Wireless Sensor Network, 2010, 2, 869-878
doi:10.4236/wsn.2010.211105 Published Online November 2010 (http://www.SciRP.org/journal/wsn)
Copyright © 2010 SciRes. WSN
Joint Closed-Loop Power Control and Adaptive
Beamforming for Wireless Networks with Antenna Arrays
in a 2D Urban Environment
Mohamad Dosaranian Moghadam1, Hamidreza Bakhshi2, Gholamreza Dadashzadeh2
1Department of Electrical Engineering, Islamic Azad University, Qazvin Branch, Qazvin, Iran
2Department of Elect r i cal Eng i ne eri n g, Shahed University, Tehran, Iran
E-mail: m_dmoghadam@qiau.ac.ir, bakhshi@shah ed.ac.ir, gdadashzadeh@shahed.ac.ir
Received July 25, 2010; revised August 31, 2010; accepted October 2, 2010
Abstract
The interference reduction capability of antenna arrays and the power control algorithms have been consid-
ered separately as means to decreas e the interference in wireless communication networks. In this paper, we
propose smart step closed-loop power control (SSPC) algorithm in wireless networks in a 2D urban envi-
ronment with constrained least mean squared (CLMS) algorithm. This algorithm is capable of efficiently
adapting according to the environment and able to permanently maintain the chosen frequency response in
the look direction while minimizing the output power of the array. Also, we present switched-beam (SB)
technique for enhancing signal to interference plus noise ratio (SINR) in wireless networks. Also, we study
an analytical approach for the evaluation of the impact of power control error (PCE) on wireless networks in
a 2D urban environment. The simulation results indicate that the convergence speed of the SSPC algorithm is
faster than other algorithms. Also, we observe that significant saving in total transmit power (TTP) are pos-
sible with our proposed algorithm. Finally, we discuss three parameters of the PCE, number of antenna ele-
ments, and path-loss exponent and their effects on capacity of the system via some computer simulations.
Keywords: Adaptive Beamforming, Closed-Loop Power Control, Matched Filter, Urban Signal Propagation
Simulator, Power Control Error
1. Introduction
Diversity and power control are two effective techniques
for enhancing the signal to interference plus noise ratio
(SINR) for wireless networks. Diversity exploits the
random nature of radio propagation by finding inde-
pendent (or, at least, high ly uncorrelated) signal paths for
communication. If one radio path undergoes a deep fade,
another independent path may have a strong signal. By
having more than one path to select from, the SINR at
the receiver can be improved. The diversity scheme can
be divided into three methods: 1) the space diversity; 2)
the time diversity; 3) the frequency diversity. In these
schemes, the same information is first received (or trans-
mitted) at different locations (or time slots/frequency
bands). After that, these signals are combined to increase
the received SINR. The antenna array is an example of
the space diversity, which uses a beamformer to increase
the SINR for a particular direction [1]. Accordingly, the
use of smart antennas is expected to have a significant
impact on future wireless communications to meet the
projected perspective of future communication networks.
A major reason to use smart antenna in wireless commu-
nication is its capability to intelligently respond to the
unknown interference environment in real time. The
process of formation of nulls in the direction of interfer-
ence and strong beams in the direction of desired user is
called adaptive array processing. These systems are called
adaptive beamforming system and consist of spatially
disposed sensor elements connected to a single channel
or to a multi channel ad aptive processor. The term adap-
tive beamforming is also referred as smart antennas.
Adaptive antenna array can be used to eliminate the di-
rectional interference by adaptive canceling and there-
fore to improve the SINR. Steering capability o f ad aptiv e
array depends on processing algorithms for null steering.
Such algorithms are called adaptive algorithm. In wire-
less communications, smart antennas are used due to
M. D. MOGHADAM ET AL.
Copyright © 2010 SciRes. WSN
870
their ability to separate the desired signal from interfer-
ing signals. By knowing the direction of the desired sig-
nals, they are able to adjust the antenna pattern intelli-
gently by adjustin g the weights of the adaptiv e algorithm
[2-4].
On the other hand, power control can be realized by
allocating different power levels to the links with differ-
ent link gains. For example, links with smaller links
gains are supposed to have larger power levels. This lar-
ger power level may cause more interference to other
users. Therefore, adequate power control is needed to
meet the SINR requirement while minimizing the power
consumption and increasing the capacity in all network.
In general, two types of power control are often consid-
ered. 1) Closed-loop power control 2) Open-loop power
control [2,3]. In a closed-loop power control, according
to the received signal power at a base station (BS), the
base station sends a command to a mobile set to adjust
the transmit power of the mobile. Also, closed-loop
power control is employed to combat fast channel fluc-
tuations due to fading. Closed-loop algorithms can effec-
tively compensate fading variations when the power
control updating time is smaller th an the correlation time
of the channel. However, in an open-loop power control,
a mobile user adjusts its transmit power according to its
received power in downlink [1-6].
The first goal of this paper is to extend our work in
[7,8] by considering closed-loop power control and
power control error (PCE). In [7], a constrained least
mean squared (CLMS) algorithm was used for tracking
mobile user in a 2D urban environment without power
control algorithm. Also in [8], we proposed the SSPC
algorithm in wireless network by the CLMS algorithm
without considering the effect of PCE in 2D urban envi-
ronment. Accordingly, in this paper we present smart
step closed-loop power control (SSPC) algorithm for
minimizing the total transmit power (TTP) in wireless
networks [9]. On the other hand, the issue of the effect of
power control errors on wireless networks has received a
great deal of attention over the last few years [2,3]. Fi-
nally, we consider the effect of PCE on wireless net-
works in a 2D urban environment [10].
The organization of the remainder of this paper is as
follows. In Section 2, propagation model in a 2D urban
environment and also functional state of urban signal
propagation simulator (USPS) are described. Section 3
considers the adaptive antenna array. The CLMS algo-
rithm is summarized in Section 4. In Section 5, we pre-
sent the SSPC algorithm. Then in Section 6, we extend
the analysis to the case of PCE on wireless networks.
Section 7 presents switched-beam (SB) technique and
equal sectoring (ES) method. Finally, simulation results
and conclusions are given in Sections 8 and 9.
2. Propagation Model
Because of using 2D urban structure in reverse link (up-
link) in this work, for computing yield for path between a
user and BS, propagation model in urban environments
are dramatized. In propagation model in urban environ-
ments and in reverse link, user antenna is radiating
beams which are diffusing in all directions and parts of
beams reach to BS.
In urban environment, delivered beam from user by
the time of collision to an obstacle like a wall surface or
a building, reflects to a new angle and continues its path,
this is called reflection phenomena. In condition when
radiated beam is conflicted to a obstacle edge then dif-
fraction phenomena is happened and diffracting point is
diffusing new beams to all directions like a transmitter.
All reflected beams, will stay in the environment till the
time their power are not reduced to a threshold limit.
Figure 1 shows both phenomena in reverse link. In this
work, USPS dramatizing is used for implementing a 2D
urban environment [7,11].
According to above dramatization, we could see be-
cause of line of sight (LoS) in un-urban environment,
only one signal is delivered from each user to receiver,
while in function and because of elimination phenomena
in an urban environment, beside to signals which are
delivered to line sight, signals which have difference in
phase or domain with this signal are also received by
receiver.
3. Adaptive Antenna Array
An adaptive antenna array consists of a set of antennas,
designed to receive signals radiating from some specific
directions and attenuate signals radiating from other di-
rections of no interest. The outputs of array elements are
weighted and added by a beamformer, as shown in Fig-
ure 2, to produce a directed main beam and adjustable
Figure 1. Diffraction phenomena and reflection phenomena
(LoS and Non-LoS paths) for a 2D urban environment in
reverse link.
M. D. MOGHADAM ET AL.
Copyright © 2010 SciRes. WSN
871
Figure 2. Antenna array and beamformer [13].
nulls. In order to reject the interference, the beamformer
has to place its nulls in the directions of sources of inter-
ference, and steer to the direction of the target signal by
maintaining constant gain at this direction [12]. In this
paper, we focus on the uplink communication path in a
single-cell wireless system with
M
users and only one
BS. Also we use a unifor m li near array (ULA) of Nan-
tenna elements.
Accordingly, the received signal vector in BS can be
written as [12]


 
1
M
iii i
i
tpst t


xvn (1)
where

i
s
t is the message signal transmitted from the
ith user; i
pis the received power of the ith user in BS
which is equal to ii
pG wherei
pand i
G denote the
transmitted power of the ith user, and the link gain be-
tween user i and BS in LoS path (or the best non-LoS
path if LoS path is not exist), as shown in Figure 1, re-
spectively. Also

tn is the thermal noise vector at the
input of antenna array at BS and i
is the correspond-
ing time delay. For simplicity, we further assume that the
time delays for all uses are equal to 0. Also the 1N
vector

i
vis the array response for user i and can be
written as follows [12]:


,,
1
i
L
iiliil
l

va (2)
where i
L is the number of paths between user i and
BS in USPS; ,il
is the direction of arrival (DoA) in the
lth path for user i; ,il
is the normalized attenuation
by the best link gain (i
G) in USPS between user i and
BS in the lth path, therefore ,
01
il
. Also, response
of the base station array to the direction ,il
is given by

 
,,
,1exp...exp ( 1)T
il il
iil jjN

 

 

a (3)
where 1j
and

,,
2/sin
il il
d
 
, in which
is signal wavelength and d is the distance between
the antenna elements that for avoid the spatial aliasing
should be defined as 0.5d
.
In non-spread spectrum systems, the transmitted signal
is given by [12]
 
ii
m
s
tbmgtmT
(4)
where
i
bm is the ith user information bit stream with
a bit period of T and
t is the pulse-shaping filter
impulse response. It has been shown that the output of a
matched filter sampled at the symbol intervals is a suffi-
cient statistic for the estimation of the transmitted signal.
The matched filter is sampled at tmT

*
*tmT
mtgt
xx (5)
Hence, the received signal at the output of the matched
filter is given by
 
  
1
M
iii ikkkk
k
ki
iii ii
mpGbm pGbm
mpGbmm m



xv v
nvIn
(6)
where
imI is the interference for user i in BS and
*
*tmT
mtgt
nn .
4. Constrained LMS Algorithm
Constrained LMS algorithm is a gradient based algo-
rithm to minimize the total processor output power,
based on the look direction constraint. The adaptive al-
gorithm is designed to adapt efficiently in agreement
with the environment and able to permanently preserve
the desired frequency response in the look direction
while minimizing the output power of the array. The
M. D. MOGHADAM ET AL.
Copyright © 2010 SciRes. WSN
872
combined form of the constraint is called constraint for
narrowband beamforming [12 -1 4] .
This form consider a narrowband beamformer where
the narrowband signal from each element of smart an-
tenna are multiplied by the complex weight calculated by
using narrowband adaptive beamforming algorithm, and
then summed to produce the output of the array. The
definition of the complex weights of this beamformer in
the mth iteration for the ith user is as follows [13-15]:
 
(1)(2)( )
... T
N
iii i
mwmwmwm


w (7)
Accordingly, the output of the array in the mth itera-
tion for user i is given by
 
mmmy H
ii xw (8)
The expected output power of the array in the mth it-
eration is given by

 

 

 
2*
EE
E
iii
HH H
iiixxi
ym ymym
mmmmmm

wxxwwRw
(9)
where

E. is denoted the expectation and
x
x
R is the
correlation matrix of the received signal vector
mx.
A real-time CLMS algorithm for determining the op-
timal weight vector for user i is [13,14]:
 


max
,g
1
1
ii i
H
ii i
mmgm
 
ww w
wa (10)
where

max
,gii
a denotes spatial response of the array
for user i in the best path gain, i.e.,,1
il
, and

1
imw is the new weight computed at the
1m
th
iteration for user i. Also, the variable scalar
de-
notes a positive scalar (gradient step size) that controls
the convergence characteristic of the algorithm, that is,
how fast and how close the estimated weights approach
the optimal weights, and

i
g
mw denotes an unbi-
ased estimate of the gradient of the power surface
(
 
H
ixxi
mmwRwwhich is the expected output power
of the array) with respect to

imw after the mth itera-
tion. The algorithm is “constrained” because the weight
vector satisfies the constraint at each iteration, that is

max
,1
H
ii ig
wa . Rewrite the CLMS algorithm as fol-
lows [14].
 



max
,
1iig
iii i
mmgm
N
 
a
wβww (11)
where

max max
,,
H
iig iig
iN


aa
βI (12)
The gradient of

H
ixxi
mmwRw with respect to
imw is give n by


 

*2
H
iixxixxi
i
g
mmmm
 
ww RwRw
w
(13)
and its computation using this expression requires
knowledge of
x
x
R, which normally is not available in
practice. For a standard LMS algorithm, an estimate of
the gradient at each iteration is made by replacing
x
x
R
by its noise sample

11
H
ii
mmxx available at
time instant
1m
, leading to

*
21
iii
g
mmym wx (14)
The CLMS is a fast convergence algorithm. However,
it is drastically sensitive to the mismatch in the direction
of arrival. Meanwhile, the weights estimated by the stan-
dard algorithm are sensitive to the signal power, requir-
ing a lower step size in the presence of a strong signal for
the algorithm to converge, which in turn regarding the
decrease of mis-adjustment error, the convergence time
is increased [14-16].
Consider the problem of beamforming as to maximize
the SINR for a specific link, which is equivalent to
minimizing the interference at the receiver of that link. In
order to minimize the variance or average power at the
output of the beamformer subject to maintaining unity
gain at the direction of the mobile user signal. Accord-
ingly, we can rewrite the average output power for user
ias [12]
ˆˆ
H
iixxi
wRw (15)
where ˆi
w is the optimum weight vector for user i
with CLMS algorithm. If the message signals
i
s
t are
uncorrelated and zero mean, the correlation matrix
x
x
R
is given by
  
2
1
M
HH
xxii iikkkkn
k
ki
H
iii ii
pG pG
pG


 

Rvvvv I
vv Φ
(16)
where
 
2
1
M
H
ikkkk n
k
ki
pG


Φvv I
(17)
is the correlation matrix of unwanted signals for user i
in BS, and 2
n
is the noise power at the input of each
array element.
Combining (15)-(17), we obtain the received signal
plus interference power as a function of weight vector
  
2
1
2
ˆˆˆ
ˆˆ
M
HHH
iiiiikkik ki
k
ki
H
ni i
pG pG
 

wvwv vw
ww
(18)
M. D. MOGHADAM ET AL.
Copyright © 2010 SciRes. WSN
873
Accordingly, the SINR at BS for user i can be writ-
ten as follows [12].




2
22
1
ˆ
ˆ
SINR ,ˆˆˆ
H
iii i
iMHH
kkikn ii
k
ki
pG
pG

wv
wv
wv ww
(19)
In order to perform the bit error rate (BER), we as-
sume Gaussian approximation for the probability density
function of interference plus noise. The conditional BER
for a BPSK modulation is [17]:




ˆˆ
BER,2 SINR,
ii
Q

wvwv (20)
where


2
1exp/2
2x
Qxu du

(21)
It should be mentioned that for the array antenna
weight vector elements in the CLMS algorithm and for
big
, will converge after a few iteration (is approxi-
mately equal to the number of beamformer weights,
i.e.,mN) [7,16]. Moreover it is obvious that, without
power control algorithm, the calculated optimal weight
vector does not guarantee desirable SINR for the mobile
user. Thus, we introduce our proposed algorithm in next
section.
5. Smart Step Closed-Loop Power Control
Algorithm
A major limiting factor for the satisfactory performance
of cellular systems is the near-far effect. Power control is
an intelligent way of adjusting the transmitted powers in
cellular systems so that the TTP is minimized, but at the
same time, the user SINRs satisfies the system quality of
service (QoS) requirements, [18,19].
Depending on the location where the decision on how
to adjust the transmitted powers is made, the po wer con-
trol algorithms can be divided into two groups: central-
ized and distributed techniques [1-6,12]. In centralized
power control, a network center can simultaneously com-
pute the optimal power levels for all users. However, it
requires measurement of all the link gains and the com-
munication overhead between a network center and base
stations. Thus, it is difficult to realize in a large system
[20]. Distributed power control, on the other hand, uses
only local information to determine transmitter power
levels. It is much more scalable than centralized power
control. However, transmitter power levels may not be
optimal, resulting in performance degradation [21,22].
The distributed closed-loop power control problem has
been investigated by many researchers from many per-
spectives during recent years [5,18,21-23]. For instance,
distributed conventional closed-loop power control st r a t eg y
used in practice in wireless cellular syste ms as code divi-
sion multiple access (CDMA) is a fixed-step controller
based on SINR measurements. The fixed-step power con-
trol (FSPC) algorithm is defined by [5]

1*
sign
nn n
ii ii
pp

 (22)
Where n
i
p, *
i
andn
i
are the transmitter power,
SINR target and measured SINR of user i at time n,
respectively, and
is the fixed step size. Also 1n
i
p
is
transmitter power control (TPC) command in the feed-
back link of BS to user i at time 1n (all signals are
in decibels).
Also, the distributed traditional closed-loop power
control (DTPC) is defined by [18]
*
1nn
i
ii
n
i
pp
(23)
In both algorithms, the simple intuition behind this it-
eration is that if the current SINR n
i
of user i is less
than the target SINR*
i
, then the power of that user is
increased; otherwise, it is decreased.
It should be mentioned that convergence speed of
DTPC algorithm is higher than FSPC algorithm. Also,
the variance of the SINR mis-adjustment in FSPC algo-
rithm is higher than DTPC algorithm. But, it has been
shown that the FSPC algorithm converges to
*2
n
ii d
k

 , where d
k is the loop delay [4].
Also in [23], variable step closed-loop power control
(VSPC) algorithm has been proposed. In this algorithm,
variable step size is discrete with mode q. It is shown
that the performance of VSPC algorithm with mode q =
4 is found to be worse than that of a fixed step algorithm
(q = 1) under practical situations with loop delay of two
power control intervals, but the convergence speed of
VSPC algorithm is higher than FSPC algorithm. Also in
this algorithm, the variance of the SINR mis-adjustment
is reduced in compared to FSPC algorithm.
Practical implementations of power control in the
CDMA cellular systems utilize closed-loop control, where
the transmitter adjusts its power based on commands
received from the receiver in a feedback channel. To
minimize signaling overhead, typically one bit is used for
the power control command. In practice, the command
must be derived based on measurements made at the re-
ceiver, transmitted over the feedback channel to the
transmitter, and finally processed and applied at the
transmitter. All these operations constitute a loop delay,
which can cause problems if it is not properly taken care
of in the design of the power control algorithm. In many
cases the loop delay is known due to a specific frame
structure inherent in the system. A typical loop delay
situation encountered in WCDMA systems is shown in
M. D. MOGHADAM ET AL.
Copyright © 2010 SciRes. WSN
874
Figure 3. The slot at time nt is transmitted using
power n
p. The receiver measures SINR n
over a
number of pilots and/or symbols and derives a TPC
command. The co mmand is transmitted to the transmitter
in the feedback lin k and the transmitter adjusts its power
at time

1nt according to the command. It should be
mentioned that since the power control signaling is stan-
dardized, the loop de lays are known exactly [5].
In this paper, we propose smart step closed-loop
power control algorithm for wireless networks. We ex-
press the SSPC algorithm as follows [8,9].

1**
sign
nn nn
iiiiii
pp
 
 (24)
The algorithm is implemented as follows.
1) Select the initial transmitted power vector
0n
for all users as 0000
12
... M
pp p


p.
2) Estimate the weight vector for all users
(ˆi
w,1iM ) with the CLMS algorithm using (11).
3) Calculate the SINR for all users (1iM ) at time
n and after the time mN, according to the following
equation:


2
22
1
ˆ
ˆˆˆ
nH
ii ii
n
iMnHH
kkiknii
k
ki
pG
pG

wv
wv ww
(25)
4) If *0
n
ii

 for each user then set 1nn
and calculate the TPC for all users at time 1n
using
(24) and go back to 2), where 0
is threshold value.
5) Finally, if *0
n
ii

 for all users then algo-
rithm ends.
As will be seen from simulation results, because of
variable coefficient in th e sign function, the converg ence
speed of our algorithm is higher than FSPC and VSPC
algorithms.
6. Power Control Error
When imperfections in power control are considered,
multipath fading is not perfectly compensated. As a re-
sult, the power received from a mobile will not be con-
stant at the base station to which the mobile is co nn ected.
Accordingly, we can be rewritten (1) as follows.


 
1
M
iii i
i
tPst t


xvn
(26)
where /
bb
PET
represents the received signal power
of all users in the presence of PCE and b
E is the energ y
per bit for all users. The variable i
is PCE for user i,
which is assumed to follow a log-normal distribu tion and
thus it can be written as/10
10 i
i
, where i
is a
Gaussian random variable with mean 0 and variance2
for all users [3]. On the other hand,

Ei
for all users
can be written as follows [24].

22
/2
Eie

(27)
where
ln 10/10
. Accordingly, we can be rewritten
the SINR in (19) as follows [10].


22
2
2
2
/2 2
1
ˆ
SINR ,,
ˆ
ˆˆˆ
i
i
H
ii
MHH
ikni i
k
ki
Pe
Pe




wv
wv
wv ww
(28)
7. Switched-Beam Technique and Equal
Sectoring Method
One simple alternative to the fully adaptive antenna is
the switched-beam architecture in which the best beam
is chosen from a number of fixed steered beams. Swit-
ched-beam systems are technologically the simplest
Figure 3. Example of power control timing in WCDMA systems [4].
M. D. MOGHADAM ET AL.
Copyright © 2010 SciRes. WSN
875
and can be implemented by using a number of fixed,
independent, or directional antennas [25]. We list the
conditions of the SB technique for this paper as follows
[11].
1) According to Figure 4, beams coverage angle is
30and overlap between consecutive beams is 20. Thus
each base station has 36 beams.
2) According to Figure 5, each user can be use one
beam for its each path to communicate with a base sta-
tion at any time.
One simple method to sectorize a cell is equal sector-
ing; in which all sectors have the same coverage angle.
In this paper, we assume three sectors for each base sta-
tion with sector angle 120 for the ES method [26].
8. Simulation Results
In this section, we evaluate the performance of our algo-
rithm by simulating the same system as in [7] with
CLMS algorithm, SB technique, and ES method. For this
purpose, we use part of two-dimensional map of the
University of Toronto campus area in Canada as shown
in Figure 6 [7]. According to this figure, we observe
beside desired user, 1
M
interference users in a stable
positioning situation with uniform distribution are also
Figure 4. 36 beams in BS with the SB technique.
Figure 5. Select of beam for two users in two different paths
with the SB technique.
sending information to BS equipped to an array antenna
in reverse link. According to the description in Section 2,
sending information by all users to BS is performed by
dramatizer USPS. Also note that the variance of the
noise (2
n
) for every element is assumed to be equal to
0.01; resolution and path loss in USPS R = 1 and
0.05dB/mL
, respectively; gradient step size in the
CLMS algorithm 0.005
; fixed step size for SSPC,
FSPC, and VSPC algorithms 0.05
; mode 4q
for VSPC algorithm [23]; threshold value in SSPC algo-
rithm 00.1 dB
; number of elements antenna array
10N
; initial value for transmitted power vector for all
users 00
p; and the SINR target value is the same for
all users and is set to

*89dB
. It also is assumed
that the distribution of users is uniform.
Figure 7 shows the comparison of the average SINR
achieved over 15M
users versus the power control
iteration index (n) for SSPC, VSPC (4q), and FSPC
algorithms and CLMS, SB, and ES techniques. Also in
this simulation, we assume that each user to have a
maximum power constraint of 1watt. It should be men-
tioned that in case of without power control (PC), the
transmitted power for all users is 1 watt [7]. Accordingly,
we observe that the convergence speed of the SSPC al-
Figure 6. Two-dimensional map of the University of To-
ronto campus area and placing users and base station con-
tain array antenna in map center [7].
Figure 7. Average SINR of all users versus power control
iteration index (n), with maximum power constraint of 1W.
M. D. MOGHADAM ET AL.
Copyright © 2010 SciRes. WSN
876
gorithm is faster than the VSPC and FSPC algorithms.
For example, the SSPC algorithm (for CLMS algorithm)
converges in about eight iterations, while VSPC and
FSPC algorithms converge in about 11 and 16 iterations,
respectively. Also this figure shows that the SSPC algo-
rithm with SB technique converges faster than CLMS
and ES methods. Also we observe that the SINR level
achieved is below the target SINR value for ES method,
because in this case the interference is higher than the
other methods.
Figure 8 shows the comparison of TTP usage versus
the power control iteration index (n), as Figure 7. But
in this simulation, we assume that users no have maxi-
mum power constraints. Similar to Figure 7, we observe
that the ES method never can achieve the target SINR
value for all users. Also this figure shows that the SSPC
algorithm offers more savings in the TTP as compared
the FSPC and VSPC algorithms. Also the TTP for the
joint SSPC algorithm and SB technique is lower than
other cases. Although not shown in the figure, in case of
without power control and because of near-far problem,
the target SINR level is not achieved for all users.
Figure 9 presents the average BER versus the signal
to noise ratio (SNR) for CLMS algorithm and SB tech-
nique and different values of 2
. In this figure, we ob-
serve that the average BER for the SB technique is lower
than the CLMS algorithm. For example, at a SNR of
10dB and 24dB
, the average BER is 0.0011 for
CLMS algorithm, while for SB technique is 0.00018.
Also it can be seen that the average BER for 20dB
(perfect power control) is lower th an the other cases. For
example, at a SNR of 10dB and for CLMS algo-
rithm, the average BER is 0.0007 for PPC, while for
28dB
the average BER is 0.0016.
Figure 10 presents the average BER versus the num-
ber of active users for SNR 10dB
and different val-
ues of 2
as Figure 9. Similar to Figure 9, we observe
that the average BER for 20dB
is lower than
22,4,8dB
. For example, at a BER of 0.001, the re-
Figure 8. Total transmit power of all users versus power
control iteration index (n). No power constraints.
Figure 9. Average BER versus the SNR for the SB tech-
nique and CLMS algorithm (M = 15).
Figure 10. Average BER versus the number of active users
for the SB technique and CLMS algorithm (SNR = 10 dB).
ceiver with CLMS algorithm support 18Musers for
20dB
, while for 22,4,8dB
support 16M
, 15,
and 12 users, respectively. Accordingly in this case, with
2
from 2 to 8 dB, the system capacity degrades from
6% to 34% compared to the case of PPC. We also ob-
serve that with SB technique can achieve lower BER
than the CLMS algorithm. For example, at a BER of
0.0001 and28dB
, the number of users allowed in
the system is 15M
users for SB technique, while for
CLMS algorithm is 5M
users.
Other results displayed in Figure 11 and Figure 12
show the influence of path-loss parameter in USPS
L
and number of antenna elements

N on the average
BER for the CLMS algorithm, SNR 10dB, and 2
4dB
. In Figure 11, we can observe that, as expected,
a decrease in the path-loss parameter entails an increase
in the interference and desired signal levels and, there-
fore using antenna arrays in BS, an improvement in sys-
tem performance. For example, at a BER of 0.005, ca-
pacity is, respectively, 16, 29, and 34 users for L = 0.5,
0.05, and 0.01d B/m. In Figure 12, it is seen that for L =
0.05dB/m and a required average BER of 0.0025, if N
increases from 5 to 15, the number of active users in-
creases by approximately 60%.
M. D. MOGHADAM ET AL.
Copyright © 2010 SciRes. WSN
877
Figure 11. Influence of path-loss parameter (L) on average
BER (SNR = 10 dB, N = 10).
Figure 12. Influence of number of antenna elements (N) on
average BER (SNR = 10 dB, L = 0.05 dB/m).
9. Conclusions
In this paper, we studied performance of single-cell
wireless communication systems in a 2D urban environ-
ment with closed-loop power control. Also, we deter-
mined the optimum weights of the elements of array an-
tenna with the CLMS algorithm.
Accordingly, we proposed the SSPC algorithm in or-
der to compensate the effects of the near-far problem. It
has been shown that, by using antenna arrays at BS, this
algorithm will decrease the interference in cell. In addi-
tion, the TTP expected by all users is less as compared to
the VSPC and FSPC algorithms. Thus, it decreases the
BER by allowing the SINR targets for the users to be
higher, or by increasing the number of users supportable
at a fixed SINR target level. It has also been observed
that the TTP in SB technique is less than CLMS algo-
rithm. Also, it has been shown that the convergence
speed of the proposed algorithm is increased in com-
parison with the VSPC and FSPC algorithms. Also, our
simulations show that the variations in power level due
to PCE have a detrimental effect on system performance.
10. Acknowledgements
This research is supported under research project by the
Islamic Azad University, Qazvin Branch, Qazvin, Iran.
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