Wireless Sensor Network, 2010, 2, 555-561
doi:10.4236/wsn.2010.27067 Published Online July 2010 (http://www.SciRP.org/journal/wsn)
Performance Analysis of Downlink MIMO WCDMA
Systems Using Antenna Selection in Transmitter and
MRC Plus LDD in Receiver over Correlated
Nakagami-Fading Channels
Siavash Ghavami1, Mahmood Mohassel Feghhi2, Bahman Abolhassani2
1School of Electrical & Computer Engineering, University of Tehran, Tehran, Iran
2School of Electrical Engineering, Iran University of Science and technology, Tehran, Iran
Received April 9, 2010; revised May 4, 2010; accepted May 12, 2010
Abstract
In this paper bit error rate (BER) performance is analyzed for multiple input-multiple output (MIMO) com-
munications systems using antenna selection in the transmitter, maximal ratio combining (MRC) and linear
de-correlating detector (LDD) in the receiver in wide band code division multiple access (WCDMA)
downlink channels with correlated Nakagami fading. The MRC maximizes signal to noise ratio of the re-
ceived signal, then the LDD cancels out multiple access interference (MAI). Theoretical results are validated
using computer simulations. Moreover, a pilot based estimation method is proposed to jointly estimate the
channel gains and the rows of the LDD operator. Simulation results show that using this proposed method,
diversity order is maintained in the receiver. Furthermore, our analysis shows the spectral efficiency degra-
dation due to the pilot based strategy is negligible.
Keywords: MIMO, Transmitter Antenna Selection, WCDMA, Maximum Ratio Combining
1. Introduction
Wide band code division multiple accesses (WCDMA)
has been proposed to satisfy ever-increasing demands for
higher data rates, as well as to allow more users to sim-
ultaneously access the network [1]. So, it is employed in
the third generation mobile networks to provide multi-
media services with required qualities. Multiuser detec-
tors (MUDs) are used to detect the desired signal and to
simultaneously cancel out interferences coming from co-
users in WCDMA systems [2]. In downlink scenario,
blind multiuser detectors are proposed for multiple ac-
cess interference (MAI) cancellation [3], but use of these
detectors increases computational complexity of mobile
stations (MSs). Another approach for MAI cancellation
in downlink multiuser scenario is the precoding method
at the base station (BS) [4], but it requires error free links
between each MS and the BS, which is not the case in
practical scenarios.
Multiple input-multiple-output (MIMO) systems sig-
nificantly increase system capacity and improve perfor-
mance [5,6] at the cost of increasing hardware complex-
ity by increasing the number of transmitting and receiv-
ing antennas. Transmitter antenna selection (TAS) can
reduce the cost of multiple antennas and at the same time
can retain many advantages of MIMO systems. A com-
bined transmitter antenna selection and maximal ratio
combining (MRC) has been proposed in [7]. This method
selects the transmitter antenna that maximizes the total
received signal power at the receiver. Inactivating other
transmitter antennas reduces the hardware complexity;
furthermore, this method reduces the number of radio
channels used in a MIMO system. Bit error rate (BER)
performance of this method has been analyzed in inde-
pendent and correlated Rayleigh fading channels, respec-
tively in [8] and [9]. As well, recently a BER perform-
ance analysis of TAS/MRC has been studied in corre-
lated Nakagami fading channels [10], however it is for a
single user scenario in a non CDMA system.
In this paper, the downlink scenario of MIMO WCD-
MA systems using TAS/MRC plus LDD has been stud-
ied. MIMO is a strong tool for capacity increasing and
performance improvement. But the limitation in the size
of a MS necessitates employing receiver antennas with a

S. GHAVAMI ET AL.
556
small distance among them; therefore the correlation
among channel gains should be considered even in rich
scattering environments. For hardware complexity re-
duction and keeping diversity order in the base station,
TAS in the transmitter is a good candidate, which is con-
sidered in this paper. Furthermore for reducing effect of
MAI, a linear de-correlating detector (LDD), which is a
sub optimum multi user detector, is used in the receiver.
The LDD has simple structure with good performance
for MAI mitigation [2]. In this paper, the BER perform-
ance of a downlink WCDMA system in the correlated
Nakagami fading channels is analyzed, and theoretical
results are validated using computer simulations. MAI
cancellation using MUDs needs to know the user’s and
co-users’ spreading sequences, which increases the com-
plexities of MSs. In this paper, we consider the case in
which the links between each MS and the BS are error
prone. So, precoding techniques can not be applied. Fur-
thermore, we give up the blind MUDs for their high
computational complexities [11]. In this paper, we pro-
pose a low complexity pilot based channel estimation
method for the joint estimation of the channel gains and
the rows of the LDD operator in order to cancel out the
MAI. The proposed method does not require the spread-
ing sequences of all active users (which are not available
in the MS), as well as the calculation of the inverse cross
correlation matrix. So, using this estimation method, the
MSs can cancel out the MAI with-out prior knowledge
about spreading sequences of co-users by decorrelating
users’ signals.
The remaining of this paper is organized as follows. In
Section 2, system models are considered. BER perform-
ance analysis has been presented in Section 3. Joint es-
timation of channel and the LDD operator is proposed in
Section 4. Simulation results are presented in Section 5
in order to validate our performance analysis and evalu-
ate the performance of our proposed joint estimation
method. Finally conclusions are presented in Section 6.
2. System Model
We consider the downlink scenario of a WCDMA sys-
tem. The jth antenna of the MS receives signals of K
users which have been sent by the ith transmitter antenna
in the base station. It is given by
,,,
1
()[] ()(),
K
ijk kijsij
kl
rtAdlhtlT nt 



 (1)
where Ak, dk[l], Ts and ,ij

are, respectively, the re-
ceived amplitude, lth data symbol of kth user, symbol
period and path delay between ith transmitter antenna
and jth receiver antenna and ()nt is additive white
Gaussian noise. The ,ij h is expressed by:
1
,,
0
1
()[ ](),
N
ijk ijc
m
ht cmptmT
N



 (2)
where N is the processing gain, c
TTN is the chip
time, ,()
ij
pt is the convolution of three components:
the chip pulse shaping waveform, the channel filter be-
tween the ith transmitter antenna and the jth receiver
antenna (which represents the channel echoes) and the
receiver filter, with unit energy. []
k
cm is the value of
the mth chip of kth user’s spreading sequence with
[] 1
k
cm

. Data symbols


[]
k
dl of different users are
independent with identical distributions (i.i.d). The
channel between the ith transmitter and the jth receiver
antenna denotes as ,()
,,
()() ij
j
t
ij ij
tte

 , is assumed to
be a quasi-static fading and its envelope ,()
ij t

follows
Nakagami-m distribution

,
2
21
2
()exp( )
ij
m
m
mmx
px x
m





 (3)
where

2
22
,ij
mE 






,


2
,ij
E  ,

1
0
nu
nuedu


. Therefore2
,,ij ij

  has gamma
distribution,

,
1
()exp().
ij
mm
mx mx
px m






 (4)
2.1. Transmitter Antenna Selection
The TAS is performed so that the total received signal
power is maximized. Mathematically, it is equivalent to
selection antenna such that:
2
,
11
arg max.
r
t
L
sij
iL j
i 
 



 (5)
The MS sends
s
iusing only 2
log ()
t
L 

bits, where




 denotes ceiling operation. In performance analysis,
channel estimation is assumed to be performed perfectly
at the receiver, also the feedback link between the re-
ceiver and the transmitter is considered to be perfect and
without delay (using forward error correction (FEC) it is
possible to send a few flag bits, i.e., 2
log ()
t
L


, without
error even in error prone link). The size of a Ms limits
the use of antenna diversity and this makes the channels
correlated. The covariance matrix among channel power
gains, e.g., ,1 , ...
ss sr
T
ii iL






δ in the receiver is

S. GHAVAMI ET AL.
557
given by

,
ss
H
ii
EΩδδ (6)
where,


Eand H , respectively denote expectation and
Hermitian operations.
2.2. BER Performance Analysis
In this section, BER performance of TAS/MRC plus
LDD in the downlink scenario of WCDMA systems is
analyzed. In the following, a bold capital letter denotes a
matrix (A), a bold small letter denotes a vector (a), and
an unbolded letter denotes a scalar (a or A). Samples of
the channel are considered to be constant for each sym-
bol; such that for the lth symbol defined as
,,
[]( )
ij ij
llT

 . Defining 1 diag( ,...,)
k
A
AA,
1
[, ...]
TT
K
Cc,c , 0.5 ...,[0],[ 1]
kkk
ccNN





c,


1
[][],..., []T
K
ldldld and 01
[][],...,[]
j
T
N
j
lnlnl


 n ,
which contains the noise samples in the jth receiver an-
tenna, the received signal form the ith transmitter an-
tenna to the jth receiver antenna is given by
,,
[][][] [].
ij ij
llll

CAdrn
(7)
For any linear detector combined with MRC, the deci-
sion variable, ˆ[]l d is obtained by a linear combination
of ,[]
ij lr, i.e.,
*
,,
1
ˆ[]sign{Re([][]))},
r
L
ij ij
j
lll 

 dDr
(8)
where the matrix D represents the operation of the mul-
tiuser detector. For the LDD, D is the Moore-Penrose
generalized inverse of the code matrix C [2], given by
T1T 1T
LDD () ,

DCCCRC (9)
where T
R=C C is a KK matrix containing the
autocorrelation coefficients of the users’ spreading codes.
In (9), it is assumed that K users’ codes are linearly in-
dependent, to guarantee the existence of 1 R. The re-
ceiver output is obtained as follows
-1 *
,
1
2
-1 -1
,
1
2-1
,
1
v[ ]C[ ] [ ]
[]CCA []C[]
[]A[]C[] .
r
r
r
L
T
ij
j
L
TT
ij
j
L
T
ij
j
lll
lll
ll l












Rr
RdRn
dRn
(10)
The 1
,
() 1
kkk


R is the noise enhancement fac-
tor produced by the de-correlating operation, therefore
noise variance in the receiver side is increased to
22
,nLDDkn

 , where 2
n

is variance of []ln, which is
equal to 02N.
In the first step of the BER performance analysis, the
probability density function (PDF) of maximum channel
gains, which has been selected by criterion given by (5)
must be obtained,

max 1
max
t
i
iL




, where ,
1
r
L
iij
j





.
The PDF of max

is obtained as [12]
max
1
()( ())()
t
ii
L
t
pxLFx fx


, (11)
where ()
i
F
x

and ()
i
f
x

are respectively, the cumula-
tive distribution function (CDF) and PDF of i

. ()
i
F
x

and ()
i
f
x

for multi user scenario over correlated Na-
kagami fading channels are extracted similar to those of
a single user scenario over correlated Nakagami fading
channels, which proposed in [10].
The TAS in the transmitter and MRC in the receiver
increase the received SNR of kth user to
2
1
||
r
s
L
kk ij
i
 

, (12)
in which


2
kbkn
E

 , where b E is average energy
per bit in the transmitter. For the BPSK modulation the
instantaneous BER of the kth user is obtained as


2k Q

, where


Q

is the Q-function. The BER is
obtained by integration of instantaneous BER from zero
to infinity, as [13]
, 0(2)( )
k
ekkkk
PQpd




. (13)
Since k

in (12) is kmax

 , the PDF of k

is also
obtained similar to (11), e.g., max () ()
k
pp

 . Hence,
calculation of integral in (13) can be performed using
max ()p


. Calculation of above integral, which is related
to BER performance of multi-user scenario, is similar to
the calculation of BER performance in a single user sce-
nario, which has been performed in [10]. The final BER
is obtained as (14), where, ! denotes the factorial opera-
tion and


,1
lr
lL   are the eigenvalues of the matrix
m. As well, lr

is defined as (15), and the ex-
pressions of ,,
j
jj
abc can be obtained using the multi-
nomial theorem [14].
3. Joint Estimation of Channel Gains and
LDD Operator
In this section, effect of joint estimation of the channel
gains and the rows of the LDD operator is investigated.

S. GHAVAMI ET AL.
558
 

(1)
(1)( 1)
2
,
11 00
1
00
12! 1
() ()
1
21
j
j
tr
r
j
cr
mm cr
LL
Lm
lrlb l
ek tjj
r
lrj jl
lbjlk
s
cr
j sbl
sbjlk
E
PLa cr
b rEb N
cr sE
sEb N
 
 





 




 


 


 










 

(14)
1,
1/
1,
1(1 ),
()!()
0,
r
l
m
L
k
kkl i
mr
m
lrk s
mr mr
kl
l
rm
d
s
rm
mr ds






















 


rm













(15)
In the downlink scenario of a WCDMA system, each MS
knows only its own spreading sequence and doesn’t have
any knowledge about spreading sequence of any other
user, however using the LDD in the receiver needs the
knowledge of spreading sequences of all other active
users. Moreover, even if a mobile user knows the code
matrix of all users (e.g., C) it needs to calculate the in-
verse cross correlation matrix among spreading se-
quences of all active users (e.g., 1-
R), which has high
computational complexity. Furthermore, the mobile user
is allowed to detect only its own data. On the other hand,
the total LDD D is not required in the mobile. And the
kth user requires only the kth row of the LDD D denoted
by
L
DD
k
D in the lth detected data as can be seen in the
following equation
2
,
1
v[][][] [],
r
LDD
L
k
kij
j
llll

 
DCAdn (16)
where [][]
LDD
k
ll

nDn . To obtain
L
DD
k
D in the receiver,
in this paper, a new method is proposed, in which the
base station sends
L
DD
k
D through a pilot signal. In the
proposed method, the base station transmits the
L
DD
k
D
periodically, whose period is much larger than the sym-
bol time since the number of mobile users changes much
slower than the symbol time. Moreover, the base station
spreads the pilot signal for transmitting
L
DD
k
D using the
kth spreading sequence. This strategy avoids generating
interference and maintains the system security since only
the kth mobile user can obtain the
L
DD
k
D for detecting its
data. The received pilot symbol is as follows:
,[] ,
s
pilot
jkijk
Al 


k
rcFn (17)
where k
L
DD
k
k
Fc D,  
k
n=c n and

denotes
element by element multiplications of two vectors. If
1
k
A

then
p
ilot
j
r will be equal to ,[]
s
ij
l




k
Fn. Fig-
ure 1 shows block diagram of the proposed strategy for
joint channel and LDD operator estimation, in which TSk
[l] denotes lth symbol of the training sequence of kth
user. Training sequences for LDD operator estimation
have been sent in non-overlapping time slots, hence MAI
is not produced due to the transmission of pilot signals.
If the pilot symbols length of each user increases, the
effect of

 n in (17) reduces and a better estimation of
L
DD
k
D can be exploited. Error reduction of
L
DD
k
D esti-
mation is obtained at the expense of increasing the train-
ing duration from NTs to qNTs, where q is the number of
pilot symbols repetition for the desired user.
In the feedback link, ,[]
s
ijk
l

F is sent from the mo-
bile user to the base-station to be used for the TAS. Since,
Fk is known at the base-station, ,[]
s
ij
l

can be easily
calculated at the base-station. Exactly like the previous
section, feedback link is assumed to be error free and
without any delay.
Using pilot based strategy for joint estimation of chan-
nel gains and LDD operator reduce the spectral effi-
ciency. Hence, effect of using pilot based strategy on the
spectral efficiency is analyzed in this section. The spec-
tral efficiency of joint estimation of channel and LDD
operator is defined as,
1,
b
TIB qK
TTB R

  (18)

S. GHAVAMI ET AL.
559
TS
k
[l]
k
LDD
D c
k
n(t)c
k
TS
k
[l]
Β
i,j
[l]
Β
i,j
[l]
k
LDD
D +n’(t)
Transmitter Module Wireless Channel Receiver Module
Figure 1. Block diagram of proposed joint channel estimation and LDD operator method.
where, TIB and TTBare transmitted information bits
and total transmitted bits, respectively; also,

and b R
are variation rate of number of arriving user to the cell
and bit rate, respectively. The spectral efficiency of the
proposed method is analyzed for practical values of q,
K
and

in the next Section.
In the next section, the currently explained algorithm
is used for the joint estimation of channel and the LDD
operator. Also, the bit error probability performance of
this method is evaluated and compared with the bit error
probability of the same system with the perfect estima-
tion of channel and the LDD operator.
4. Simulation Results
In this section, we validate our analysis, equation (14),
using computer simulations. We simulate the TAS/MRC
plus LDD scheme in flat Nakagami correlated fading
channels. Furthermore, the effect of the proposed method
for joint estimation of channel and the LDD operator is
studied on the BER performance of TAS/MRC plus
LDD system.
The base station transmits data with equal amplitudes
for each of K = 25 users. Random sequence with length
of 63 has been used for short spreading codes. A rectan-
gular pulse shaping waveform ()pt is used for shaping
filter in the transmitter side. The type of modulation is
BPSK. Simulations are performed for a MIMO system
with 2 transmitter antennas and 3 receiver antennas over
correlated Nakagami flat fading channels. The normal-
ized correlation antenna matrix is the same as the one
given in [9], it is given by a 3 × 3 matrix denoted by
123
,,  

, where


110.7270.913 T
 ,


20.72710.913T
  and


30.9130.9131 T
 .
Figure 2 shows the BER of the TAS/MRC plus LDD
in the aforementioned Nakagami correlated fading chan-
nels for m = 1, 2 and 3. It is obvious that our analytical
result given by (14) is validated by computer simulations.
Moreover, the system with TAS/MRC plus LDD has a
better performance so that it has approximately 3.5 dB
SNR gain relative to that of the MRC plus LDD without
the TAS at 4
,10 ek
P

 with the diversity order m = 1.
Figure 3 shows the effect of proposed joint estimation
of channel gains and the LDD operator on the perform-
ance of the TAS/MRC plus LDD with a training sequence
having length of either 25 or 50, which needs once (q = 1)
or twice (q = 2) repetition of LDD D elements, respec-
tively. From Figure 3, it is obvious that the diversity
order remains almost constant since the slope of the three
0246810 12
10
-5
10
-4
10
-3
10
-2
10
-1
SNR[dB]
BER
m = 1, MRC+ LDD , Sim.
m = 1, MRC + LDD, Theo.
m = 1, TAS/MRC + LDD, Sim.
m = 1 TAS/MRC + LDD, Theo.
m = 2, MRC+ LDD , Sim.
m = 2, MRC + LDD, Theo.
m = 2, TAS/MRC + LDD, Sim.
m = 2 TAS/MRC + LDD, Theo.
m = 3, MRC+ LDD , Sim.
m = 3, MRC + LDD, Theo.
m = 3, TAS/MRC + LDD, Sim.
m = 3 TAS/MRC + LDD, Theo.
SNR [dB]
0 2 4 6 8 10 12
BER
10
-1
10
-2
10
-3
10
-4
10
-5
Figure 2. BER performance of MRC plus LDD and TAS/
MRC plus LDD.
SNR
[
dB
]
0 2 4 6 8 10 12
BER
10
-1
10
-2
10
-3
10
-4
Figure 3. BER performance of TAS/MRC plus LDD for m
= 1 with imperfect channel estimation.

S. GHAVAMI ET AL.
560
curves are approximately the same, and there is only 4.5
dB or 3 dB loss in the SNR at 4
,10 ek
P  due to using
the proposed joint estimation of channel and the LDD
operator with training sequence whose length is 25 or 50,
respectively. It is notable that by increasing q the SNR
loss reduces.
The mean square error (MSE) of the proposed joint
estimation of channel and the LDD operator is defined
as,


2
,: ,:
ˆ
LDD LDD
kk
MSEE  


DD (19)
where


,:
ˆLDD k
D is kth row of the estimated LDD op-
era- tor, {}Edenotes expectation operator and


2
,: ,:
ˆ
LDD LDD
kk
DD
denotes square norm of matrix.
Figure 4 shows MSE of the proposed joint estimation of
channel and the LDD operator over AWGN, in terms of
number of pilot repetition q, for different values of SNR.
It is obvious that by increasing q, MSE of


,:
LDD k
D
estimation is reduced.
Figure 5(a) shows the

in terms of the q for dif-
ferent values of active users in the cell with traffic varia-
tion of 10 user/sec

and 5 Mbps
b
R. It is obvious
even with q = 50 bits and k = 90 users, the efficiency is
greater than 0.99. Figure 5(b) is similar to Figure 5(a)
with 20 user/sec

. It can be seen with q = 50 bits
and k = 90 users, the efficiency is greater than 0.98. Fig-
ure 5(c) and 5(d) are similar to Figure 5(a) with
50 user/sec

 and 100 user/sec

, respectively.
12345678910
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Training Length, q
MSE
SNR = 0 dB
SNR = 3 dB
SNR = 6 dB
SNR = 9 dB
SNR = 12 dB
SNR = 15 dB
Training Length, q
1 2 3 4 5 6 7 8 9 10
MSE
10
-1
10
-2
10
-3
10
-4
10
-5
10
0
10
-6
10
-7
Figure 4. Mean Square error of joint estimation of channel
and the LDD operator in terms of training length.
05 10 15 20 25 30 35 40 45 50
0. 99
0. 992
0. 994
0. 996
0. 998
1
1. 002
Training Length, q

k = 10
k = 30
k = 50
k = 70
k = 90
(a) λ
1
= 10 user/sec
05 10 15 2025303540 45 50
0. 98
0. 985
0. 99
0. 995
1
1. 005
Training Length, q

k = 10
k = 30
k = 50
k = 70
k = 90
(b)
λ
2
= 20 user/sec
0510 15 20 25 30 35 40 45 50
0.95
0.96
0.97
0.98
0.99
1
Training Length, q

k = 10
k = 30
k = 50
k = 70
k = 90
(c)
λ
3
= 50 user/sec
0510 15 202530 354045 50
0. 9
0. 92
0. 94
0. 96
0. 98
1
Training Length, q

k = 10
k = 30
k = 50
k = 70
k = 90
(d)
λ
4
= 100 user/sec
Figure 5. Efficiency in terms of number of pilot symbols
repetition for different number of active users in cell with
(a) variation of input traffic of 1 λ=10 user/sec, (b) 2 λ=20
user/sec, (c) 3
λ=50 user/sec and (d) 4 λ= 100 user/sec.

S. GHAVAMI ET AL.
561
4. Conclusions
In this paper, the BER performance analysis of the TAS/
MRC plus LDD is performed for the downlink WCDMA
network in correlated Nakagami fading channels. Equa-
tion (14), derived in the analysis, was validated using
computer simulations. Also a pilot based channel estima-
tion method is proposed for joint estimating of the chan-
nel gains and the LDD operator. Simulation results show
that with joint estimation of channel gains and the LDD
operator, diversity order is kept in the receiver. Moreover,
our analysis shows that the spectral efficiency degrada-
tion due to using the pilot based strategy for joint estima-
tion of channel gains and LDD operator is negligible.
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