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Archive of SID
IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 11, NO. 2, SUMMER-FALL 2012
1682-0053/12$20 © 2012 ACECR
77
Abstract—The main purpose of this article is to evaluate
and to compare the performance metrics, array factor (AF),
signal to interference plus noise ratio (SINR), mean square
error (MSE), bit error rate (BER), and also computational
complexity of different modified blind adaptive beamforming
algorithms based on constrained constant modulus (CCM).
Two modified algorithms use adaptive step size mechanisms
in the stochastic gradient (SG) algorithm for adjusting the
step size. The third one, CCM-RLS, uses recursive least
squares (RLS) optimization algorithm which is replaced by
the inverse correlation matrix instead of the step size. In the
case of a uniform linear array (ULA) and 5 users, one as
desired signal and the others as interference signals,
simulation results show that the modified algorithms, CCM-
RLS, CCM-SG-time averaging adaptive step size (TAASS)
and CCM-SG-modified adaptive step size (MASS), offer
higher performance with respect to conventional CCM-SG,
respectively. Comparing the performance of CCM-RLS and
adaptive step size versions of CCM-SG show that CCM-RLS
converges faster and it can cancel the interferences close to
the desired signal, more effectively. Moreover, the resulting
SINR level is higher and BER is less than the other methods.
However, CCM-SG-MASS and CCM-SG-TAASS have less
computational complexity, additions and multiplications.
Index Terms—Adaptive blind beamforming, constrained
constant modulus (CCM), adaptive step size (ASS), recursive
least squares (RLS).
I. INTRODUCTION
DAPTIVE antenna array beamforming (smart antenna)
is widely used in current communication and array
processing systems, such as wireless and cellular
communication systems, radar, sonar and medical imaging
as well as broadband wireless communications [1]. During
the last decade, wireless communications have experienced
rapid growth as the demand for developing new wireless
multimedia services such as internet access, multimedia
data transfer and video conferencing increased. In order to
meet this demand and to overcome the limited capacity of
conventional single input single output (SISO) systems,
multiple-element antennas have been widely considered at
the transmitter, receiver or both of them [2], [3].
Smart antenna technology includes an array of antennas
with adaptive beamforming and signal processing. It
increases both the system capacity and quality of the
reception by sequentially reducing the co-channel
interference and signal not of interest (SNOI) as well as
Manuscript received January 25, 2012; revised October 26, 2012.
S. Shirvani Moghaddam is with the Faculty of Electrical and Computer
Engineering, Shahid Rajaee Teacher Training University (SRTTU),
Lavizan, 16788-15811, Tehran, Iran, (e-mail: sh_shirvani@srttu.edu).
H. Sadeghi was with the Engineering Faculty of Tehran South Branch,
Islamic Azad University (IAU), Tehran, Iran,
(e-mail: hajar.sadeghi82@gmail.com).
Publisher Item Identifier S 1682-0053(12)1982
fading effects and also increasing the reliability of the
received signal of interest (SOI) [4], [5]. Various methods
are available for adaptive beamforming which can be
implemented with high speed digital signal processing
units. These techniques may be either training-based or
blind. Training-based or non-blind approaches use a
reference signal to adapt weights. The reference signal,
temporal sequence, is considered to be known in both
transmitter and receiver and is used for updating the weight
vector at the receiver. The least mean square (LMS),
normalized LMS (NLMS), sample matrix inversion (SMI)
and recursive least squares (RLS) are examples of training-
based beamforming algorithms [4]-[6]. Blind adaptive
beamforming intends to form the array direction response
towards the desired user without knowing its information
beforehand. It is an interesting topic that deals with
interference cancellation, tracking improvement and
complexity reduction. Blind algorithms do not use the
reference temporal signal and are usually based on known
properties of the desired signal and an estimation of signal
direction of arrival (DOA). Algorithms such as the constant
modulus (CM), decision directed (DD), least squares (LS)
and stochastic gradient (SG) are categorized as blind
algorithms [6]-[8]. The desired user's DOA can be obtained
by receiver through different estimation methods such as
minimum variance distortionless response (MVDR),
multiple signal classification (MUSIC), estimation of signal
parameters via rotational invariance technique (ESPRIT),
Min-Norm, or maximum likelihood (ML) [3], [9]-[11].
The design criterion is an important issue that has been
taken into account in a number of adaptive beamforming
works. Some of the most promising criteria are minimum
mean square error (MMSE), minimum variance (MV), and
CM [12]-[14]. The results in [13] show that MV leads to a
computationally efficient solution identical to that obtained
by minimizing the mean square error (MSE). The CM
criterion exploits the low modulus fluctuation exhibited by
communication signals employing constant modulus
constellations to extract them from the array input. Here,
we only consider the CM criterion since its performance is
higher than that of MV [15], especially under mismatch
conditions. However, CM may converge to the local
minima due to its higher order nature, its associated
optimization problem and the fact that typical designs do
not usually obtain the optimal solutions. To avoid this
problem, a constrained constant modulus (CCM) criterion
is proposed by employing a certain set of constraints in the
CM criterion [16]. Hence, in this investigation, CCM-based
methods are used due to their superior performance for
constant modulus constellations in comparison with the
conventional CM-based ones.
Many adaptive CCM-based algorithms have been
Performance Evaluation of CCM-Based
Antenna Array Beamforming
S. Shirvani Moghaddam and H. Sadeghi
A
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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 11, NO. 2, SUMMER-FALL 2012
78
reported for implementation of adaptive beamforming. The
SG algorithm [16] is a low-complexity one that uses
instantaneous gradient values for iteratively computing the
adaptive weight vector. Its sensitivity to the step size makes
it important to be adjusted so that a good tradeoff between
fast convergence rate and small maladjustment is obtained.
Among the existing SG-based algorithms, the fixed step
size (FSS) method is strongly dependent on the step size
chosen [17]. It also encounters some difficulties in time-
varying channels. In order to improve the performance,
some adaptive step size (ASS) mechanisms [18], [19] are
employed in the SG weight vector update. However, using
a simple implementation, fast tracking and small
maladjustment cannot be achieved jointly.
Another well-known algorithm is RLS, which has a good
performance. It updates the weight vector with a fast
convergence rate at the expense of a large increase in
computational complexity. A comparison between SG
algorithm, representing a simple and low-complexity
solution but subjecting to slow convergence, and RLS
method, possessing fast convergence but high
computational load, suggests that SG beamformers to be
adopted due to their complexity and cost [20]-[22]. Wang
and de Lamare [20] proposed the CCM-RLS algorithm
which uses constant modulus criterion for the array weight
adaptation, and then derives an RLS-type algorithm. This
algorithm does the inversion of the correlation matrix by a
simple scalar division.
The decorrelating detector and the linear minimum mean
square error (LMMSE) detector are known to be effective
strategies to counter the presence of multiuser interference
in code division multiple access (CDMA) channels; in
particular, those multiuser detectors provide optimum near-
far resistance. When training data sequences are available,
the LMMSE multiuser detector can be implemented
adaptively without knowledge of signature waveforms or
received amplitudes. Authors of [13] introduced an
adaptive multiuser detector which converges to the
LMMSE detector without requiring training sequences.
This blind multiuser detector requires no more knowledge
than does the conventional single user receiver.
A CCM design criterion for linear receivers is
investigated in [23] for direct sequence CDMA (DS-
CDMA) in multipath channels based on constrained
optimization techniques. A computationally efficient
RLS type algorithm for jointly estimating the parameters of
the channel and the receiver is developed in order to
suppress multi-access interference (MAI) and inter-symbol
interference (ISI). An analysis of the method examines its
convergence properties and simulations under non-
stationary environments show that the novel algorithms
outperform existent techniques.
In addition, a multistage decomposition for blind
adaptive parameter estimation in the Krylov subspace with
the CCM design criterion was proposed in [24]. Based on
constrained optimization of the constant modulus cost
function and utilizing the Lanczos algorithm along with
Arnoldi-like iterations, they developed a multistage
decomposition for blind parameter estimation, a family of
computationally efficient blind adaptive reduced-rank SG
and RLS type algorithms and an automatic rank adaptation
technique. An analysis of the convergence properties
of the method was carried out and convergence conditions
for the reduced-rank adaptive algorithms were established.
Simulation results considered the application of the
proposed techniques to the suppression of MAI and ISI in
DS-CDMA systems and have shown that the proposed
blind algorithms achieve a performance equivalent to the
best known supervised reduced-rank approaches without
the need for training data.
Recently, Shirvani and Sadeghi [25] proposed a new
combination of CCM-RLS and RAKE receiver in multi
user detection (MUD) wideband CDMA systems. In
this paper, the performance of four receivers, correlator,
1D-RAKE, correlator +CCM-RLS beamforming, and 2D-
RAKE with CCM-RLS beamforming is evaluated in
terms of bit error rate (BER) for different signal to noise
ratios (SNRs), modulation sizes and the number of array
elements. Using both spatial and temporal diversities,
the proposed 2D-RAKE equipped with CCM-RLS
beamforming shows higher performance in multipath
fading channels.
Here, we compare the behavior of CCM-SG, CCM-SG-
modified adaptive step size (MASS) and CCM-SG-time
averaging adaptive step size (TAASS) algorithms which
use two adaptive step size mechanisms, and CCM-RLS
algorithm. These algorithms are compared based on signal
to interference plus noise ratio (SINR), absolute value of
array factor (AF), MSE and BER.
This article is organized as follows. In Section 2, the
system model for smart antenna and CCM-SG algorithm
is briefly introduced. The existing SG algorithms based
on the constant modulus cost functions with two adaptive
step size mechanisms and RLS are described in Section 3.
In Section 4, some simulation results for the above
mentioned algorithms in different iterations and array sizes
are plotted and illustrated. Finally, Section 5 concludes
this research.
II. SYSTEM MODEL
Suppose that q narrowband signals impinge on the
uniform linear array (ULA) of ()mm q≥ sensor elements
from sources with unknown DOAs, 01 1
,, ,
q
θθ θ
−
…. It is also
assumed that in transmitter and receiver models, the
propagating signals are produced by point sources which
are in the far field, namely, so that the spherically
propagating wave can be reasonably approximated using a
plane wave [15], [26]. The vector of the i-th snapshot
relating to the received signal of the array sensors can be
modeled as [27]
01 1
2
2( )cos 2( )cos
(1).
2( )cos
() ( ). () () , 1,2, ,
() [( ),( ), ,( )]
()[1, ,
,, ]
kk
k
q
dd
jj
k
md
jT
x
iAsini i N
Aaa a
ae e
e
πθ π θ
λλ
πθ
λ
θ
θθθ θ
θ
−
−−
−
−
=+ =
⎧
⎪=
⎪
⎪
⎨=
⎪
⎪
⎪
⎩
…
…
…
(1)
where 1q
C
θ
×
∈ represents the DOAs vector of unknown
signal, () mq
AC
θ
×
∈ is a complex matrix including the
steering vectors, 1
() , 0,1,, 1
m
k
aCk q
θ
×
∈= −…,
λ
is the
wavelength, 2d
λ
= is the inter-element spacing of the
ULA, 1
() q
s
iR
×
∈ is a vector representing the real values of
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SHIRVANI MOGHADDAM AND SADEGHI: PERFORMANCE EVALUATION OF CCM-BASED … 79
the uncorrelated source data, 1
() m
ni C ×
∈ is the complex
vector of additive white Gaussian noise (AWGN) with
zero-mean, and N is the number of snapshots.
The output of a narrowband beamformer is given by
1
12
() (). ()
[, ,, ]
H
Tm
m
yi W i xi
Www w C
×
⎧=
⎪
⎨=∈
⎪
⎩… (2)
where W is the complex weight vector.
The constant modulus beamformer minimizes the W
J
cost function as follows
2
arg min( )
arg min{ [( ( ) ) ]}
1,2, ,
opt W W
p
Wp
WJ
Eyi R
iN
=
⎧
⎪
⎪=−
⎨
⎪=
⎪
⎩…
(3)
where the constant
p
R is chosen so that the optimal weight
solution becomes close to the global minimum [14] and
1p≥ is an integer. But, as it is a high order cost function
for 2p≥, multiple local minima occur, making it not
amenable to an optimal solution with respect to the desired
signal. To solve this problem, a constraining condition is
applied in (3), which results in CCM criterion. By
constraining optimization, it is meant that the technique
minimizes the contribution of undesired interference while
causing the gain along the look direction to be constant.
The CCM optimization using Lagrange multipliers [17]
can be described as
22
0
arg min{ [( ( ) 1) ]} , 1, 2, ,
subject to ( ) ( ) 1
opt W
H
WEyiiN
Wia
θ
⎧=−=
⎪
⎨
=
⎪
⎩
…
(4)
22
0
[( () 1) ] 2 { [ () ( ) 1]}
H
CCM
JEyi Wia
ηθ
=−+ℜ − (5)
where 0
θ
denotes DOA of the desired signal known
through the estimation algorithms deployed at the receiver,
0
()a
θ
is the normalized steering vector of the desired
signal, and
η
is a scalar Lagrange multiplier. The solution
can be obtained by taking the instantaneous gradient of (4)
with respect to ()Wi , setting it equal to a null vector,
and using the constraint [20]. Finally, the weight update is
given by
*
00
2
(1)
() () () ()[ ( ) ( )] ()
() () 1
H
Wi
Wi ieiy i I a a xi
ei yi
µθθ
⎧+=
⎪
⎪−−
⎨
⎪=−
⎪
⎩
(6)
where ()i
µ
is the step size, which is constant for the FSS
and variable for the ASS.
The solution is obtained by initializing ()Wi and
estimating a priori ()yi to start the weighting process.
Since DOA of the desired signal is obtained by the
estimation algorithm, 0
(0) ( )Wa m
θ
= is defined. For
the FSS algorithm [16], m is predetermined to make a
compromise between fast convergence rate and small
maladjustment. In the ASS methods [18], [19], both fast
tracking and small maladjustment cannot be achieved
simultaneously. On the other hand, their complexity is
proportional to the number of sensor elements m, which
forces a high and additional computational load for
large arrays.
III. MODIFIED BLIND ADAPTIVE ALGORITHMS
In this section, two adaptive step size mechanisms in the
SG algorithm and one fast converging RLS-type algorithm
according to the CCM criterion are described.
A. Modified Adaptive Step Size (MASS)
Wang and de Lamare were motivated by the algorithm
proposed in [28], [29], so they first proposed an algorithm
adjusted by the step size that is controlled by the square of
the prediction error as
2
(1) .() .()iiei
µαµγ
+= + (7)
where ()ei is a prediction error, 01
α
<<, and 0
γ
> is an
independent variable to control the prediction error and
scale it at different levels. Here, when the prediction error
is large, the step size increases to provide faster
convergence rate, and while the prediction error is small, a
decrease in the step size results in smaller maladjustment.
Note that (1)i
µ
+ should be in the range below
max max
min min
if ( 1)
(1) if (1)
(1)otherwise
i
ii
i
µµµ
µµµµ
µ
+>
⎧
⎪
+= +<
⎨
⎪+
⎩
(8)
where min
µ
makes a trade-off between the desired level of
steady-state maladjustment and the minimum level of
tracking ability. To increase the convergence speed, max
µ
is
chosen close to the instability point of the algorithm [20].
B. Time Averaging Adaptive Step Size (TAASS)
This method was inspired by the robust variable step
size algorithm proposed in [21], [30]. It uses a time
average estimation of the correlation of ()ei and (1)ei−
as follows
() . ( 1) (1 ). () ( 1)vi vi eiei
ββ
=−+− − (9)
and updating formula for the step size is
2
(1) .() .()iivi
µαµγ
+= + (10)
where the limitation of the (1)i
µ
+,
α
and
γ
are similar
to the MASS mechanism. 01
β
<< and it controls the
averaging time constant, namely, the quality of the
estimation. In stationary environments, it is important for
β
to be close to 1 so that the information contained in
previous samples, relevant to determining a measure of
adaptation state, should be saved [20].
While the MASS mechanism employs the current
prediction error to adjust the step size, the TAASS
mechanism uses the error autocorrelation to estimate the
time average of adjacent error terms. As the latter contains
more information about adaptation, it controls the updating
of the step size more efficiently. When the weight vector
is far from the optimum, the algorithm tries to operate
in a large ()i
µ
. Closing to the optimum, results in a
reduction in ()i
µ
. Specifically, at the early stage, the
estimation of error correlation 2()vi is large. Therefore,
()i
µ
is large to increase the convergence rate. As it
approaches the optimum, 2()vi becomes small enough to
result in a small step size for keeping low maladjustment
near optimum.
C. CCM-RLS Algorithm
CCM-RLS algorithm was proposed by Wang and de
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80
Lamare optimizes a cost function based on the constant
modulus criterion for the array weight adaptation, and then
derives an RLS-type algorithm. The optimization equation
is as
2
12
1
0
[()()1], 1,2,,
subject to ( ) ( ) 1
i
iH
l
H
J
Wixl i N
Wia
α
θ
−
=
⎧=−=
⎪
⎨
⎪=
⎩
∑…
(11)
where
α
is a positive parameter close to 1. As seen in
(11), this method is not sensitive to step size value. The
constraint condition ensures that we can get the optimal
solution. Equation (11) is related to the LS algorithm, and
by making some changes the conventional solution is
achieved as (12)
111
00 0
2
1
1
() [ ( ) () ( )] () ( )
() 2 [ () () 1] () ()
H
i
iH H i
l
Wi a R ia R ia
Ri W i xl xl x l I
θθ θ
αδα
−−−
−
=
⎧=
⎪
⎨=−+
⎪
⎩∑ (12)
where () mm
Ri C ×
∈ is the correlation matrix. i
I
δα
solves
the inverse problem by smoothing the solution to the
algorithm and makes the correlation matrix ()Ri
nonsingular at all stages of the computation.
δ
is a
positive real number called the regularization parameter
which is small for high SNRs and vice versa.
I
is the
mm× identity matrix.
Consider 2
() () () 1
H
ei W ixl=−. Using the matrix
inversion lemma, the inverse recursive correlation matrix,
can be expressed as
111
21 1
11
() ( 1)
(1)() () (1)
1() () ( 1) ()
2
H
H
Ri Ri
Ri xixiRi
ei x i R i xi
α
α
α
−−−
−− −
−−
=−
−−
−
+−
(13)
For simplification we define 1
() ()Pi R i
−
= and introduce
a vector 1
() m
K
iC
×
∈ as
1
1
(1)()
() 1() () ( 1) ()
2
H
Pi xi
Ki
ei x iPi xi
α
α
−
−
−
=
+−
(14)
replacing these equations in (13) results in
11
() ( 1) () () ( 1)
H
Pi Pi Kix iPi
αα
−−
=−− − (15)
finally, the RLS solution is obtained by
1
00 0
() [ ( ) () ( )] () ( )
H
Wi a Pia Pia
θθ θ
−
= (16)
An important feature of this algorithm is that the
inversion of the correlation matrix ()Ri is replaced at each
step by a simple scalar division. To initialize the CCM-
RLS method, the following quantities are considered:
- The initial weight vector, (0) 0W=.
- The initial correlation matrix, (0)RI
δ
=.
In terms of complexity, the LS requires 3
()Om
arithmetic operations, whereas the RLS requires 2
()Om .
Furthermore, the step size
µ
in the SG algorithms is
replaced by 1()Ri
−. This modification has a significant
impact on improving the convergence behavior [15].
IV. SIMULATION RESULTS
In this section, the effectiveness of the CCM-SG-MASS,
CCM-SG-TAASS and CCM-RLS algorithms over the
CCM-SG method is numerically investigated. Simulations
are carried out under stationary scenarios in MATLAB. All
simulations are performed by a ULA containing 8m= or
16m= sensor elements with half-wavelength spacing. To
obtain each simulated point in different curves, 1000
iterations are done. In all experiments, the power of the
desired signal is considered to be unit, 2
01
σ
=. Four
interference signals have been assumed in our simulations,
two with 0 dB and two others with 0.5 dB below the power
of the desired signal. In all simulations, the DOA of the
SOI is 00
θ
= and SNOIs are located in
[ 30, 10,40,90]
−−
. The noise is temporally AWGN with
zero mean. In addition, the binary phase shift keying
(BPSK) modulation is employed to modulate the signals.
The values of 0.998
α
=, 0.001
γ
= and 0.99
β
= are
considered so that they optimize the performance of the
MASS and TAASS algorithms. Furthermore, in RLS-type
algorithm 0.998
α
=, 10
δ
=.
The curves of four metrics, BER, MSE, normalized
antenna radiation pattern known as |AF|, and SINR versus
the number of weight updating are illustrated for
comparing the efficiency of these algorithms.
Fig. 1 shows BER, MSE, output SINR and |AF| for each
method versus the number of snapshots. The total samples
are 1000. The step size is set 4
510
−
× in CCM-SG,
5
(0) 10
µ
−
=, 4
max 310
µ
−
=× , 6
min 10
µ
−
= in CCM-SG-MASS,
5
(0) 10
µ
−
=, 4
max 10
µ
−
=, 6
min 10
µ
−
= in CCM-SG-TAASS.
It is also assumed that SNR =20 dB. The slope of curves in
the transient region of Fig. 1(b, c) show that the CCM-RLS
algorithm converges faster and has a higher performance
with respect to the CCM-SG-based algorithms. Besides,
according to Fig. 1(d), CCM-RLS can cancel the
interferences close to the desired signal. Also, CCM-SG-
TAASS and CCM-SG-MASS algorithms have higher
performance than CCM-SG, respectively. To increase the
convergence rate of SG algorithms we can choose a larger
step size, but the accuracy will be reduced and there is the
possibility of divergence. When the convergence rate is
high, we can use short sequences for channels with rapid
changes in CCM-RLS.
Fig. 2 shows the ability of the CCM-RLS in cancelling
the interferences close to the desired signal. By changing
the DOAs of interference signals to [30, 10,5,20]
−−
,
no reduction in SINR level of CCM-RLS will be observed.
In the other hand, SG-based algorithms will be converged
slower and their errors will be increased. Also, 5,6,7 dB
reduction in the SINR levels of CCM-SG-TAASS,
CCM-SG-MASS and CCM-SG algorithms will be
experienced, respectively.
By reducing the number of array elements to 8, and
changing the step size to 4
max 310
µ
−
=× , it is observed that
in all algorithms the number of the side lobes, the requiring
physical space and production costs will be reduced but in
return, as shown in Fig. 3, error will be increased i.e.,
reduction in the convergence speed. As depicted in Fig.
3(d), the power of side lobes and beam width are increased.
Also, the number and depth of the nulls are decreased
which deteriorates the cancellation of interference.
Experiments show that initial step size and lower bound
have no noticeable effect on the performance of CCM-SG-
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SHIRVANI MOGHADDAM AND SADEGHI: PERFORMANCE EVALUATION OF CCM-BASED … 81
(a)
(b)
(c)
(d)
Fig. 1. Comparison of performance metrics (BER, MSE, SINR, |AF|) of different algorithms in a 16-element ULA considering 4 interferers in DOAs:
[ 30, 10,40,90]−−
.
TABLE I
COMPUTATIONAL COMPLEXITY AND REQUIRED RUN TIME FOR CCM-BASED ALGORITHMS
Algorithm No. of multiplications No. of additions Run time (s) Extra time (%)
CCM-SG 6 3 1444 -
CCM-SG-MASS 10 5 1514 4.85
CCM-SG-TAASS 14 7 1512 4.71
CCM-RLS 16 2 1676 16.1
MASS and CCM-SG-TAASS but the higher bound has
significant effect on it. When it is not chosen well, the
convergence speed will not be satisfactory. Therefore, to
increase the convergence speed in the beginning, the initial
step size should be close to its higher bound. Due to the
high amount of error and also to compensate it fast, a large
step size is necessary in the beginning.
Considering the same processors to run the above
mentioned algorithms, the associated computational
complexities and required processing times are reported in
Table I. Higher number of multiplications and lower
number of additions belong to CCM-RLS. As expected,
CCM-SG has lower complexity and offers lower run time.
The fifth column of this table shows the percentage of extra
processing time with respect to CCM-SG. CCM-RLS,
CCM-SG-MASS and CCM-SG-TAASS experience 16.1%,
4.85%, 4.71% additional, respectively.
V. CONCLUSION
In this paper we compared the performance of three
modified versions of CCM-based blind adaptive antenna
array beamforming algorithms over the conventional CCM-
SG. CCM-SG-MASS and CCM-SG-TAASS use the
energy of prediction error and the time average of the
correlation of the estimation error to adjust the step size,
respectively. The CCM-RLS which is used for deriving a
RLS-type optimization algorithm uses the correlation
matrix inversion in order to increase the convergence rate
and to decrease the complexity. Numerical experiments are
conducted to simulate the BER, MSE, output SINR and
|AF|. According to the simulation results of this
investigation, CCM-RLS shows superior results than the
others in terms of convergence rate, SINR level,
interference cancellation and also BER and MSE in an
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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 11, NO. 2, SUMMER-FALL 2012
82
(a)
(b)
(c)
(d)
Fig. 2. Comparison of performance metrics (BER, MSE, SINR, |AF|) of different algorithms in a 16-element ULA considering 4 interferers in DOAs:
[30, 10,5,20]−−
.
AWGN channel considering 4 interferers. In addition,
CCM-RLS offers highlighted performance if the number of
interference signals close to the desired signal are increased
and the number of array elements are decreased.
Despite the CCM-RLS is more complicated and offers
higher complexity with respect to the other algorithms, it
can be converged in lower iterations. Therefore, the
required processing time to achieve good performance
for adaptive step size mechanisms, CCM-MASS and
CCM-TAASS, and CCM-RLS are approximately the same.
In other word, a small increase in processing time (about
16%) for CCM-RLS algorithm causes achieving more
improvement in the performance metrics.
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SHIRVANI MOGHADDAM AND SADEGHI: PERFORMANCE EVALUATION OF CCM-BASED … 83
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Shahriar Shirvani Moghaddam was born in Khorramabad, Iran, on July
1969. He received the B.Sc. degree from Iran University of Science and
Technology (IUST), Tehran, Iran, and M.Sc. degree from Higher
Education Faculty of Tehran, Iran, both in Electrical Engineering, in 1992
and 1995, respectively. Also, he received the Ph.D. degree in Electrical
Engineering from Iran University of Science and Technology (IUST),
Tehran, Iran, in 2001. He has more than 70 refereed international scientific
journal and conference papers, two text books on digital communications
and one book chapter on MIMO systems. Since 2003, he has been with the
Faculty of Electrical and Computer Engineering, Shahid Rajaee Teacher
Training University (SRTTU), Tehran, Iran. He was nominated as the best
researcher and lecturer in SRTTU University in 2010, 2011, and 2013.
Currently, he is an Associate Professor in Digital Communications Signal
Processing (DCSP) research laboratory of SRTTU. His research interests
include digital communications signal processing, cognitive radio
communications, adaptive antenna beamforming, direction of arrival
(DOA) estimation, and also power control and beamforming in MIMO and
cellular relay networks.
Hajar Sadeghi was born in Isfahan, Iran, in 1982. She received the M.Sc.
degree from Islamic Azad University- South Tehran Branch, Tehran, Iran,
in Electrical Engineering, in 2011. Since 2008, she has been with Data
Process Co. as a mobile telecommunication analyst. Her research interests
include wireless and mobile communications systems and smart antennas.
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