89

CHAPTER 4

PERFORMANCE ANALYSIS OF THE ALAMOUTI STBC

BASED DS-CDMA SYSTEM

4.1 INTRODUCTION

This chapter investigates a technique, which uses antenna diversity

to achieve full transmit diversity, using an arbitrary number of transmit

antennas for secure communications, and to improve the system performance

by mitigating interference. The work is focussed on the performance of DS-

CDMA systems over the Rayleigh, Rician and AWGN fading channels, in the

case of the channel being known at the receiver. The diversity scheme used in

the analysis is the Alamouti STBC scheme. Using analytical and simulation

approach, we have shown that the STBC CDMA system has increased

performance in cellular networks. We also compared the performance of this

system with that of the typical DS-CDMA system, and shown that the STBC

and multiple transmit antennas for the DS-CDMA system, provide

performance gains without any need of extra processing. The evaluation and

comparison of the performances of the DS-CDMA system in the AWGN,

Rician and the Rayleigh fading channels are provided.

In this chapter, fading channel STBC DS-CDMA system has been

implemented and analyzed. And the analysis is made under two conditions,

by assuming (i) Two transmit and One receiving antenna and (ii) Two

transmit and two receiving antennas. Both the schemes in the AWGN,

Rayleigh and Rician fading channels have been analyzed. Using the analytical

90

and

sim

ulat

ion

appr

oach

, it i

s sh

own

that

the

latte

r cas

e is

adv

anta

geou

s ov

er

the

tradi

tiona

l C

DM

A s

yste

m, i

nclu

ding

bet

ter

BER

per

form

ance

and

low

er

com

plex

ity. I

t has

bee

n ob

serv

ed th

at th

e B

ER p

erfo

rman

ce o

f th

e sy

stem

is

impr

oved

with

ant

enna

div

ersi

ty sc

hem

es.

The

sim

ulat

ion

resu

lts s

how

tha

t th

e B

ER p

erfo

rman

ce i

s be

tter,

usin

g th

e A

lam

outi

sche

me

unde

r the

AW

GN

and

Ric

ian

chan

nel,

whe

reas

it

is w

orse

und

er t

he R

ayle

igh

fadi

ng c

hann

el.

In g

ener

al,

the

BPS

K s

chem

e

shou

ld h

ave

the

leas

t prio

rity

com

pare

d to

the

othe

r map

ping

sch

emes

, whi

le

cons

ider

ing

spec

tral

effic

ienc

y, b

andw

idth

and

bit

rate

sup

port.

Bec

ause

, if

one

bit i

s tra

nsm

itted

per

sym

bol,

as w

ith B

PSK

, the

n th

e sy

mbo

l rat

e w

ould

be th

e sa

me

as th

e bi

t rat

e. If

two

bits

are

tran

smitt

ed p

er sy

mbo

l, as

in Q

PSK

,

then

the

sym

bol r

ate

wou

ld b

e ha

lf of

the

bit r

ate.

The

Cha

nnel

s pe

rfor

m in

the

follo

win

g or

der,

in te

rms

of th

e be

st (l

ess

SNR

req

uire

men

t) to

the

wor

st

(mor

e SN

R r

equi

rem

ent)

to m

aint

ain

the

requ

ired

BER

: AW

GN

, Ric

ian

and

Ray

leig

h.

4.2

AL

AM

OU

TI

ST

BC

SC

HE

ME

4.2.

1 Sp

ace

Tim

e M

ultiu

ser

CD

MA

Sys

tem

The

STB

C i

s an

eff

ectiv

e tra

nsm

it di

vers

ity t

echn

ique

, us

ed t

o

trans

mit

sym

bols

fro

m m

ultip

le a

nten

nas,

whi

ch e

nsur

es t

hat

trans

mis

sion

from

var

ious

ant

enna

s is

orth

ogon

al,

as h

as b

een

depi

cted

by

Taro

kh e

t al

(199

9) a

nd B

logh

& H

anzo

(20

02).

Wire

less

tra

nsm

issi

on w

ith a

hig

h da

ta

rate

, as

wel

l as

dive

rsity

and

cod

ing

gain

, is

quite

ach

ieva

ble

usin

g th

e ST

BC

,

whi

ch c

omba

ts f

adin

g in

wire

less

com

mun

icat

ions

. Th

e ST

BC

is

a hi

ghly

effic

ient

app

roac

h to

sig

nalin

g w

ithin

wire

less

com

mun

icat

ion,

that

take

s th

e

adva

ntag

e of

the

spat

ial d

imen

sion

by

trans

mitt

ing

a nu

mbe

r of d

ata

stre

ams,

usin

g m

ultip

le c

o-lo

cate

d an

tenn

as a

s ha

s be

en re

porte

d by

Gol

dsm

ith (2

001)

.

91

The

mai

n fe

atur

e of

the

STB

C i

s th

e pr

ovis

ion

of f

ull

dive

rsity

with

a v

ery

sim

ple,

yet

eff

ectiv

e en

codi

ng a

nd d

ecod

ing

mec

hani

sms.

Her

e, S

ij is

the

mod

ulat

ed s

ymbo

l to

be tr

ansm

itted

fro

m a

nten

na j

in ti

me-

slot

i. T

here

sho

uld

be T

time-

slot

s, nT

num

ber

of tr

ansm

it an

tenn

as,

and

nR n

umbe

r ofr

ecei

ve a

nten

nas.

This

blo

ck is

usu

ally

con

side

red

to b

e of

leng

th T

. We

cons

ider

two

dive

rsity

sche

mes

for o

ur a

naly

ses:

1. S

chem

e-I:

two

trans

mit

ante

nnas

, one

rece

ive

ante

nna

2. S

chem

e-II

: tw

o tra

nsm

it an

tenn

as, t

wo

rece

ive

ante

nnas

4.2.

2 Sc

hem

e-I:

Tw

o tr

ansm

it an

tenn

as, o

ne r

ecei

ve a

nten

na

Fi

gure

4.1

show

s th

e ba

sic

two-

bran

ch t

rans

mit

Ala

mou

ti sc

hem

e,

with

onl

y on

e an

tenn

a at

the

rece

iver

. Thi

s pa

rticu

larly

sim

ple

and

prev

alen

t

sche

me,

with

tw

o tra

nsm

it an

tenn

as a

nd o

ne r

ecei

ve a

nten

na,

uses

sim

ple

codi

ng,

whi

ch i

s th

e on

ly S

TBC

tha

t ca

n ac

hiev

e its

ful

l di

vers

ity g

ain,

with

out

any

chan

ge

in

the

data

ra

te.

As

per

Ala

mou

ti’s

sche

me,

th

e

trans

mitt

er s

ends

out

dat

a in

gro

ups

of tw

o bi

ts. T

he s

chem

e m

ay b

e an

alyz

ed

by th

e fo

llow

ing

thre

e fu

nctio

ns, t

hat h

ave

been

illu

stra

ted

by F

ettw

eis

et a

l

92

Figure 4.1 Two-branch transmit Alamouti scheme

4.2.2.1 The Encoding and Transmission Sequence

At a given symbol period, two signals, transmitted from two

antennas, antenna zero and antenna one, are denoted by and

simultaneously. During the next symbol period, signal ( ) is transmitted

from antenna zero, and signal is transmitted from antenna one, where

stands for a complex conjugate operation. The encoding is done in space and

time (and hence, space-time coding). The assumption made for this scheme is

that, the channel state remains fairly constant over the transmission of two

consecutive symbols as has been reported by Alamouti (1999) & Antony et al

(2004). It can be clearly understood from Table 4.1.

1s0s

93

Table 4.1 Transmission sequence in two-branch transmit Alamouti

scheme

Antenna 0 Antenna 1

t s s

t+T - s* s *

Assuming that fading is constant across two consecutive symbols,

the channel at time t, may be modeled as

( ) ( + ) = (4.1)

( ) ( + ) = (4.2)

where, T is the symbol duration.

The received signals, and at time T and t + T respectively, can

be expressed as

= ( ) + (4.3)

= ( + ) + (4.4)

where, and are complex random variables representing the receiver

noise and interference.

4.2.2.2 The Combining Scheme

The combiner builds the following two combined signals that are

sent to the maximum likelihood detector

94

( + ) (4.5)

( + ) (4.6)

4.2.2.3 The Maximum Likelihood Decision Rule

The combined signals obtained above are sent to the ML detector,

in order to obtain the symbol decision. In the case of PSK or BPSK, the

detection rule can be expressed as follows: d2(s0, si ) d2(s0, sk ), where i k

=> choose symbol si . It is interesting to note that the signals at the output of

the combiner are equivalent to the signals obtained in the two-branch MRRC,

as depicted in Figure 4.1. That is the reason why it is affirmed, that the

Alamouti scheme with two-branch transmit diversity is equal to the two-

branch MRRC, in terms of the diversity order. A slight difference is that the

noise components are rotated; however, this fact does not affect the SNR.

4.2.3 Two-branch transmit with M receivers

Under some circumstances, when the air channel presents bad

characteristics, or when it is possible to implement more than one antenna at

the receiver, the use of a higher order of diversity could be interesting. The

order that we would get in a system with two-transmit antennas and N receive

antennas is 2N. In this section, a detailed view of the two-transmit and two

receive antennas is given, with the aim of simplicity, but the generalization

can easily be done in the case of using any number of antennas. Figure 4.2

shows the scheme in this particular case.

4.2.3.1 The Encoding and Transmission Sequence

The encoding and transmission sequence for this configuration is

identical to the case discussed in Section 4.1.2.1. The channel at time t can be

modeled by complex multiplicative distortions, ( ), ( ), ( ), ( ),

95

between transmit antenna zero and receive antenna zero, transmit antenna one

and receive antenna zero, transmit antenna zero and receive antenna one,

transmit antenna one and receive antenna one, respectively.

Table 4.2 shows the signal notation for each antenna in each

symbol time.

Table 4.2 Notation of received signals at the receive antennas

Antenna 0 Antenna 1

Receiving antenna 0 h0 h2

Receiving antenna 1 h1 h3

Figure 4.2 Two-branch transmit with two receive antennas scheme

96

Assuming that fading is constant across two consecutive symbols, it

can be written as,

( ) ( + ) = (4.7)

( ) ( + ) = (4.8)

( ) ( + ) = (4.9)

( ) ( + ) = (4.10)

where, T is the symbol duration.

The received signals can then be expressed as

+ (4.11)

+ (4.12)

+ (4,13)

+ (4,14)

The complex random variables, , , and represent the

receiver thermal noise and interference.

4.2.3.2 The Combining Scheme

The combiner builds the following two combined signals, which

are sent to the maximum likelihood detector

(4.15)

(4.16)

97

The combined signals seen above are equal to those obtained using

a four-branch MRRC. Hence, the diversity order obtained with the two

schemes is the same. Another property is that the combined signals of the

receive antennas are simply the addition of the combined signals from each

receive antenna, so it is possible to implement a combiner for each antenna

and then simply sum the output of each combiner.

4.3 CHANNEL MODEL

The Channel is a physical medium between the transmitter and

receiver. This channel results in the random delay or random phase shift of

the original signal. The AWGN channel model has been explained in the last

chapter. The Rayleigh and Rician fading channels can be modeled as follows:

4.3.1 Fading in Communication Channels

In wireless communication systems, the radio frequency signal

propagates from the transmitter to the receiver via multiple different paths,

due to reflectors existing in the wireless channel and the obstacles. These

multipaths are caused by the mechanisms of diffraction, reflection and

scattering from structures, buildings and other obstacles existing in the

propagation environment, as has been studied by Andersen et al (1995). As

shown in Figure 4.3, multipath propagation is described by the Line of Sight

(LOS) path and Non Line of Sight (NLOS) paths.

Figure 4.3 Multipath Propagation

98

When the mobile unit is considered far from the base station, there

is no LOS signal path, and reception occurs mainly from the indirect signal

paths. These multiple paths have different propagation lengths, and thus will

cause time delay, amplitude and phase fluctuations in the received signal. And

hence, the multipath propagation effect can be mainly described in terms of

delay spread and fading, as reported by Sklar (1997).

When the multipath signal waves are out of phase, the reduction of

the signal strength at the receiver can occur. This causes significant

fluctuations in the received signal amplitude, and leads to a phenomenon

known as multipath fading or small scale fading. A representation of

multipath fading is shown in Figure 4.4.

Figure 4.4 Representation of Multipath Fading

Rayleigh fading is also called Small-scale fading because if a large

number of multiple reflective paths is present, and there is no LOS signal

component, the envelope of the received signal is statistically described by the

Rayleigh distribution. When there is a dominant non fading signal component

present, such as an LOS propagation path, the small scale fading envelope is

described by the Rician distribution and, thus, is referred to as Rician fading,

which has been investigated by Rappaport (2002).

99

When the mobile unit is moving, there is a shift in the frequency of

the transmitted signal along each signal path, due to its velocity. This

phenomenon is known as the Doppler shift. Signals traveling through

different paths can have different Doppler shifts, corresponding to the

different rates of change in phase. The difference in the Doppler shifts

between different signal components contributing to a single fading signal

component, is known as the Doppler spread. Channels with a large Doppler

spread have signal components, that are each changing independently in

phase over time, as has been pointed out by Tse & Viswanath (2005). If the

Doppler spread is significant, relative to the bandwidth of the transmitted

signal, the received signal will undergo fast fading. On the other hand, if the

Doppler spread of the channel is much lesser than the bandwidth of the

baseband signal, the signal undergoes slow fading, as has been reported by

Shankar (2002). So, the terms slow and fast fading refer to the rate, at which

the magnitude and phase change imposed by the channel on the signal,

change. Because multiple reflections of the transmitted signal may arrive at

the receiver at different times, this can result in inter-symbol interference (ISI)

due to the crashing of bits into one another. This time dispersion of the

channel is called multipath delay spread, and is an important parameter to

assess the performance capabilities of wireless communication systems, as

has been stated by Manninen & Lempiainen (2002).

4.3.2 Modeling of Rayleigh Fading

As stated previously, Rayleigh fading results from the multiple Non

Line of Sight paths of the signal propagating from the transmitter to the

receiver. If the transmitted signal s(t) is assumed to be an unmodulated

carrier, then it can be written as:

( ) = cos (2 ) (4.17)

100

where, fc is the carrier frequency of the radio signal.

The received signal, after propagation over N scattered and

reflected paths, can be considered as the sum of N components with random

amplitude and phase for each component. Thus, when the receiving station is

assumed to be stationary, the received signal r(t) can be written as

( ) = cos (2 + ) (4.18)

where, ai is a random variable corresponding to the amplitude of the ith signal

component, and i is another uniformly distributed random variable,

corresponding to the phase angle of the ith signal component.

Using the trigonometric identity:

cos( + ) = cos .cos sin .sin (4.19)

equation (4.18) can be re-written in the form:

( ) = cos(2 ) . (2 ) . (4.20)

Equation (4.20) can be expressed as

r(t) =X.cos(2 ) -Y.sin(2 ) (4.21)

where,

= (4.22)

= (4.23)

X and Y can be considered as two identical and independent

Gaussian random variables when N tends to a large value. Equation (4.25)

represents the received Radio frequency signal, when the receiver is assumed

to be stationary. If the mobile unit is moving at a speed of v meters/second

101

relative to the base station, the received signal will acquire a frequency

Doppler shift. The maximum Doppler shift is given by

= (4.24)

The instantaneous frequency Doppler shift is dependent on

the angle of arrival of the incoming signal path component, as shown in

Figure 4.5.

Figure 4.5 A Mobile Unit Moving at Speed v

The instantaneous value of the Doppler shift fdi can be expressed as:

= (4.25)

where i is the angle of arrival for the ith path signal component.

On the other hand, the instantaneous frequency of the received RF

signal becomes:

= + cos (4.26)

Accordingly, the received signal can be expressed in the form:

( ) = cos (2 ( + ) + ) (4.27)

Equation (4.27) can alternatively be written in another form, using

the trigonometric identity (4.19):

102

( ) = cos (2 ). cos(2 + ) (2 ) . (2 + )

(4.28)

The received signal can also be formulated as:

( ) = cos(2 ) . ( ) sin(2 ) . ( ) (4.29)

where:

( ) = cos (2 + ) (4.30)

( ) = (2 + ) (4.31)

and = .

X(t) is the in-phase component, and Y(t) is the quadrature

component of the received signal. It is seen from equation (4.29) that the

received signal is like a quadrature modulated carrier. The envelope of the

received signal is given by:

( ) = [ ( ) + ( ) ] (4.32)

It can be shown that the probability density function (pdf) of the

envelope A(t) of the received signal is Rayleigh distributed, as has been

illustrated by Papoulis (1991).

The instantaneous power of the received signal is given by:

P(t) = X (t)2 + Y(t)2 (4.33)

On the other hand, the average value of the received power Pav is

the statistical mean of P(t):

103

Pav = mean[P(t)] = P(t) (4.34)

At the receiver side, the in-phase and quadrature components X(t)

and Y(t) can be obtained by demodulating the received signal r(t).

4.3.3 Modeling of Rician Fading

When the received signal consists of multiple reflective paths, plus

a significant LOS component, the received signal is said to be a Rician faded

signal, because the probability density function of the RF signal's envelope

follows Rician distribution, as has been illustrated by Couch (2001). The

received RF signal in this case can be written as:

( ) = . cos(2 ( + ) ) + cos(2 ( + ) + ) (4.35)

where KLOS -amplitude of the direct (LOS) component,

fd - frequency Doppler shift in the LOS path,

and fdi - frequency Doppler shift along the ith NLOS path signal component.

In terms of the in-phase and quadrature components, the received signal can be written as:

( ) = . cos(2 ( + ) ) + cos(2 ) . ( ) + sin(2 ) . ( ) (4.36)

where X(t) and Y(t) are the equations given by (4.30) and (4.31) respectively.

4.4 SYSTEM MODEL AND DESCRIPTION

Figure 4.6 presents the block diagram of the Alamouti STBC based

DS-CDMA communication system, with antenna diversity. The system model

can be explained as follows:

104

4.4.1 Transmitter Part

At the transmitter, the data generated from a random source,

consists of a series of ones and zeros. The Modulation process is used to

convert the data input bits into a symbol vector. The QPSK scheme is used to

map the bits to symbols. Then, these PSK symbols are the input to the STBC

encoder.

Modulation techniques are expected to have three positive

properties:

a. Good Bit Error Rate Performance

Modulation schemes should be able to achieve a low bit error rate

in the presence of fading, Doppler spread, interference and thermal noise.

b. Power Efficiency

Power limitation is one of the crucial design challenges in portable

and mobile applications. Power efficiency can be increased by using Non-

linear amplifiers. However, non-linearity may degrade the BER performance

of some modulation techniques. Constant envelope modulation techniques are

used to prevent the regeneration of the spectral side lobes during nonlinear

amplification

c. Spectral Efficiency

The power spectral density of the modulated signals should have a

narrow main lobe and fast roll-off of the side lobes. Spectral efficiency is

measured in units of bits/sec/Hz. The Walsh Hadamard codes are used for

spreading and despreading the modulated sequence. The spreading factors of

4,8 and 16 are used for spreading.

105

Figure 4.6 Block Diagram for the simulated Alamouti STBC based

CDMA system

The application of the STBC in the DS-CDMA multi-user

communication system is considered, and presented the simulation results for

the performance of DS-CDMA channels with STBC.

Figure 4.6 shows the transmitter and receiver models with two

transmit antennas at the base station and one receive antenna at the remote

unit, and two transmit antenna and two receive antennas at the receiver. In our

simulations, the output of each STBC was spread by the Walsh Hadamard

code of length 64. The spread signals from different users for the same

transmit antenna were summed up, before they were transmitted from

antennas 1 and 2 at the base station, respectively. A matched filter is used to

decorrelate the received signal. The output of the matched filter is fed to the

STBC decoder.

106

4.4.2 Signal Model for DS-CDMA Based on the Alamouti Scheme

Consider the discrete time complex baseband model for the

downlink channel of a single cell direct sequence CDMA system. As before,

there are K users in the system and the base station employs long spreading

codes. We consider the Alamouti transmit diversity scheme with two transmit

antennas, as shown in Figure 4.7.

Figure 4.7 Block diagram of the transmitter with the Alamouti scheme

Let bk[m] be the mth symbol of transmission to mobile station k,

independent and identically distributed (i.i.d.). It is assumed that the

quadrature phase shift keying signaling is used. That is, bk[m] {±1±j}.

Then, the outputs of the space time encoder, as has been reported by Alamouti

(1998), become:

( )[2 ] = [2 ] (4.37)

107

( )[2 + 1] = [2 + 1] (4.38)

( )[2 ] = [2 + 1] (4.39)

( )[2 + 1] = [2 + 1] (4.40)

where ( )[ ] is the data symbol from the transmit antenna i to the kth user.

From the Figure 4.7, it is observed that the same user spreading

sequence is used for the data symbol ( )[ ]. That is,

[ + ] = ( )[ + ] i=1, 2 (4.41)

[ + ] is the kth user long spreading sequence.

It is also assumed that the long spreading sequence is normalized

as | [ + ]| = .

For coherent combining and channel estimation at the receiver, two

different orthogonal pilot spreading sequences ( ( )[ ], = 1,2), with

different pilot symbols ( )[ ], = 1,2) can be transmitted through two

transmit antennas.

Assume that the complex channel attenuations associated with each

pair of transmit and receive antennas are time-invariant. Then, the received

signal at the jth receive antenna can be written as:

( )[ + ] = [ ] ( )[ + ] + ( )[ + ] (4.42)

where,

( )[ + ] = ( ) [ + ] + ( )[ + ]

108

( )[ + ] = ( )[ ] [ + ]

( )[ + ] = ( )[ ] ( )[ + ]

In the vector notation, J ×1 received signal vector can be written as:

[ ] = ( )[ ] + [ ] (4.43)

where the channel matrix Hi, the received signal vector r[n], the transmitted

signal vector u(i)[n], and the noise vector n[n] are given by

= , = 12, … … , (4.44)

where,

= ( [0] [1] … … . [ 1])

Furthermore,

[ ] = ( ( )[ ] … … ( )[ ] ) (4.45)

( )[ ] = ( ( )[ ] … … . ( )[ + 1])

[ ] = ( ( )[ ] … . ( )[ ])

where, ( )[ ] is the received signal at receive antenna J, and ( )[ ] is the

baseband transmission signal from transmit antenna i.

4.5 RESULTS AND DISCUSSION

The aim of this chapter is to review the performance of the DS-

CDMA system, using two different diversity schemes. For this, some

assumptions are made. The first assumption is that the total power transmitted

109

by the two antennas in the Alamouti scheme, is equal to the power that the

unique antenna in the MRRC scheme would transmit. Another assumption is

that fading along all the paths between the transmit and receive antennas is

mutually uncorrelated, and follows a Rayleigh distribution. Moreover, it is

supposed that the average power received in every single receive antenna is

the same, and that the receiver has a perfect knowledge of the channel.

4.5.1 Performance of Alamouti STBC (2 Tx & 1 Rx) based DS-

CDMA system over Rayleigh channel

Figure 4.8 shows the BER performance for the coded DS-CDMA

system using Alamouti’s STBC technique (nTx=2 & nRx=1) in the Rayleigh

fading condition. It is assumed that the receiver has a perfect knowledge of

the channel condition. It is clear that Alamouti’s STBC technique using two

transmitting antennas and one receiving antenna for the CDMA system, is the

same as that of the system which uses the Maximum ratio Combiner, using

two transmitting antennas and one receiving antenna. And both the schemes

are better than the typical DS-CDMA system.

It is also observed that transmit diversity has a 13 dB advantage at

BER of 10-3, when compared to the system without transmit diversity. If the

transmitted and received power for these two cases is the same, then the

performance would be identical. At a BER of 0.01, there is a 9 dB

improvement in the SNR obtained, as compared to that without Alamouti

diversity.

110

Figure 4.8 BER vs Eb/No for Alamouti STBC (2 Tx & 1 Rx) based DS-

CDMA system over Rayleigh fading channel

If the performance of the Alamouti scheme in diversity terms is

equal to that of the MRRC, why are the two-branch transmit Alamouti results

3dB under the MRRC? The reason is, one of the assumptions that have been

made, is that each antenna transmits half the power; so, in total, the power

radiated by the two antennas is the same as the power radiated by the single

antenna in of MRRC. If each of the antennas in the Alamouti scheme would

transmit the same power as the single antenna, the results would overlap. The

most important conclusion we can get from this graph is the fact, that the

Alamouti scheme provides the same performance as the MRRC, independent

of the codification and modulation used.

0 5 10 15 20 2510

-5

10-4

10-3

10-2

10-1

SNR (dB)

without AlamoutiWith MRCAlamouti nTx=2 nRx=1

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4.5.2 Performance of Alamouti STBC (2 Tx & 1 Rx) based DS-

CDMA system over Rician fading channel

Figure 4.9 presents a comparison of the performance of the typical

DS- CDMA system, the system using Maximal Ratio Combiner technique

and the CDMA system implementing Alamouti’s STBC technique.

Figure 4.9 BER vs Eb/No for Alamouti STBC (2 Tx & 1 Rx) based DS-

CDMA system over Rician channel

When Alamouti’s STBC technique is used for the CDMA system,

in the Rician fading channel, the performance drastically improves by around

8 dB at BER of 10-5 due to the presence of LOS component (direct path). This

0 5 10 15 20 2510-5

10-4

10-3

10-2

10-1

SNR (dB)

without AlamoutiWith MRCAlamouti nTx=2 nRx=1

112

means, that it will require less power to transmit for same BER for CDMA

system using Alamouti’s STBC technique. It can be explained alternatively,

that transmitting signals at the same power will give a better BER for the

CDMA system with Alamouti’s STBC technique, than for the typical CDMA

system. It is evident that Eb/N0 is decreased for the CDMA system, when

Alamouti’s scheme is used. The capacity of any system is inversely

proportional to Eb/N0, which indicates that the capacity increases while using

Alamouti’s scheme.

4.5.3 Performance of Alamouti STBC (2 Tx & 2 Rx) based DS-

CDMA system over Rayleigh fading channel

Figure 4.10 shows the BER performance for the coded DS-CDMA

system, using Alamouti’s STBC technique (nTx=2 & nRx=2) in Rayleigh

fading condition. Here, the BER plots are shown for both systems, with and

without the antenna diversity scheme. The BER of 10-3 is obtained for 3dB,

while considering Alamouti’s STBC technique (nTx=2 & nRx=2), whereas

the same BER is obtained for 11 dB with the MRC technique. And hence, an

8 dB improvement in SNR is obtained. While comparing it without the

Alamouti technique, a 21 dB SNR improvement is obtained, because at 24

dB, the BER of 10-3 is obtained.

The BER performance of the simulation result without the diversity

scheme is worse than that with the diversity scheme, and the BER

performance is improved dramatically in low SNR, but not in high SNR. In

low SNR, white Gaussian noise dominates the BER, which can be improved

by enhancing the SNR; but in high SNR, the error due to phase estimation

dominates the BER, which cannot be improved by simply enhancing the

SNR.

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Figure 4.10 BER vs Eb/No for Alamouti STBC (2 Tx & 2 Rx) based DS-

CDMA system over Rayleigh fading channel

4.5.4 Performance of Alamouti STBC (2 Tx & 2 Rx) based DS-

CDMA system over Rician fading channel

Figure 4.11 shows the simulated performance of the Alamouti

STBC technique (nTx=2 & nRx=2) in Rician fading channel. It shows the

performance from 0 dB to 25 dB where upto105 bits are transmitted. The BER

of 10-3 is obtained for 2.5 dB, while considering Alamouti’s STBC technique

(nTx=2 & nRx=2), whereas the same BER is obtained for 11 dB with the

MRC technique. And hence, 8.5 dB improvement in SNR is obtained. While

comparing it without the Alamouti technique, 21.5 dB SNR improvement is

obtained, because at 24 dB, the BER of 10-3 is obtained.

0 5 10 15 20 2510-5

10-4

10-3

10-2

10-1

SNR (dB)

without AlamoutiWith MRCAlamouti nTx=2 nRx=2

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Figure 4.11 BER vs Eb/No for Alamouti STBC (2 Tx & 2 Rx) based DS-

CDMA system over Rician fading channel

Table 4.3 shows that, in the presence of Rayleigh fading channel,

the BER of 0.0016 is achieved for the SNR value of 10 dB, using the

Alamouti STBC (nTx=2 & nRx=1) encoding, whereas the BER of 0.0014 is

achieved for the SNR value of 6 dB, using the same encoding technique in the

presence of AWGN and Rician channel. Thus, a lower BER is obtained when

Alamouti encoding is used.

0 5 10 15 20 2510

-5

10-4

10-3

10-2

10-1

SNR (dB)

without AlamoutiWith MRCAlamouti nTx=2 nRx=2

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Table 4.3 BER values of STBC DS-CDMA system for the above two

schemes upto SNR values of 10 dB

SNR(dB)

nTx=2 & nRx=1 nTx=2 & nRx=2

Rayleigh fading

channel

Rician fading

channel

Rayleigh fading

channel

Rician fading

channel

0 0.0581 0.0352 0.0055 0.0043

1 0.0440 0.0235 0.0033 0.0024

2 0.0328 0.0145 0.0018 0.0013

3 0.0239 0.0086 0.0010 0.0007

4 0.0169 0.0049 0.0005 0.0004

5 0.0118 0.0027 0.0003 0.0002

6 0.0081 0.0014 0.0001 0.00009

7 0.0055 0.0007 0.00008 0.00007

8 0.0037 0.0004 0.00006 0.00005

9 0.0025 0.0002 0.000032 0.00002

10 0.0016 0.0001 0.000014 0.0000098

Also from Table 4.3, in the presence of Rayleigh fading channel,

the BER of 0.0003 is achieved for the SNR value of 5 dB using Alamouti’s

STBC (nTx=2 & nRx=2) technique, whereas for the SNR of 4 dB in the

presence of Rician fading channel, the BER value is .0004.

In the presence of Rayleigh channel, the BER of 0.001 is achieved for the

SNR value of 3 dB using Alamouti’s STBC, whereas for the SNR of 2 dB in

the presence of Rician channel, the BER value is .0013. Hence 1 dB

improvement in the SNR is obtained when compared to the Rayleigh channel

due to the presence of line of sight component in Rician fading channel.

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4.5.5 Performance comparison of extended Alamouti STBC based

DS-CDMA system over Rician fading channel

Figure 4.12 shows the BER performance for the coded DS-CDMA

system, using multiple antennas of Alamouti’s STBC technique in AWGN

and Rician fading condition. Here, the BER plots are shown for three different

cases, with various number of receiving antenna diversity. The BER of 10-4 is

obtained for 6 dB, while considering Alamouti’s STBC technique (nTx=2 &

nRx=2), whereas the same BER is obtained for 2 dB and 1 dB for (nTx=2 &

nRx=4) and (nTx=2 & nRx=6) respectively. And hence, 4 dB to 5 dB

improvement in SNR is obtained. While comparing it without the Alamouti

technique, 18 dB SNR improvements is obtained, because at 24 dB, the BER

of 10-3 is obtained.

Figure 4.12 BER vs Eb/No comparison of extended Alamouti STBC

based DS-CDMA system over AWGN and Rician channel

0 1 2 3 4 5 6 7 8 9 1010-6

10-5

10-4

10-3

10-2

SNR(dB)

Alamouti based DS-CDMA nTx=2 nRx=2Alamouti based DS-CDMA nTx=2 nRx=4Alamouti based DS-CDMA nTx=2 nRx=6

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Table 4.4 BER values of STBC DS-CDMA system for the three different

diversity schemes upto SNR values of 10 dB

SNR(dB)

BER values in the presence of AWGN & Rician channel

nTx=2 & nRx=2 nTx=2 & nRx=4 nTx=2 & nRx=6

0 0.004 0.000585 0.000251 0.0024 0.000345 0.0001352 0.0012 0.000145 0.000063 0.0007 0.000095 0.000024 0.0004 0.000065 0.000015 0.0002 0.000015 0.0000056 0.0001 0.00001 0.00000167 0.00004 0.000005 0.00000028 0.00001 0.0000025 0.00000005

9 0.000005 0.0000014 0.00000003

10 0.000001 0.0000004 0.000000012

From Table 4.3, in the presence of Rician and AWGN channel, the

BER of 0.000005 is achieved for the SNR value of 9 dB using Alamouti’s

STBC (nTx=2 & nRx=2) technique, whereas the same BER is obtained for

the SNR of 7 dB and 5 dB when receiver diversity increases as 4 and 6

respectively. Similarly, BER rate of 0.0002 is obtained for 5 dB while

Alamouti’s STBC (nTx=2 & nRx=2) technique is assumed. Approximately,

the same BER is obtained for 2 dB and 0 dB respectively for receiver

diversity increases from 4 to 6. Hence, a maximum of 5 dB improvement in

the SNR is obtained when receiver diversity increases from 2 to 6.

4.5.6 Capacity Analysis

Determining the capacity of the communication channel is very

important in order to satisfy the quality of service requirements. Capacity

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determines the maximum limit of data that can be transmitted over the

channel. ‘‘Shannon defined capacity as the mutual information maximized

over all possible input distributions’’.

The main theoretical aspect of MIMO is one of channel capacity. The

Shanon’s capacity theorem for a simple RF channel is:

= (1 + ) (4.46)

where C= capacity (bits/s), B=bandwidth (Hz), N= signal to noise ratio.

The above capacity equation is widely used and refers to a system with

one transmitter and one receiver (with possibly added diversity, but ultimately

combined into one receiver); now we consider a system of N × M

antennas: N transmitters, and M receivers.

The H-matrix is a matrix [Hij] defines complex throughput correlation

parameters (with amplitude and phase) from each transmit antenna i to each

receive antenna j. The new capacity equation for MIMO systems is

= 1 + ( ) (4.47)

where n is the number of independent transmit/receive channels (which

is no greater than min(N,M)), and reflects the number of sufficiently

uncorrelated paths, Si are the signal power in channel i, N- the noise power,

and i2(H) are singular values of the H matrix.

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Figure 4.13 MIMO capacity: capacity curves versus average SNR at receiver;

M = MR=MT

Figure 4.13 shows the performance of the MIMO system in which

SNR and Capacity are considered. In the above figure four different numbers

of receiving antennas are considered. Figure 4.13 shows that as the SNR

increases the capacity also increase, so at 20 dB SNR the capacity for nTx=

nRx = 6 is 35 bits/s/Hz. Figure 4.13 implies that the Shannon channel

capacity for the higher SNR is higher than the case of low values of SNR,

which means that the system operating in higher SNR has more ability to

admit new users without any disconnection in the service for the old users.

The channel capacity difference between the five cases becomes larger after a

12 dB SNR, the Figure 4.13 also shows that at a lower SNR values the five

curves is relatively close to each other.

When the Alamouti based CDMA system is compared with the work

reported by Ahlen (2002), 4G IP based wireless systems, the spectral

2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

35

SNR(dB)

MIMO Capacity

Shannon CapacityMIMO, nTx=nRx=2MIMO, nTx=nRx=4MIMO, nTx=nRx=5MIMO, nTx=nRx=6

120

efficiency difference for single user is 4.8 bps/Hz is obtained. So as the

number of user increases, the spectral efficiency also increases

correspondingly. And also when compared with the capacity of wireless

system, there is a gradual increase in spectral efficiency at each and every

points of SNR value.

4.6 CONCLUSION

In this chapter, the STBC DS-CDMA system has been

implemented and analyzed. Using the analytical and simulation approach, it

has been shown that using the STBC in the DS-CDMA system is

advantageous over the traditional CDMA system, including a better BER

performance and lower complexity. Both the schemes in AWGN channel,

Rayleigh Fading channel and Rician Fading channel have been analyzed. The

Alamouti scheme has been used as the antennal diversity. It has been

observed that the BER performance of the system is improved with antenna

diversity schemes.

The simulation results show that the BER performance is better,

using the Alamouti scheme under the Rician fading channel, whereas it is

worse under Rayleigh fading channel. The channels perform in the following

order, in terms of the best (less SNR requirement) to the worst (more SNR

requirement) to maintain the required BER: AWGN, Rician and Rayleigh.

The main conclusions of this chapter are as follows:

1. With two transmit antennas and one receive antenna, the Alamouti technique is comparable to the MRRC, with two receive antennas and one transmit antenna, in terms of diversity.

121

2. Using the receive diversity results in larger performance gain than using additional transmit antennas.

3. When there is a strong line-of-sight component available, signal fading is negligible and space-time coding will not provide any performance gain.

4. A 3 dB of disadvantage from the BER performance in comparison with the MRRC, is obtained. That is because each antenna transmits half the power in order to maintain the total radiated power.

5. Generalisation can be done by adding more receive antennas. In this case, the diversity order reaches up to 2N.

6. Low computation complexity, similar to MRRC.

7. Soft fail advantages, and multiple transmission branches assure communication, when one of them is disrupted.