Int. J. Communications, Network and System Sciences, 2010, 3, 418-424
doi:10.4236/ijcns.2010.34054 Published Online April 2010 (http://www.SciRP.org/journal/ijcns/)
Copyright © 2010 SciRes. IJCNS
Comparative Study of Different Space-Time Coding
Schemes for MC-CDMA Systems
Lokesh Kumar Bansal1, Aditya Trivedi2
1Department of ECE, Nikhil Institute of Engineering and Management, Mathura, India
2Department of Information and Communication Technology, ABV-Indian Institute of Information Technology and
Management, Gwalior, India
Email: lokesh_bansal@rediffmail.com, atrivedi@iiitm.ac.in
Received January 5, 2010; revised February 9, 2010; accepted March 10, 2010
Abstract
In this paper, performance of space-time trellis-code (STTC), space-time block code (STBC), and space-time
trellis-code concatenated with space-time block code (STTC-STBC) for multi-carrier code-division multi-
ple-access (MC-CDMA) system are studied. These schemes are considered by employing different detection
techniques with various multi input multi output (MIMO) antenna diversity for different number of states in
multi-path fading channel. The corresponding bit error rate (BER) is obtained using simulation for minimum
mean-square error (MMSE), maximum-ratio combining (MRC), and equal-gain combining (EGC) receivers
employing Viterbi decoder. The simulation results show that the STTC-STBC MC-CDMA system perform
better compared to other schemes considered in this paper using MMSE detection and it is also observed that
the performance can also be enhanced by increasing diversity using more transmitter and receiver antennas.
However, this improvement in performance comes at the cost of increased computational complexity, which
is calculated for different transmitting and receiving antennas.
Keywords: Space-Time Code, Space-Time Trellis-Code (STTC), Space-Time Block-Code (STBC), MIMO,
MMSE, Multi-Path Channel
1. Introduction
Cellular services are now being used every day by mil-
lions of people worldwide and the demand is increasing
exponentially. Also, there is a demand for integration of
a variety of multimedia services namely short messaging,
voice, data, and video. Consequently, the bit rate is requ-
ired to vary from 1.2 kbps for paging to several Mbps for
video transmission. The data rate of the second genera-
tion is limited up to 9.6 kbps [1].
The third generation cellular systems are being de-
signed to support wideband services like high-speed int-
ernet access, video and high quality image transmission
with the same quality as the fixed networks. The third
generation can provide the maximum data rate ranging
from 64 kbps for mobile users to 2 Mbps for stationary
users. The drawbacks arising in the third generation sys-
tem are the limitations of data rate, capacity, inter sym-
bol interference (ISI), and inter chip interference (ICI).
For solving the problems of third generation wireless
communication systems, and fulfilling the demand of hi-
gh performance and broadband internet access with high
spectrum efficiency, the fourth generation systems which
may employ multi-carrier code-division multiple-access
(MC-CDMA) technology in combination with multi-in-
put multi-output (MIMO) antennas are proposed [2]. In
the fourth generation wireless communication systems
the data rate may be as high as 1Gbps. Space-time cod-
ing techniques may be employed in conjunction with the
MC-CDMA system to achieve very high data rate [3,4].
In this paper, the space-time trellis-code (STTC), spa-
ce-time block code (STBC), and space-time trellis-code
concatenated with space-time block code (STTC-STBC)
techniques are studied and applied in multi-carrier code-
division multiple-access (MC-CDMA) systems. These
techniques are considered with multi input multi output
(MIMO) antenna diversity in multi-path fading channel.
The bit error rate (BER) is obtained for 4, 8, and 16 states
using simulation. At the receiver side minimum mean-
square error (MMSE), maximum-ratio combining (MRC),
and equal-gain combining (EGC) techniques are used by
employing Viterbi algorithm.
The organization of the rest of this paper is as follows:
in Section 2, MC-CDMA systems and the space-time
L. K. BANSAL ET AL. 419
code techniques are presented. In Section 3, the mathe-
matical representation for the space-time trellis code
(STTC) MC-CDMA system is described. In Section 4,
the STTC concatenated with STBC (STTC-STBC) MC-
CDMA system is discussed. The MMSE detector is dis-
cussed briefly in Section 5. Simulation of the error rate
performance of STTC-MC-CDMA systems, STBC- MC-
CDMA systems, and STTC-STBC MC-CDMA systems
for different states with computational complexity is car-
ried out in Section 6. The conclusions are presented in
Section 7.
2. MC-CDMA and Space-Time Code
Systems
Multi-carrier modulation is being proposed for fourth
generation wireless communication systems for high data
rate application to reduce the effect of ISI. These systems
solve the ISI problem by transmitting the same data
symbol over a large number of narrow band orthogonal
carriers [5].
An MC-CDMA signal is composed of N narrowband
sub-carrier signals each with symbol duration, Tb, much
larger than the delay spread of the channel, Td, hence
MC-CDMA signal does not experience significant ISI.
Multiple accesses is achieved with different users trans-
mitting at the same set of sub-carriers but with spreading
codes that are different to the codes of other users.
Initially, the data stream is serial to parallel converted
to a number of lower rate streams. Each stream feeds a
number of parallel streams with the same rate. On each
of the parallel streams, bits are interleaved and spread by
a PN code with a suitable chip rate. Then, these streams
modulate different orthogonal carriers with a succes-
sively overlapping bandwidth [6,7].
In recent years, antenna systems which employ multi-
ple antennas at both the base station (BS) and mobile
station (MS), have been proposed and demonstrated to
significantly increase system performance as well as ca-
pacity [8]. The merit of using multiple antennas or space
diversity is that no bandwidth expansion or increase in
transmitted power is required for capacity and perform-
ance improvements.
Space-time (S-T) coding is a technique designed for
use with multiple transmits antennas. There are various
approaches in coding structures, which include Alamouti
space-time code (STC), space-time block code (STBC),
space-time trellis code (STTC), space-time turbo trellis
codes (STTTC), and layered space-time (LST) codes.
STC with multiple transmit and receive antennas mini-
mizes the effect of multi-path fading and improves the
performance and capacity of digital transmission over
wireless radio channels [9,10].
STBC can achieve a maximum possible diversity ad-
vantage with a simple decoding algorithm. It is very at-
tractive because of its simplicity. However, no coding
gain can be provided by STBC. Tarokh, Seshadri, and
Calderbank first introduced STTC. STTC are able to
combat the effects of fading. However, STTC have a
potential drawback due to the fact that its decoder com-
plexity (maximum likelihood) grows exponentially with
the number of bits per symbol [1].
3. STTC-MC-CDMA System Model
Trellis Coded Modulation (TCM) is a bandwidth effi-
cient technique that combines coding and modulation,
without reducing the data rate. STTC-MC-CDMA sys-
tem provides coding gain and diversity. Figure 1 shows
the general block diagram of space-time coded MC-
CDMA system. In this, the space-time trellis encoder
encodes the source data; next the encoded data is inter-
leaved, and then mapped according to the desired signal
constellation. Finally, the space-time trellis encoded data
symbols are modulated at each time interval, and trans-
mitted simultaneously over different transmit antennas.
At the receiver, the received data is combined accord-
ing to the different combining techniques described for
MC-CDMA systems. The soft output of the combiner is
sent to the deinterleaver and then finally it is applied to a
space-time Trellis decoder, employing Viterbi algorithm
to decode the data [11,12].
At the transmitter, K users transmit simultaneously the
space-time trellis coded information symbols from the
two transmit antennas. The frequency selective channel
between transmit and receive antennas is divided into Q
subchannels such that each subchannel is approximately
flat. For the kth user, let the input message sequence ,
is given by,
k
A
 
123
kkkkk
n =,,,...,n ,...Aaaaa (1)
where
kna
n
is a group of information
bits at time and given by,
Mm 2
log
123 m
kkkk
n=a ,a,a ,...,aak
(2)
The encoder maps the input stream into an M-ary PSK
modulated signal sequence, which is given by,
nX
be the ST-Trellis encoded output. For the kth user, the
output of ST-Trellis encoder, which is modulated by
MC-CDMA system, is represented by the following code
matrix:
 
=0,1 ,3,...,,...
kkkkk
nnXxxxx (3)
where
knx is a nth STT coded symbol and is given
by,
 
12
, ,...,
TT
T
nn
kkkk
nxnxn xnx (4)
 
T
n
12
kk k
x
n ,xn ,...,xn , are The modulated signals,
Copyright © 2010 SciRes. IJCNS
420 L. K. BANSAL ET AL.
through transmit
and
be two ading codes for user k withocessing gain
ter the
(5)
For the ST-MC-CDMA
su
transmitted simultaneously an-
tennas. Here each user is assigned two dtinct spreading
codes to spread symbols transmitted from the two anten-
nas. Let
T
n
is
c
c
pr
qu
 
1111
0,1 ,...,1T
kkkk
pc cp


c
 
222 2
0,1,.....,1T
kkk k
pc cp



c
spre
p which spread user k’s symbols transmitted from Tx1
d Tx2, respectively, where

.Tdenotes vector/matrix
transpose.

n
1
k
u is defined as the signal associated
with Tx1 af spreading. Then, we have
 
111
kkk
n=x nuc
an
system under study, we as-
me that the numbers of subcarriers equal to the proc-
essing gainp. Each element in

n
1
k
u is then modu-
lated onto a b-carrier with centerency at

su fre
p
-1
p
=0
,
which is common for all K users. The MC-C
modulation can be implemented by the inverse fast Fou-
rier transform (IFFT) (consequently, the received signal
can be demodulated by FFT). Performing p-point IFFT
on

n
1
k
u yields

n=
1
kk
z
DMA

-1
F nu
1
(6)
where
1
F
denotes the
froasso
Following the same procedurthe signal
as
pp IFFT matrix. The contri-
butionsm all K users ciated with Tx1 are given
by the superposition
1
Z
 
K
1
k
k=1
n= n
z.
e, we obtain
sociated with Tx2 as
2nZ. Both
1nZ and
2nZ are converted into asequencee be-
nsmitted through the frequency selective channels
[13-15].
For the forward link, let J be the number of resolvable
pa
serial s befor
ing tra
7)
where we pad with zeros
(8)
where
ths. If we model the common channel between Tx1
and Rx for all K users as a FIR filter with coefficients:

110 T
pJ
=h0,....,hJ-,


h (
1
h
e
p-J
onse
to make its total
length p, its frequncy resp is then given by
 
11 0 ,....,1T
Fg gp 


gh
denotes the
pp
×
FFT ix
we defithe FIR cha
matr
with length
. Similarly,
, and its
oncy respcorrespding frequenonse between Tx2 and Rx
as 2
h and 2
g
, respectively.
 
K
111
kk
=x n
Yg
ne nnel, also
J
 
 
1
=n+n
2 22
k k
kk
n+xn +ng
CHx v
K
k=
1
k=
v
(9)
we her

112
kkk
ag,=diagφcφc
2
k
(10) =di
kk
12
k
=,
Cφφ , (11)
1
2
0
=0
Hg
g
, (12)

kk
k
n
 
12
,T
xnxn
x
and where

01p-
n =vn ,....,vn
T
v
p
n
σ
r
y, ho
(STTC
he
contains sam
and va
e dive
versit
les of the channel noise with zero-mean
riance. At the receiver, the received signals
m
m
to achi-
rsitwever there is not much significant cod-
-STBC) also provides coding gain. As
sh
BC. The
so
A systems (without transmit
iy), tdemodulated signals are often combined in
Typical signal combining schemes include the maximum
2
are first converted into parallel format and demodulated
via FFT transfo and then applied to deinterleaver. The
interleaved data is applied to MMSE detector and then
for ST-Trellis decoder for demodulation.
4. STTC-STBC MC-CDMA Syste
Space time block coding is a simple technique
ev
ing gain. An outer channel code is required to yield cod-
ing gain.
Space time trellis code concatenated with space time
block code
own in Figure 1, first the STTC encoder encodes the
source data. Next, the encoded data is applied to S-T
block encoder & interleaver, and then mapped according
to the desired signal constellation. Finally at each time
interval, the symbols are modulated and transmitted si-
multaneously over different transmit antennas.
At the receiver, the received data is combined accord-
ing to the combining techniques described for ST
ft output of the combiner is sent directly to the deinter-
leaver, and then finally, it is applied to a STTC decoder,
such as the Viterbi algorithm, to decode the data.
5. MMSE Detection
In conventional MC-CDM
d
the frequency domain in order to collect the overall re-
ceived signal energy scattered on different subcarriers.
Copyright © 2010 SciRes. IJCNS
L. K. BANSAL ET AL. 421
Copyright © 2010 SciRes. IJCNS
(a) Transmitter
(b) Receiver
Figure 1. General block diagrcoded MC-CDMA system.
ratio combining (MRC) an
GC). Both MRC and EGC are single-user detection
am of S-T
nY
d the equal gain combining By applying on
1
W;
(E
(
1
)
()
M
MSE n
'
1
DWY
(19)
The output of the MMSE detect
Viterbi decoder for decoding ST
data is then compared with origin
schemes based on per-subcarrier combining, i.e. the sig-
nals at individual subcarrier are independently weighted
and summed to generate decision variables. In [16], a
linear multiuser minimum mean-squared error (MMSE)
detector for the STC-MC-CDMA systems is presented
which performs joint weighting and combining on all
subcarriers by utilizing the mean-squared error (MSE)
criterion. We consider the two demodulated symbols at a
time. Define

11
diag= ,G
g
(13)
or is employed to
TC data. This decoded
al transmitted sequence
kn for findibit erre (B
ang or ratER) [17,18].
6. Simulation Results
CDMAfferent
mbinations of diversity for K = 5 users. The user sym-
energy BPSK (binary phase
Walsh-Hadamard codes with
The simulation is done for STBC MC-CDMA systems,
STTC MC-CDMA systems, and STTC-STBC MC-
systems for 4, 8, and 16 states with di
1
1k
= ,...,cc (14)
co
And let and be t
(15)
2
G2
he counterpart of 1
Gand bols are drawn from a unit-
ift keying) constellation.
1
respectively, which are associated with Tx2.
1 22
2*21* 1
=-




G
SGG
sh
1

Gprocessing gain P=Q=32 are used for spreading.
We assume a rich scattering environment and generate
the FIR channel coefficients as i.i.d. complex Gaussian
random variables with zero mean and variance 1/M
[15]. The SNR (signal to noise ratio) is defined as
'2
z
n
=+σ
R
SSI (16)
11
1
zb1 2*21* 1
11
=-

Gc
RGcGc
2 2
1
Gc (17)
10 2
1
10log
n
SNR
in dB.
-1
z
zb1
=
1
WRR (18) In Table 1 we present the bit error rate (BER) of
422 L. K. BANSAL ET AL.
pendent trials are taken for each SNR and their average
is plotted. This taows the BER of two stan-
dard single-usersity 2 × 1 employing
M
iff
BER
MMSE detector for different states of STTC-MC-CDMA
systems versus the SNR in a Rayleigh fading environ-
ment for K = 5 users and 10000 bit sequences. 100 inde-
ble is also sh
er signals combining schemes (MRC and
EGC) for comparison. From Table 1, it is concluded that
the MMSE detector outperforms the single-user signals
combining schemes in known channel. This is due to the
reason that EGC/MRC is basically single user detection
techniques and is not able to effectively suppress the
MAI as compared to MMSE detector. Here, we have also
studied the BER performance of the MMSE detector for
the STTC-MC-CDMA system with the different states of
STTC-MC-CDMA systems.
Table 2 show the performance of STBC MC-CDMA
Table 1. Comparison with d
systems, STTC MC-CDMA systems, and STTC-STBC
MC-CDMA systems for div
MSE detector. Simulations results are also shown in
Figures 2, 3 and 4 for MIMO antenna systems. With all
these simulations it is noted that the performance gain
can be enhanced up to around 5 dB at 10-3 BER by in-
creasing the diversity from 2 × 1 to 2 × 3 in 16 states
STTC-STBC MC-CDMA systems with MMSE detector
as shown in Figures 5, 6 and 7.
erent detection techniques.
SNR STTC-MC-CDMA
Using MRC Detect
STTC-MC-CDMA STTC-MC-CDMA
g MMSE Detection ion Using EGC Detection Usin
4-State 8-State 16-State 4-State 8-StaState 4-State 8-State 16-State te 16-
0 0.3568 0.3743 0.3882 0.2552 0.30 0.4053 0.3101 0.3648 0.3978 97
2 0.3255 3389 0.1802 0.3454 0.2448 3236
4 0.2967 2703 0.1025 2649 0.1618 2072
0.
0.2748 0.
0.3262 0.2143 0.2849 0.
0.1764 0. 0.1260 0.
6 0.2692 0.2246 0.1993 0.0497 0.0541 0.1712 0.0756 0.0706 0.0823
8 0.2533 0.1777 0.1412 0.0171 0.0180 0.0901 0.0208 0.0159 0.0170
10 0.2390 0.1432 0.0996 0.0043 0.0036 0.0402 0.0025 0.0014 0.0015
. Cson werent sche
E D
Table 2ompariith diff codingmes.
BER Using MMSetection
STTC-MC-CDMA STTC-STBC-MC-CDMA
SNR
STBC-MC-CDM
4-State
A
4-State
0 0.0606 0.0684 0.2680
2 0.0191
4
0.1853 0.0174
0.0025 0.0996 0.0020
0 2 46 810 12
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR(dB)
BER
MMSE 4STTC MCCDMA R1
MMSE 4STTC MCCDMA R2
MMSE 4STTC MCCDMA R3
0246810 12 14
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR(dB)
BER
MMSE 8STTC MCCDMA R1
MMSE 8STTC MCCDMA R2
MMSE 8STTC MCCDMAR3
Figure 3. BER performance for 8 states STTC-MC-CDMA
system using 2 Tx and 1, 2, & 3 Rx antennas.
Figure 2. BER performance for 4 states STTC-MC-CDMA
system using 2 Tx and 1, 2, & 3 Rx antennas.
Copyright © 2010 SciRes. IJCNS
L. K. BANSAL ET AL. 423
0 2 46 81012
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR(dB)
BER
MMSE 16STTC MCCDMA R1
MMSE 16STTC MCCDMA R2
MMSE 16STTC MCCDMA R3
Figure 4. BER performance for 16 states STTC-MC-CD-
MA system using 2 Tx and 1, 2, & 3 Rx antennas.
0246810 12 14
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR(dB)
BER
MMSE 4STTC MCCDMA R2
MMSE 8STTC MCCDMA R2
MMSE 16STTC MCCDMA R2
Figure 5. BER performance for 4, 8, & 16 states STTC-MC-
CDMA system using 2 Tx and 2 Rx antennas.
0123456
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
SNR(dB)
BER
MMSE 4STTC-STBC MCCDMA R3
MMSE 8STTC-STBC MCCDMA R3
MMSE 16STTC-STBC MCCDMA R3
re 6. BER performance for 4, 8, & 16 states STTC-
STBC MC-CDMA system using 2 Tx and 3 Rx antennas.
Figu
0 1 2345 6 78910
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR(dB)
BER
MMSE 16STTC-STBC MCCDMA R1
MMSE 16STTC-STBC MCCDMA R2
MMSE 16STTC-STBC MCCDMA R3
Figure 7. BER performance of 16 states STTC-STBC MC-
CDMA system using 2 Tx and 1, 2, & 3 Rx antennas.
6.1. Computational Complexity Calculations
Computational complexity in decoding is an important
issue. Viterbi algorithm is used to decode the actual trel-
lis codeword. The numeric computational complexity
involved is calculated as follows.
Consider L= 2v is the number of states where v is the
number of delay elements in the STTC encoder. The
number of operations for multiplication/division are
{
12
L
RT
nn
tions/ subtract
}, comparisons are {}, and addi-
ions are {2
21
L
1]

[1
L
RT
nn
ber of transm
 }.
it
It may be
is the numting and noted that T
n
R
n is
the number of receiving antennas.
For example the numeric computational complexity
for 4 states, 2 transmitter and 2 receiver antennas are:
Multiplication/Division are
=

12
L
RT
nn=96; (20)
Comparisons are == 15; (21)
& Addition/Subtraction are
= ]2
21
L

[11
L
RT
nn = 80 (22)
Compare to one receive antenna the no. of multiplica-
tion/division operations involved are two times (as evi-
dent from Equation (20)). However, the improvement in
the performance is approximately 2 dB at 10-3 probability
of error employing MMSE detection as shown in the
simulation results. This demonstrates the tradeoff in-
volved in computational complexity and performance
improvement.
this paper, BER performance for STBC-MC-CDMA
7. Conclusions
In
Copyright © 2010 SciRes. IJCNS
424 L. K. BANSAL ET AL.
Copyright © 2010 SciRes. IJCNS
BC
C-CDMA systems is evaluated using simulation for
r sc
l the schemeease
ty. In particular,
S
ity
wned in this paper.
8. References
erbank, “Space-
rate Wireless Communication:
Performance Criterion and Code Const
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M
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evaluation of the multi transmit multi receive antenna
systems employing Viterbi decoding.
It is noted that the performance of STTC–STBC
MC-CDMA system using MMSE detector is better than
othehemes considered in this paper. Performance of
als improves with the incr in number of
states and antenna diversi it is observed
that STTC-STBC MC-CDMA systems using MMSE
detector gives advantage of around 5 dB in terms ofNR
while increasing diversity from 2 × 1 to 2 × 3, 16 states
and at 10-3 BER. This improvement in performance is
no computational complexted at the cost of increased
hich is calculated and mentio
Rim
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