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
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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
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.