Multipath fading and spectral crowding are the major challenges in dealing higher data rate in future broadband wireless communication system. Multi-carrier Modulation like Multicarrier code division multiple access (MC-CDMA) can tackle the problem and provide higher data rate for future wireless communication system. However, through a frequency selective fading channel, the subcarriers in MC-CDMA signal have different amplitude levels and phase shifts which result in loss of the orthogonality among users and generates Multiple access interference (MAI). To combat the MAI, various amplitude and phase equalizing techniques such as Maximum Ratio Combining (MRC), Equal Gain Combining (EGC), Orthogonal Restoring Combining (ORC), Threshold Orthogonal Restoring Combining or Minimum Mean Square Error (MMSE) may be used. Out of these MMSE offers better performance since the MMSE criterion is applied independently on each subcarrier. Further improvement in performance is possible through space–time block coding, which offers maximum diversity gain and multiplexing gain. This paper combines MC-CDMA with MMSE equalization and space–time block coding which proves to be a powerful physical layer solution in combating delay spread and inter symbol interference (ISI).

1. Short Paper
©2011ACEEE
DOI:01.IJRTET.06.02.
Int. J. on Recent Trends in Engineering and Technology, Vol. 6, No. 2, Nov 2011
233
PerformanceoftheMIMO-MC-CDMASystemwith
MMSE Equalization
N. Tamilarasan1
, L. Nithyanandan2
1
Assistant Professor – Sri Ganesh College of Engineering and Technology,
Puducherry. Email: neithalarasu@gmail.com
2
Associate Professor - Pondicherry Engineering College,
Puducherrry
Abstract—Multipath fading and spectral crowding are the
major challenges in dealing higher data rate in future
broadband wireless communication system. Multi-carrier
Modulation like Multicarrier code division multiple access
(MC-CDMA) can tackle the problem and provide higher data
rate for future wireless communication system. However,
through a frequency selective fading channel, the subcarriers
in MC-CDMA signal have different amplitude levels and phase
shifts which result in loss of the orthogonality among users
and generates Multiple access interference (MAI). To combat
the MAI, various amplitude and phase equalizing techniques
such as Maximum Ratio Combining (MRC), Equal Gain
Combining (EGC), Orthogonal Restoring Combining (ORC),
Threshold Orthogonal Restoring Combining or Minimum
Mean Square Error (MMSE) may be used. Out of these MMSE
offers better performance since the MMSE criterion is applied
independently on each subcarrier. Further improvement in
performance is possible through space–time block coding,
which offers maximum diversity gain and multiplexing gain.
This paper combines MC-CDMA with MMSE equalization
and space–time block coding which proves to be a powerful
physical layer solution in combating delay spread and inter
symbol interference (ISI).
Index Terms—MC-CDMA, MIMO, Equalization, MMSE, ISI.
I. INTRODUCTION
To meet continuing growth of the customer demand in
wireless communication it is necessary to use available
spectrum efficiently to the extent possible. The combination
ofmulticarrier modulation and code-division multiple-access
schemes can offer good spectral efficiency, high data rate
transmission, multiple access and interference rejection
capabilities as well as robustness against multipath
propagation. Its basic principle is that the total transmission
bandwidth is divided into many narrowband sub channels,
and each data symbol is spread in the frequency domain.
ISI caused by multipath fading of wireless channels lead
to distortion of signal, causing bit errors at the receiver. ISI
has been recognized as the major obstacle to high-speed
data transmission over wireless channel. Equalization is a
technique to combat ISI [1-3]. Several combining and
equalization techniques for MC-CDMA signals have
appeared in the literature [4-7]. As analyzing is done in the
down-link of a cellular radio system and the computation is
made in the mobile unit, a lowcomplexityscheme is required.
In single user communication system, conventional EGC and
MRC can achieve better performance in Gaussian and
Rayleigh fading channels, respectively. However, in a multi-
access MC-CDMA system, frequency diversity reduces the
orthogonality of spreading codes and results in the MAI [8].
Since in downlink, the system is assumed to be synchronous,
the information associated with different users undergoes
the same channel effect. However, at the receiver side, the
orthogonality between spreading sequences is degraded by
the fading or noise. Hence, the choice ofequalization becomes
a critical point impacting the trade-off between the residual
amount of multiple access interference and the increase in
thermal noise.
S. Kaiser [1], has derived the approximation of the bit
error rate(BER) for MC-CDMAwith MRC, EGC andMMSE.
However, it is based on the law of large numbers; the
spreading code length must be sufficiently large. In [4], the
BERperformanceofMC-CDMAwith MRCand EGChasbeen
simulated over a Rayleigh fading channel with correlated
envelopes and phases. However, it is observed that both
EGC and MRC have very poor performance due to
orthogonality loss between the spreading sequences. The
orthogonality loss results in a high error floor making these
techniques difficult for practical use. In addition, K. Zhang
and Y.Guan [5], proposed a lower bound and a tight
approximation on the BER of MC-CDMA with ORC. When
ORC is used, the error floor is eliminated but the error
probabilityis still poor especiallyat low signal to noise ratio
due to the noise enhancement.
Among the various equalization methods for MIMO and
MC-CDMA, MMSE is considered to be a good solution for
data recovery since it can effectivelyreduce the ISI and utilize
the diversity of the frequency-selective channel [9]. As
mentioned before, however, most of the results are
concentrated on MRC and EGC, and the analytical results on
MMSE are well matched onlywhen the spreading code length
is sufficiently large [1]. In addition, in the channel-coded
system, a large spreading code does not improve performance
but only increases system complexity.
In future wireless communication spectral efficiency is
the major challenge. To increase the data rate without
bandwidth expansion, MIMO is attractive [10], [11]. The
combination ofMC-CDMA with MMSE alongwith MIMO is
very effective for solving the ISI problem by converting the
frequency selective nature of the MIMO channel to flat
fading [12-14]. Each pair of transmit and receive antennas
223

2. Short Paper
Int. J. on Recent Trends in Engineering and Technology, Vol. 6, No. 2, Nov 2011
©2011ACEEE
DOI:01.IJRTET.06.02.233
provides a signal path from the transmitter to the receiver. By
sending same information through different paths, multiple
independently faded replicas of the data symbol can be
obtained at the receiver end; hence, more reliable reception
is achieved. The rest of the paper is organized as follows;
system model is described in section II, the simulation result
and discussion is in section III.
II. SYSTEM MODEL
Fig. 1 Simple Model of MIMO-MC-CDMA Transmitter
Fig. 2 Simple Model of MIMO-MC-CDMA Receiver
Figure 1and 2shows thesimple model of MIMO-MC-CDMA
transmitter and receiver. In this system the signal from the
users are multiplexed at the transmitter and transmitted as
one entitythrough the radio channel. In transmitter, the data
is first modulated using Binaryphase shift keying (BPSK) or
quadrature phase shift keying(QPSK) modulation, multiplied
by the spreading sequence of the user and then modulated
using an OFDM modulator.The received signal in the receiver
is demodulated using an FFT, equalized and decoded.
Consider a MC-CDMA system with Nu
users, having Nc
subcarrier, the transmitted signal corresponding to the kth
user with BPSK modulation can be expressed [15] as
2
,
1
(1)( ) ( ) ( )cos( )
c
b
sc s
N
E
k k k n T s nN T
i n
s t b i c u t iT t

 
  
where Eb
and Ts
are the bit energy and symbol duration re-
spectively, uTs
(t) represents a rectangular waveform with am-
plitude 1 and pulse duration Ts
, bk
(i) is the ith
transmitted data
bit of user k, ck
,n
is the spreading code,
is the radian frequencyof the nth
subcarrier, and the frequency
spacing is f = 1/Ts
.
The received signal r(t) after cyclic prefix removal is given
by
2
,
1 1
( ) ( ) ( )
u c
b
c s
N N
E
n k k nN T
i k n
r t t h b i c

    
    
(2). ( )cos( )sT s n nu t iT t  
Where hn
is the subcarrier flat fading gain, φn
is the subcarrier
fading phase ((hn
, φn
) are common to all users), and η(t) is
AWGN with single-sided power spectral density No
. After
phase compensation, the receiver performs amplitude cor-
rection described by ( 1,.., ),n cn N  called equalizer
coefficient. In the literature, different equalizer coefficient
expressions for MMSE have been proposed for MC-CDMA
systems [16-18]. After demodulation the received signal
on the nth
subcarrier is given by
0
(3)( )cos( )
sT
n n n n n ny r t t dt D I      
Where Dn
is the desired signal and In
is the multi-user
interference Components and n
 is the noise component with
zeromean and variance 0
/ 4s
N T .
Denoting 1, ,n nc  ,
' ' ' '
1 2,[ , ..., ]cN    , 1 2[ , ,... ] .c
T
NY y y y
After equalization and de-spreading, the decision variable
'T
U Y  . Where
1
1
( 4 )' Y Y b YR R 

Let 1, 2,
[ ..., ]c
T
N
    , 1, 2,[ ..., ]u
T
Nb b b b , d
C is a
c uN N matrix with kth
column being the spreading code for
kth
user, and H is a diagonal matrix with nth
diagonal element
equals to n
h .
2 (5)b s
c
E T
dNY H C b  
Then the matrix 1b YR is
 1 1 2
b s
c
E T
b Y dNR E b HC b   
  
 12 (6)b s
c d
E T
N E b HC b
Thematrix YY
R is
2 4 (7)b s o s
cc
T
d d
E T N T
NN HC C H I
Where cNI is an identitywith c cN N . Substituting (6) and
(7) into (4), the set of equalizer coefficients for MMSE scheme
for downlink as
 
1
2
2 (8).c c
cb s b o
T
d d
N N
NE T E NHC C H I h

 
Where 1 2,[ , ..., ]C
T
N    and 1 2,[ , ..., ]C
T
Nh h h h
224

3. Short Paper
©2011ACEEE
DOI:01.IJRTET.06.02.
Int. J. on Recent Trends in Engineering and Technology, Vol. 6, No. 2, Nov 2011
233
III. SIMULATION RESULT
Simulation is performed using MATLABversion 9.1 with
BPSK/QPSK modulation and the simulation parameter is
shown in Table 1. The system is tested using 16, 64 and 128
subcarrier (SC). To understand the impact of MIMO and
equalization simulations are carried out for 2x2, 3x3 and 4x4
transmitting and receiving antenna respectively, with and
without MMSE equalization.
TABLE I. SIMULATION PARAMETER
Fig. 3 BER Performance (BPSK, 16 SC)
Fig. 4 BER Performance (BPSK, 64 SC)
Figures 3, 4 and 5 show the BER performance of MIMO-MC-
CDMAwith (line graphs) and without (legend graphs)MMSE
for BPSK modulation, with different antenna configuration and
16, 64and 128SCrespectively. Fromthegraphsit isevident that
Fig. 5 BER Performance (BPSK, 128 SC)
Fig. 6 BER Performance (QPSK, 16 SC)
Fig. 7 BER Performance (QPSK, 64 SC)
the system with MMSE performs better due tothe reduction of
ISI. It can also be inferred that the increase in number of
transmitting andreceiving antennasand increase in number of
subcarriers improve the performance due to the diversity and
multiplexinggain.
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4. Short Paper
Int. J. on Recent Trends in Engineering and Technology, Vol. 6, No. 2, Nov 2011
©2011ACEEE
DOI:01.IJRTET.06.02.233
Fig. 8 BER Performance (QPSK, 128 SC)
Figures6, 7 and8 showthe BERperformance of MIMO-MC-
CDMA with and without MMSE for QPSK modulation.
Comparing figures 3, 4 and 5 with figures 6, 7 and 8, the latter
figures show slightly lesser performance, because of the
higher order modulation used. From the simulation results it
is quite clear that whatever is the modulation used the system
with MMSE performs better.
CONCLUSION
The EGC, MRC and ORC are suitable for single carrier
communication. Ifit is used in multi-carrier system, it reduces
the orthogonalityofuser thus creating additional interference
in the receiver. Hence, in this paper the performance of
MIMO-MC-CDMA signals in frequency selective fading
channels with MMSE isanalyzed. From the simulation results,
it is inferred that the system with MMSE reduces the BER of
MIMO MC-CDMA in the Rayleigh fading channel as ISI is
drasticallyreduced.
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