.16e WiMAX

broadband mobile standard. All upcoming 4G systems will also employ MIMO technology.

Several research groups have demonstrated over 1 Gbit/s prototypes.

3.1 Space-Time Block Codes

Spacetime block coding is a technique used in wireless communications to transmitmultiple copies of a data stream across a number of antennas and to exploit the various received

versions of the data to improve the reliability of data-transfer. The fact that the transmitted signal

must traverse a potentially difficult environment with scattering, reflection, refraction and so on

and may then be further corrupted by thermal noise in the receiver means that some of the

received copies of the data will be 'better' than others. This redundancy results in a higher chance

of being able to use one or more of the received copies to correctly decode the received signal. In

fact, spacetime coding combines all the copies of the received signal in an optimal way to

extract as much information from each of them as possible.

The input to the encoder is a stream of modulated symbols from a real or complex

constellation. The encoder operates on a block ofKsymbols producing anMt x Tcodeword XQ

whose rows correspond to transmit antennas and columns correspond to symbol times. At the

receiver, maximum likelihood decoding is simplified by the orthogonal structure imposed on the

codeword. The system used here is shown in Figure 3.1.1, where an outer TCM encoded decoder

is concatenated with the STBC encoder decoder. The coding gain of the end toend system

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Figure 3.1Concatenated space-time block coding system

is only due to the outer TCM encoder since we consider full rate STBCs. The STBC decoder

outputs scalar symbols which are then processed by the TCM decoder using the conventional

scalar Viterbi algorithm. The effective channel induced by space-time block coding of complex

symbols (before ML detection) is where y e is the 2Kx 1 vector after STBC decoding of the

received matrix Ynt , xnt is a vector with two K x 1 blocks corresponding to the real and

imaginary parts of the input (each entry of xnthas power = Es/2Mt), and wntis the noise vector

after STBC decoding. With some computation it can be shown that the SNR (signal to noise

ratio) at the receiver is equal to

2

2

02

2

4

FHP

NFH

tM

sEFH

= (3.1)

The key observation here is that (1) is effectively a scaled AWGN channel with

SNR=PI [H: 1 I2

fand code rate equal to KIT. The fact that STBC converts the matrix channelinto a scalar AWGN channel motivates the concatenation of traditional single-antenna TCM with

STBC.

Space-time block codes operate on ablock of input symbols producing a matrix output

whose columns represent time and rows represent antennas. Unlike traditional single antenna

block codes for the AWGN channel, most space time block codes do not provide coding gain.

20


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Their key feature is the provision of full diversity with extremely low encoded decoder

complexity. In addition, they are optimal over all unitary codes with respect to the union bound

on error probability. The best known codes for real constellations have been designed for a

practical range of transmit antennas (2 to 8).

Space-time trellis codes operate on one input symbol at a time producing a sequence of

vector symbols whose length represents antennas. Like traditional TCM (trellis coded

modulation) for the single-antenna channel, space time trellis codes provide coding gain. Since

they also provide full diversity gain, their key advantage over space-time block codes is the

provision of coding gain. Their disadvantage is that they are extremely difficult to design and

require a computationally intensive encoder and decoder.

The input to the encoder is a stream of modulated symbols from a real or complex

constellation. The encoder operates on a block ofKsymbols producing an Mt x Tcodeword XQ

whose rows correspond to transmit antennas and columns correspond to symbol times. At the

receiver, maximum likelihood decoding is simplified by the orthogonal structure imposed on the

codeword. The system used here is shown in below Figure, where an outer TCM encoded coder

is concatenated with the STBC encoder/decoder. The coding gain of the end to end system is

only due to the outer TCM encoder since we consider full rate STBCs. The STBC decoder

outputs scalar symbols which are then processed by the TCM decoder using the conventional

scalar Viterbi algorithm.

3.2 Orthogonality

STBCs as originally introduced, and as usually studied, are orthogonal. This means that

the STBC is designed such that the vectors representing any pair of columns taken from the

coding matrix are orthogonal. The result of this is simple, linear, optimal decoding at the

receiver. Its most serious disadvantage is that all but one of the codes that satisfy this criterion

must sacrifice some proportion of their data rate (see Alamouti's code).

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Moreover, there exist quasi-orthogonal STBCs that achieve higher data rates at the cost

of inter-symbol interference (ISI). Thus, their error-rate performance is lower bounded by the

one of orthogonal rate 1 STBCs that provides ISI free transmissions due to orthogonality.

3.3 Design of STBCs

The design of STBCs is based on the so-called diversity criterion derived by Tarokh et al.

in their earlier paper on spacetime trellis codes. Orthogonal STBCs can be shown to achieve the

maximum diversity allowed by this criterion.

Figure 3.2 Block diagram of the transmitter and the receiver.

3.4 Generalized Complex Orthogonal Designs as SpaceTime Block Codes

The simple transmit diversity schemes described above assume a real signal constellation.

It is natural to ask for extensions of these schemes to complex signal constellations. We recover

the Altamonte scheme as a 2X2 complex orthogonal design. Motivated by the possibility of

linear processing at the transmitter, but we shall prove that complex linear processing orthogonal

22


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designs only exist in two dimensions. This means that the Alamouti Scheme is in some sense

unique. However, we would like to have coding schemes for more than two transmit antennas

that employ complex constellation. We then prove by explicit construction that rate(1/2)

generalized complex orthogonal designs exist in any dimension. it is shown that this is not the

best rate that can be achieved. Specifically, examples of rate (3/4) generalized complex linear

processing orthogonal designs in dimensions three and four are provided.

3.4.1 Complex Orthogonal Designs

We define a complex orthogonal design of size as an orthogonal matrix with

entries the indeterminate nxxxx ,.......,, 321 . Their conjugates

nxxxx ,.......

3,

2,

1 , or

multiples of these indeterminate by i where 1=i . Without loss of generality, we may

assume that the first row of co is nxxxx ,.......,, 321 .

The method of encoding presented in Section (BPSK Signaling) can be applied to obtain a

transmit diversity scheme that achieves the full diversity nm . The decoding metric again

separates into decoding metrics for the individual symbols nxxxx ,.......,, 321 .

An example of 2x2 a complex orthogonal design is given by

.*

1

*

2

21

xx

xx

3.4.2 The Alamouti Scheme

The spacetime block code proposed by Alamouti uses the complex orthogonal design

*

1*2

21

xx

xx

Suppose that there are 2b signals in the constellation. At the first time slot 2b, bits arrive

at the encoder and select two complex symbols s1 and s2. These symbols are transmitted

simultaneously from antennas one and two, respectively. At the second time slot, signals and

23


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are transmitted simultaneously from antennas one and two, respectively. Maximum-likelihood

detection amounts to minimizing the decision statistic

=

++

mj

sj

sj

jrs

js

jj

r1

2*1,2

*2,12

2

2,21,11

(3.2)

Over all possible values of and S2. The minimizing values are the receiver estimates of S1

and S2, respectively. As in the previous section, this is equivalent to minimizing the decision

statistic.

2

11

2

1

2

,1

2

1)1),2

*)

2(

,

*

11( s

m

j ijis

m

j jj

rj

jr

=

=

++=

+ (3.3)

for detecting S1 and the decision statistic

2

21

2

1

2

,1

2

2)1)

,1

*)

2(

,

*

21( s

m

j ijis

m

j j

jr

j

jr

=

=

++=

(3.4)

for decoding S2. This is the simple decoding scheme described and it should be clear that a result

analogous to Theorem 3.2.1 can be established here. Thus Alamoutis scheme provides full

diversity using receive antennas. This is also established by Alamouti, who proved that this

scheme provides the same performance as level maximum ratio combining.

3.5 T-Designs

Definition: A t-(v, k, lambda) design, or (for short) a t-design, is an incidence structure of

points and blocks with the following properties:

a) There are v points;

b) Each block is incident with kpoints;

c) Any tpoints are incident with lambda common blocks.

d) Here t, v, k, lambda are non-negative integers.

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Some non-degeneracy conditions are usually assumed, though there is no agreement

about exactly what these should be. It is reasonable to assume that t


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M8 0111

1000

C8(t) C4(t) C1(t) C3(t)

TABLE 3.1 T-DESIGN PERMUTATION SPREADING TABLE FOR= 4.

3.6 Space-Time Block Code Based Permutation

The design of the spreading code permutations is based on a Space-Time Block Code

matrix. The advantage of using STBC-based spreading code permutations is to give transmit

diversity by providing orthogonality between the transmit messages.

Figure 3.3 Receiver for the proposed system

3.6.1 BPSK Signaling

A BPSK modulated MIMO-CDMA system that employs permutation spreading requires 8

spreading sequences per user. An 88 space-time block code matrix can be used for designing

the permutation table which is given by:

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12345678

21436587

34127856

43218765

56781234

65872143

78563412

87654321

ssssssss

ssssssss

ssssssss

ssssssss

ssssssss

ssssssss

ssssssss

ssssssss

The STBC-based spreading code permutation is given in Table 3.1. Rows 1, 5, 8, and 6 are

respectively assigned to column 1, 2, 3 and 4 of Table 3.1. This is done to create orthogonality

between the different message cosets. The low pass equivalent of the received signal at the jth

receive antenna in Figure 2 is the sum of all the message bits multiplied by the channel gain,

which is given by:

)()(.....)(1.11)( tnttNw

tNb

tjNtwbjtRx +++= (3.5)

where ji is the complex channel gain for the ith transmit-jth receive antenna link; and n(t) is the

total complex noise at the receiver The output from the kth matched filter in thejth receive

antenna would be given as

(t),c=(t)wif ki,

.

+

= otherwisejkzjk

zjki

b

jkr

(3.6)

where zjkis the sampled noise from the kth matched filter on the jth antenna. Maximum likelihood

detection (MLD) is used to determine which message has been transmitted by finding the

minimum Euclidean distance between the received signal and all the possible received message

vectors in the absence of noise.

Coset Message vector w1 (t) w2(t) w3(t) w4(t)

M1 0000

1111

C1(t) C5(t) C8(t) C6(t)

M2 0001

1110

C2(t) C6(t) C7(t) C5(t)

M3 0010

1101

C3(t) C7(t) C6(t) C8(t)

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M4 0011

1100

C4(t) C8(t) C5(t) C7(t)

M5 0100

1011

C5(t) C1(t) C4(t) C2(t)

M6 0101

1010

C6(t) C2(t) C3(t) C1(t)

M7 0110

1001

C7(t) C3(t) C2(t) C4(t)

M8 0111

1000

C8(t) C4(t) C1(t) C3(t)

Table 3.2: BPSK Signaling STBC-Based Code Permutations forNt=4

3.6.2 QPSK Signaling

Space time block code can be used forM-PSK signal constellations; the STBC-based

spreading code permutations can also be used for MIMO-CDMA systems employing QPSK

modulation. Gray coding, in which adjacent code words differ in one bit position, is used for

QPSK signal mapping. The Gray Coding constellation is given in figure 3.6.2.

Figure 3.4 QPSK Modulation with Gray Code Mapping

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In a 2 transmit antenna MIMO-CDMA system employing QPSK modulation, the total

number of message bits transmitted on a given time interval is 4, and the total number of

spreading sequences used is 8. The QPSK signaling STBC-based spreading code permutation is

given in Table 3.2. We redesign columns 1 and 2 in Table 3.2 to ensure that all the message

cosets are orthogonal to each other.

Coset Message

symbolvectorm

Corresponding

binary vector

w1 (t) w2(t)

M1 Q1Q1Q3Q3

0000

1111

C1(t) C5(t)

M2 Q1Q2Q3Q4

0001

1110

C2(t) C6(t)

M3 Q1Q4Q3Q2

0010

1101

C3(t) C7(t)

M4 Q1Q3Q3Q1

0011

1100

C4(t) C8(t)

M5 Q2Q1Q4Q3

0100

1011

C5(t) C1(t)

M6 Q2Q2Q4Q4

0101

1010

C6(t) C2(t)

M7 Q2Q4Q4Q2

0110

1001

C7(t) C3(t)

M8 Q2Q3Q4Q1

0111

1000

C8(t) C4(t)

Table 3.3 QPSK Signaling STBC-Based Code Permutations forNt=2

Similar to the BPSK modulated MIMO-CDMA system, the output from the kth matched

filter in the jth receive antenna would be given as

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(t),c=(t)wif ki,

.

+

=otherwise

jkz

jkz

jkis

jkr

(3.7)

Where si is the QPSK modulated signal message transmitted from transmits antenna i.Once

again, ML detection is used to determine the most likely transmitted message.

3.6.3 Error Correcting Codes

This section is a brief introduction to the theory and practice of error correcting codes

(ECCs). We limit our attention to binary forward error correcting (FEC) block codes. This means

that the symbol alphabet consists of just two symbols (which we denote 0 and 1), that the

receiver can correct a transmission error without asking the sender for more information or for a

retransmission, and that the transmissions consist of a sequence of fixed length blocks, called

code words This code is single error correcting (SEC), and a simple extension of it, also

discovered by Hamming, is single error correcting and, simultaneously, double error detecting

(SEC-DED). Still sticking to binary FEC block codes, the basic question addressed is: for a

given block length (or code length) and level of error detection and correction capability, how

many different code words can be encoded. The reader is cautioned that over the past 50 years

ECC has become a very big subject. Many books have been published on it and closely related

subjects [Hill, LC, MS, and Roman, to mention only a few]. Here we just scratch the surface and

introduce the reader to two important topics and to some of the terminology used in this field.

Although much of the subject of error correcting codes relies very heavily on the notations and

results of linear algebra, and in fact is a very nice application of that abstract theory, we avoid it

here for the benefit of those who are not familiar with that theory. The following notation is used

throughout this chapter. It is close to that used in [LC]. The terms are defined in subsequent

sections.

kNumber of information or message bits. mNumber of parity-check bits (check bits, for short).

N Code length,

n = m + k.

uInformation bit vector, u0, u1, uk-1.

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pParity check bit vector,p0,p1, ,pm-1.

sSyndrome vector, s0, s1, , sm-1.

3.6.4 The Hamming Code

Hammings development [Ham] is a very direct construction of a code that permits

correcting single-bit errors. He assumes that the data to be transmitted consists of a certain

number of information bits u, and he adds to these a number of check bits p such that if a block is

received that has at most one bit in error, then p identifies the bit that is in error (which may be

one of the check bits). Specifically, in Hammings code p is interpreted as an integer which is 0

if no error occurred, and otherwise is the 1-origined index of the bit that is in error. Let kbe the

number of information bits, and m the number of check bits used. Because the m check bits must

check themselves as well as the information bits, the value ofp, interpreted as an integer, must

range from 0 to which is a distinct value. Because mbits can distinguish cases, we must have

1kmm

2 ++ (23)

This is known as the Hamming rule. It applies to any single error correcting (SEC) binary

FEC block code in which all of the transmitted bits must be checked. The check bits will be

interspersed among the information bits in a manner described below.

Becausep indexes the bit (if any) that is in error, the least significant bit ofp must be 1 if

the erroneous bit is in an odd position, and 0 if it is in an even position or if there is no error. A

simple way to achieve this is to let the least significant bit ofp,p0, be an even parity check on

the odd positions of the block, and to put p0 in an odd position. The receiver then checks the

parity of the odd positions (including that ofp0). If the result is 1, an error has occurred in an odd

position, and if the result is 0, either no error occurred or an error occurred in an even position.

This satisfies the condition thatp should be the index of the erroneous bit, or be 0 if no error

occurred.

Similarly, let the next from least significant bit ofp, p1, be an even parity check of

positions 2, 3, 6, 7, 10, 11, (in binary, 10, 11, 110, 111, 1010, 1011, ), and put p1 in one of

these positions. Those positions have a 1 in their second from least significant binary position

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number. The receiver checks the parity of these positions (including the position ofp1). If the

result is 1, an error occurred in one of those positions, and if the result is 0, either no error

occurred or an error occurred in some other position.

Continuing, the third from least significant check bit,p2, is made an even parity check on

those positions that have a 1 in their third from least significant position number, namely

positions 4, 5, 6, 7, 12, 13, 14, 15, 20, , andp2 is put in one of those positions.

4.1 Proposed Methodology

The parity bit selected spreading code technique, based on systematic linear block codes,

and was first proposed. In code division multiple access (CDMA) systems employing this

technique, the calculated parity bits are used to select a spreading sequence from a set of

mutually orthogonal spreading sequences. This technique was extended to CDMA systems using

multiple input multiple output (MIMO) techniques. In a MIMO-CDMA system with

transmit antennas, instead of selecting one spreading sequence, the parity bits select different spreading sequences from a set of mutually orthogonal spreading sequences; and

each transmit antenna uses one of the selected spreading sequences. A different permutation of

spreading sequences is assigned to different sequences of parity bits, hence the technique is

referred to as permutation spreading. T-designs are used to design the different spreading

permutations. In this paper, we design the spreading code permutations based on Space-Time

Block Codes (STBC).Compared to the results presented, the STBC-based design can improve

the bit error rate (BER) performance over the flat fading channel without increasing the system

complexity. We compare the performance of the two techniques for MIMO-CDMA systems

operating on frequency-flat slowly Rayleigh fading channels.

4.2 MIMO-CDMA System Employing Permutation Spreading

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The block diagram of a MIMO-CDMA transmitter receiver pair

employing permutation spreading.

The input bit stream is converted intotparallel data streams. On one signaling

interval, the bits to be transmitted are used to selectt spreading sequences from a set of

mutually orthogonal spreading sequences, where>t.

Figure 4.1 Block diagram of MIMO-CDMA system employing permutation spreading.

The message bits are then modulated using binary phase shift keying (BPSK) and each

bit is spread using the spreading sequence selected in the previous step. The spreading sequences

employed on a given signaling interval {1(), ..., ()} are chosen from a set of

orthogonal spreading sequences {1(), 2(), , ()}. At the receiver, the output of

each antenna is connected to a bank of matched filters. There is one matched filter for each of the

spreading codes in the users set {1(),2(), ,()}. We can estimate the transmitted

data sequence based on the received vector, which is given by:

T

NrNr

rNrr

Nrrrr ],....,

1,...

21,

1,...

12,

11[= (4.1)

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4.3 Space-Time Block Code Based Permutation

The design of the spreading code permutations is based on a STBC matrix. The 4

transmit antenna MIMO-CDMA system that employs permutation spreading requires 8

spreading sequences per user. An 8 8 space-time block code matrix can be used for designing

the permutation table. This matrix is:

12345678

21436587

34127856

4321876556781234

65872143

78563412

87654321

ssssssss

ssssssss

ssssssss

ssssssss

ssssssss

ssssssss

ssssssss

ssssssss

34

Coset Message vector w1 (t) w2(t) w3(t) w4(t)

M1 0000

1111

C1(t) C5(t) C8(t) C6(t)

M2 0001

1110

C2(t) C6(t) C7(t) C5(t)

M3 0010

1101

C3(t) C7(t) C6(t) C8(t)

M4 0011

1100

C4(t) C8(t) C5(t) C7(t)

M5 01001011

C5(t) C1(t) C4(t) C2(t)

M6 0101

1010

C6(t) C2(t) C3(t) C1(t)

M7 0110

1001

C7(t) C3(t) C2(t) C4(t)

M8 0111

1000

C8(t) C4(t) C1(t) C3(t)


35/48

TABLE 4.1 STBC-Based Code Permutations for= 4.

The STBC-based spreading code permutation is given in Table 4.3. Columns 1, 5, 8, and

6 are respectively assigned to columns 1, 2, 3 and 4 of Table 4.3. The output (normalized to the

signaling interval) from the kth matched filter of the jth receive antenna would be given as

(t),c=(t)wif ki,

+=

otherwisejk

n

jkn

rNb

E

ib

jkr (4.2)

Where ji is the complex channel gain for theth transmit-th receive antenna link;bis the

average received energy per bit; and kjis the sampled noise from theth matched filter of the

th receive antenna. The received vector, r = ub+ n where uis the received data vector that

is dependent on the transmitted data vector, b = [1, 2, ..., Nt ]T and n = [11, ..., 1N,

21, ..., 2N, ..., Nr1, ..., NrN]T is a vector made up of noise samples. For example, if the

transmitted message m = [0, 0, 0, 0], then b = [1,1,1,1] and ub = [11, 0, 0,

0,12,14, 0,13,21, 0, 0, 0,22,24, 0,23, ...,Nr1, 0, 0, 0,Nr2,Nr4,

0,Nr3]T.

Maximum likelihood detection (MLD) is used to detect which message has been

transmitted by finding the minimum squared Euclidean distance between the received vector and

all the possible received vectors in the absence of noise. The expression is given as

2min

bur

bb =

(4.2)

4.4 BIT Error Probability Analysis

Let us consider the case when the transmitted message m = [0, 0, 0, 0]. Let us assume

that we are transmitting a narrowband MIMO-CDMA signal so that the channel can be assumed

to be frequency-nonselective. We further assume that the channel gains are independent. We can

determine a union bound on the BER by finding the squared Euclidean distance between the

different us and the ucorresponding to b = [1,1,1,1]. Let us start by considering the

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distance between the received vectors associated with messages [1,1,1,1] and [0,0,0,0]. This

scenario corresponds to messages in the same coset. We will refer to this distance as

. It is given by:

2

1 1

42 = =

= rN

jt

N

l jlrNb

E

samed (4.3)

We can show that 2 has a chi-square distribution with 2 degrees of

freedom. Therefore the probability that we transmit 0000 but detect 1111

+

=

+=

k

tNrN

k k

ktNrN

sameP

11

0

1

2

1

(4.4)

wherebr

Nb

4

4

+=and is the average received energy per bit to single sided noise

spectral density ratio. Next let us consider the probability of detecting a message vector in a

different coset that does not have any spreading codes in common as the desired message 0000.

In Table I, we see that coset 7 does not share any spreading codes with coset 1. We refer to

this distance as0. We can show that20 is:

=

=

=rN

j

tN

ljl

rN

bE

od

1 1

222 (4.5)

Therefore the probability of incorrectly detecting a message from a coset that does not

have any spreading codes in common where

.2

2

brN

b

+= (4.6)

Next we consider the incorrect detection of a message from a coset that shares 2

spreading waveforms with the desired message. If we observe Table I, we see that six cosets

share two spreading codes with coset 1. However it is important to note that the common

codes of coset simply swap transmit antennas compared to those of coset1. For

example1 uses1() from antenna 1 and 5() from antenna 2 while 5 uses 1()

from antenna 2 and 5() from antenna 1. We refer to this as code symmetry. The distance

between a message in5 and the desired message is then given by

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++

==

=2

21

2

211 3

2221,5

4

jjjjr

N

bErN

j l jlrNb

Ed (4.7)

We can show that

222

22BABABA +=++ (4.8)

therefore the last term in (8) becomes

= +

rN

j jjrNb

E

1

2

2

2

1

2 (4.9)

Therefore 2 5,1 has the same distribution as 20 . Since the STBC-based design maintains

thecode symmetry between all cosets that share two spreading codes then they all have the same

distance properties, therefore the probability of incorrectly detecting a message from a coset that

shares two spreading codes with the desired message is also given by (4.6) with

.2

2

brN

b

+=

Therefore the union bound for the BER for a single user MIMO-CDMA system

employing STBC-based permutation spreading is given by:

diffp

MM

samepbp 2+< (4.10)

provided that the code symmetry discussed above is maintained. In (4.9) is given in (4.6)

with

.4

4

brN

b

+= (4.11)

While is also given by (6) but with

.2

2

brN

b

+=

andis the total number of message which is 16 in our case.

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5.1 Simulation Parameters

Table 5.1 Simulation parameters

5.2 Simulation Results

The simulation results for bit error rate (BER) performances are presented in this section.

MIMO-CDMA system with 4 transmit antennas and 1 or 4 receive antennas are considered. The

following assumptions are used in the simulation model: 1) The channel is a frequency

nonselective (flat), slowly Rayleigh fading channel, and there is no channel induced intersymbol

interference (ISI). 2) The channel gains of different transmit and receive links are uncorrelated.

3) It is assumed that perfect channel state information (CSI) is available at the receiver. Figure 2

shows the BER performances of MIMO-CDMA system employing STBC permutation vs. the

system employing T-design permutation with 4 transmit antennas and 1 or 4 receive antenna.

The T-design permutation table is given in Table 3.1. The BER performances of MIMO-CDMA

38

No. of Message Cosests 8

Length of Message Coset 8 bits

Noise Random Noise

Modulation BPSK

No. of Transmitting

Antennas

4

No. of Receiving Antennas 1,4


39/48

systems employing conventional spreading are also given as references. In the conventional

system, each transmit antenna is assigned a unique spreading sequence that is orthogonal to the

others. The spreading code assignment is fixed and does not depend on the data being

transmitted.

From Figure 5.1.1, we see that permutation spreading provides significant gains over

conventional MIMO-CDMA. Also the MIMO-CDMA system using STBC-based code

permutations has a better BER performance compared to the system employing T-design

permutations. From Table 3.1, we see that the T-design method does not respect the code

symmetry discussed in the previous section for cosets that have two spreading codes in common

and therefore some degrees of freedom are lost in the squared Euclidean distance between

different messages. The lack of code symmetry accounts for the slightly increased BER. Figures

5.1.1 shows, at the BER of 103, the STBC permutation systems have 0.7 dB and 0.2 dB gain

over T-design permutation system in the case of 1 and 4 receive antennas, respectively.

Figure 5.1 BER for STBC Permutation vs. T-Design Permutation with = 4,= 1 and= 4.

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5.3 Introduction to MATLAB

What Is MATLAB?

MATLAB 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

Typical uses of MATLAB

1. Math and computation

2. Algorithm development3. Data acquisition

4. Data analysis, exploration and visualization

5. Scientific and engineering graphics

The main features of MATLAB

1. Advance algorithm for high performance numerical computation, especially in the Field

matrix algebra

2. A large collection of predefined mathematical functions and the ability to define ones own

functions.

3. Two-and three dimensional graphics for plotting and displaying data

4. A complete online help system

5. Powerful, matrix or vector oriented high level programming language for individual

applications.

6. Toolboxes available for solving advanced problems in several application areas

Features and capabilities of MATLAB

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

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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 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 matrix/array language with control flow statements, functions, data

structures, input/output, 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

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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.

5.4 Functions used in MAT Lab code

Functions used in

MAT Lab Code

DESCRIPTION

Clear Erases variables and functions from memory

Clear x Erases the matrix 'x' from your workspace

Close By itself, closes the current figure window

Figure Creates an empty figure window

For Repeat statements a specific number of times

hold on Holds the current plot and all axis properties so that subsequent

graphing commands add to the existing graph.

hold off Sets the next plot property of the current axes to "replace"

Break Terminate execution of m-file or WHILE or FOR loop

Diff Difference and approximate derivative

Save Saves all the matrices defined in the current session into the file,

matlab.mat, located in the current working directory

Load Loads contents of matlab.mat into current workspace

xlabel('text' ) Writes 'text' beneath the x-axis of a plot

ylabel('text' ) Writes 'text' beneath the y-axis of a plot

Randint Generate matrix of uniformly distributed random integers.

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subplot() Allows you to create multiple plots in the same window

plot(x,y) Creates a Cartesian plot of the vectors x & y

plot(y) Creates a plot of y vs. the numerical values of the elements in the

y-vector

semilog x(x,y) Plots log(x) vs y

smiologies(x,y) Plots x vs log(y)

Grid Creates a grid on the graphics plot

title('text') Places a title at top of graphics plot

Table.5.2 Functions used in MAT Lab

5.5 Applications

1) Communication Network: Broadcasting network, cellular network, satellite

communication, and etc.

2) Narrowband Application: Limited bandwidth and lower data rate

3) Higher Performance Required

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4) Space-Time Coding is attractive

Future scope

Orthogonal Space-Time Block Codes (O-STBC) has been proposed as a transmit

diversity scheme that can provide full transmit diversity with linear decoding complexity.

Despite of these advantageous, O-STBC has a code rate that is less than one when more than two

transmit antennas and complex constellation are used. Quasi-Orthogonal STBC (QO-STBC)

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with constellation rotation (CR) or group-constrained linear transformation have been proposed

to provide transmit diversity at a higher code rate than O-STBC. The maximum-likelihood (ML)

decoding of QO-STBC can be achieved by jointly detecting a sub-group of the transmitted

symbols, rather than all the symbols, hence QO-STBC leads to a lower decoding complexity than

general non-orthogonal STBC.

Hence it is of interest to design QO-STBC with low decoding complexity, as a result

Minimum-Decoding- Complexity QO-STBC (MDC-QOSTBC) has been designed. MDC-

QOSTBC has a simple ML decoding and is only next to O-STBC, i.e. the ML decoding of

MDCQOSTBC only need a joint detection of two real symbols, this is the simplest among all

possible non-orthogonal STBCs. But the maximum achievable code rate of MDCQOSTBC is

less than one for more than four transmit antennas.

Conclusion

A new design method to find the permutation spreading table for MIMO-CDMA systems

is proposed in this paper and we have analyzed the performance of MIMO-CDMA with

comparision to conventional Code Division Multiple Access (CDMA) system. The performance

is often measured as the average bit rate (bits/s) the wireless link can provide or as the average

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bit error rate (BER). These simulations are done to design the simulation model which is

conventional CDMA, MIMO-CDMA with four-transmit-one receive (4Tx1Rx) and MIMO-

CDMA with four-transmit-four receive (4Tx4Rx). Then the comparision between conventional

CDMA systems is made to investigate the system performance. The result shows that MIMO-

CDMA technique gives better performance than conventional CDMA system in term of bit error

rate (BER) and also the number of antennas increase.

References

[1] C.DAmours, Parity Bit Selected Spreading Sequences: A Block Coding Approach to

Spread Spectrum,IEEECommun. Letters, vol.9, pp. 16-18, Jan. 2005.

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[2] C. DAmours, J-Y Chouinard, Parity Bit Selected and Permutation Spreading for

CDMA/MIMO Systems,Proc. IEEEVehicular Technologies Conf., pp. 1475-1479, Apr. 2007.

[3] V. Tarokh, H. Jafarkhani, A. R. Calderbank, Space-time Block Codes from Orthogonal

Designs,IEEETrans. Info. Theory, Vol. 45, pp.1456-1467, July 1999.

[4] L.C. Tran, T.A. Wysocki, M.Alfred, S.Jennifer, Complex Orthogonal Space-time Processing

in Wireless Communications, Springers Science Business Media, Inc, 2006

[5] S. Sandhu, R. Heath and A. Paul raj Space-time Block Codes versus Space-time Trellis

Codes, IEEE Commun.Letters, July.2001.

[6] K.J. Sankar, V.M. Pandharipande, P.S. Moharir, Generalized Gray Codes,IEEE Proc. Int.

Symp. on Intelligent signal processing and communication systems,pp. 654-659, Nov 2004

[7] J. G. Proakis,Digital Communications, 4th. Ed., New York: McGraw-hill, 2001.

[8] Y. Song, Parity Bit Selected Spreading Sequences for Spread Spectrum and Code Division

Multiple Access Systems, M. A. Sc thesis, University of Ottawa, 2005.

[9] K. Yao, Error Probability of Asynchronous Spread Spectrum Multiple Access

Communication Systems,IEEE Trans. on Commun., Vol.25, pp.803-809, Aug.1977

[10] H.V. Poor, V. Sergio, Single User Detectors for Multiuser Channels, IEEE Trans. on

Commun. Vol. 36, pp. 50-60, Jan. 1988

[11] M.B.Pursley, Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access

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1977

[12] M.Shi, Spreading Code Assignment Techniques for MIMO-CDMA Systems, M. A. Sc

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[13] Erik G. Larsson, Petre Stoica Space-time block coding for wireless communications

,Cambridge University press,2003.

[14] M. Ahmed, J. Pautler, and K. Rohani, CDMA receiver performance for multiple-input

multiple-output antenna systems, inProc. Of IEEEVeh. Tech. Conf., vol. 3, Oct. 2001.

[15] Kaveh Pahlavan, Prashant Krishnamurthi Principle of Wireless Network Prentice Hall

PTRUpperSaddleRiver,2001.

[16] H. Huang, H. Viswanathan, and G. J. Foschini, Multiple antennas in cellular CDMA

systems: transmission, detection, and spectral efficiency, IEEETrans. Wireless Commun, vol.

1, no. 3, July 2002.

Documents

Design of Spreading Permutations Based on Stbc