Abstract—In this paper, we propose smart step closed-loop power control (SSPC) algorithm in a direct sequence-code division multiple access (DS-CDMA) receiver in the presence of frequency-selective Rayleigh fading. This receiver consists of three stages. In the first stage, with constrained least mean squared (CLMS) algorithm, the desired users’ signal in an arbitrary path is passed and the inter-path interference (IPI) is reduced in other paths in each RAKE finger. Also in this stage, the multiple access interference (MAI) from other users is reduced. Thus, the matched filter (MF) can be used for the MAI and IPI reduction in each RAKE finger in the second stage. Also in the third stage, the output signals from the matched filters are combined according to the conventional maximal ratio combining (MRC) principle and then are fed into the decision circuit of the desired user. 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 possible with our proposed algorithm.
Index Terms— Adaptive beamforming, constrained LMS, closed-loop power control, DS-CDMA, total transmit power.
I. INTRODUCTION
ODE-DIVISION multiple access (CDMA) for cellular communication networks requires the implementation of some forms of adaptive power control. In the uplink of CDMA systems, the maximum number of supportable users per cell is limited by multipath fading, shadowing, and near-far effects that cause fluctuations of the received power at the base station (BS). Two types of power control are often considered:
closed-loop power control and open-loop power control [1], [2]. In a closed-loop power control, according to the received signal power at a base station, 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
This work was funded by the Islamic Azad University, Qazvin Branch, Qazvin, Iran.
1 Mohamad Dosaranian Moghadam and Mehran Godarzvand Chegini are with the Electrical Engineering Department, Islamic Azad University, Qazvin Branch, Qazvin, Iran. (e-mails: {m_dmoghadam, m_chegini}@qiau.ac.ir).
2 Hamidreza Bakhshi and Gholamreza Dadashzadeh are with the Electrical Engineering Department, Shahed University, Tehran, Iran.
(e-mails: {bakhshi, gdadashzadeh}@shahed.ac.ir).
combat fast channel fluctuations due to fading. Closed-loop algorithms can effectively compensate fading variations when the power control updating time is smaller than 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 the downlink [1]-[5]. In this paper, an adaptive closed-loop power control algorithm is proposed.
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 independent (or, at least, highly 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 transmitted) 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 [6]-[8]. In this work, we use constrained least mean squared (CLMS) algorithm for the space diversity.
The goal of this paper is to extend the works in [9] and [10]
by considering multiple-cell system and closed-loop power control. In these works, a RAKE receiver in a single-cell system with conjugate gradient (CG) adaptive beamforming was proposed in the presence of frequency-selective Rayleigh fading channel, and perfect power control (PPC) was considered. In this paper, smart step closed-loop power control (SSPC) algorithm is proposed to compensate for near-far effects. This algorithm is a variable and smart step algorithm based on SINR measurement in base station [11].
In this work, the performance analysis of direct-sequence (DS)-CDMA system in frequency-selective Rayleigh fading channel has been studied. If the delay spread in a multipath channel is larger than a fraction of a symbol, the delayed components will cause inter-symbol interference (ISI).
Adaptive receiver beamforming schemes have been widely used to reduce both co-channel interference (CCI) and ISI and to decrease the bit error rate (BER) by adjusting the beam pattern such that the effective SINR at the output of the beamformer is optimally increased [12].
Joint Closed-Loop Power Control and Constrained LMS Algorithm for DS-CDMA Receiver in
Multipath Fading Channels
M. Dosaranian-Moghadam1, H. Bakhshi2, G. Dadashzadeh2, and M. Godarzvand-Chegini1
C
978-1-4244-9003-5/10/$26.00 ©2010 IEEE
In this paper, a RAKE receiver in DS-CDMA system is analyzed in three stages according to Fig. 1 [9]. In the first stage, this receiver uses CLMS adaptive beamforming to find optimum antenna weights assuming perfect estimation of the channel parameters (direction, delay, and power) for the desired user. The desired user resolvable paths’ directions are fed to the beamformer to reduce the inter-path interference (IPI) from other directions. Also, the RAKE receiver uses conventional demodulation in the second stage and conventional maximal ratio combining (MRC) in the third stage to reduce multiple-access interference (MAI). Reducing the MAI and the CCI will further decrease the system BER.
The organization of the remainder of this paper is as follows. The system model is presented in Section II. The RAKE receiver structure is described in Section III. In Section IV, we present the SSPC algorithm. Section V describes CG adaptive beamforming (CGBF) algorithm, switched-beam (SB) technique, and equal sectoring (ES) method. Finally, simulation results and conclusions are given in Section VI and Section VII, respectively.
II. SYSTEMMODEL
In this paper, we focus on the uplink communication paths in a DS-CDMA cellular system. The channel is modeled as a frequency selective channel with Rayleigh distribution and lognormal distributed shadowing. Initially, we consider L paths for each link that optimally combined through a RAKE receiver according to Fig. 1. Also, we assume that there are M active base stations in the network, with Km users connected to mth base station. At each base station, an antenna array of S sensors andNweights is employed, whereS=N, to receive signals from all users. Also, for simplicity we assume a synchronous DS-CDMA scheme and BPSK modulation in order to simplify the analysis of proposed methods.
Additionally, in this paper we assume a slow fading channel.
Hence, the received signal in the base station q and sensor s from all users can be written as [9], [13].
( ) ( ) ( )
(
t) (
jsk)
n( )
tc
t b y
x p t
r
l m k d l
m k m k
L
l
l m k m k l m k k
k m k s
q
+
−
−
×
−
′ Γ
=
∑ ∑
=
, , ,
, ,
1
, , , , , ,
,
sin exp
,
θ τ
τ
α (1)
where ck,m
( )
t is the pseudo noise (PN) chips of user k in cell m (user k,m) with a chip period of Tc; bk,m( )
t is the information bit sequence of user k,m with a bit period ofc
b GT
T = where G is processing gain; τk,m,l is the lth path time delay for user k,m; θk,m,l is the direction of arrival (DoA) in the lth path for user k,m; αk,m,l is the complex Gaussian fading channel coefficient from the lth path of user
m
k, ; kd =2πd/λ whereλ is signal wavelength and d is the distance between the antenna elements that for avoid the spatial aliasing should be defined as d =0.5λ; n
( )
t is an additive white Gaussian noise (AWGN) process with a two- sided power spectral density (PSD) of N0/2 and( ) { ( ) }
( )
⎪⎪
⎩
⎪⎪
⎨
⎧
∈
∈
=
Γ ∈Θ
L o q k
L m m k
q
k k S
y x d
y x d
S k y
x
q k
m k
k ;
10 ,
10 , min
; 1
,
10 / ,
10 / ,
BS
, ,
ξ ξ
α
α (2)
where Lα is path-loss exponent; dk,m
(
x,y)
and dk,q(
x,y)
are the distance between user k and BSm and BSq, respectively (see Fig. 2). Also the variable Θk defined the set of the nearest BSs to userk; ξk,m is a random variable modeling the shadowing between user k and BSm;SBSq is the set of users that connected to BSq and So is the set of users that not connected to BSq[2], [14]. Also in (1):
( )
kmL m m k
k d x y p
p′, = −,α , 10−ξk,m/10× , (3) Fig. 1. Block diagram of a three-stage RAKE receiver in DS-CDMA system [9].
is the received power in the BSm of user k,m in the presence of closed-loop power control where pk,m is the transmitted power of user k,m that in the case of the PPC, pk′,m is fixed for all users within cell m (pk′,m =Eb/Tb where Eb is the energy per bit for all users) [2], [9].
The received signal in the base station q in sensor s for user i, is given by [9] q
( ) ( ) ( )
(
jsk)
I( )
t n( )
tt c t
b p t
r
s q i l q i d l
q i
l q i q i L
l
l q i q i q i s
q i
+ +
−
×
−
′ −
′ =
∑
=
, , , , ,
,
, , , 1
, , , , ,
,
sin
exp θ
α
τ
τ (4)
where Ii,q,s
( )
t is the interference for user i, in sensor q s and can be shown to be( ) ( ) ( )
(
kml)
kml(
d kml)
m k
M
m
l m k m k K
q i m k
k L
l
k m k s
q i
sk j t
c
t b y x p t
I
m
, , ,
, , , ,
1
, , ,
, ,
1 1
, ,
,
sin exp
,
θ α
τ
τ
−
−
×
−
′ Γ
=
∑ ∑ ∑
=
≠
= =
(5)
where Km is the number of users in cell m and M is the number of base stations/cells.
III. RAKERECEIVERPERFORMANCEANALYSIS The RAKE receiver structure in the DS-CDMA system is shown in Fig. 1. The received signal is spatially processed by a beamforming circuit with CLMS algorithm, one for each resolvable path (L beamformers). The resultant signal is then passed on to a set of parallel matched filters (MFs), on a finger-by-finger basis. Also, the output signals from the L matched filters are combined according to the conventional MRC principle and then are fed into the decision circuit of the desired user.
A. Adaptive Beamforming Stage
It is well known that an array of N weights has
−1
N degree of freedom for adaptive beamforming [9], [13].
This means that with an array of N weights, one can generates 1N− pattern nulls and a beam maximum in desired directions. From (5), it is clear that the number of users is
∑
== M
m m
u K
K 1 and the number of interference signals is
−1
LKu . To null all of these interference signals; one would have to have LKu weights, which is not practical. So, we focus only on the L paths of the desired user. Thus, the minimum number of the antenna array weights is L where, typically, L varies from 2 to 6 [9].
In this paper, we use the CLMS adaptive beamforming algorithm. This algorithm is a gradient based algorithm to minimize the total processor output power, based on the look direction constraint. The adaptive algorithm 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 combined form of the constraint is called constraint for narrowband beamforming [7], [14], [15].
This form consider a narrowband beamformer where the narrowband signal from each element of smart antenna 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 user i, in the jth path is as follows [13], [15], [16]. q
( ) [ ( ) ( )
... (, ), 1( ) ]
.) (
1 , , ) (
0 , , )
( ,
j T N q i j
q i j
q i j
q
i m = w m w m w − m
w (6)
Accordingly, the output of the array in the mth iteration in the jth path for user i, is given by q
( )
( )( )
,( )
., )
(
, m m m
yijq =wijq Hri′q (7) where ri′,q =
[
ri′,q,0 ri′,q,1 ... ri′,q,N−1]
T.The expected output power of the array in the mth iteration is given by
( ) ( ( ) ( ) )
( ) ( ) ( ) ( )
( )
( )
m( )
mm m
m m
m y m y m
y
j q r i r H j q i
j q i H q i q i H j q i
j q i j q i j
q i
) (
, )
( ,
) ( , ,
, ) (
,
* ) (
, ) (
, ) 2
( ,
E E E
w R w
w r
r w
′
= ′
′
= ′
⎟⎟=
⎠
⎜⎜ ⎞
⎝
⎛
(8)
where E
( )
. is denoted the expectation and Rr′r′ is the correlation matrix of the received vectorr′i,q( )
m .Fig. 2. The distance between two pairs of mobile transmitters and base- station receivers [14].
A real-time CLMS algorithm for determining the optimal weight vector for user i,q in the jth path is [15], [16]:
( ) ( ) ( ( ) )
( )
⎪⎩
⎪⎨
⎧
= +
= +
1 1
, ) , (
, ) (
,
) (
, )
( , )
( ,
j q i j q i H j q i
j q i j
q i j
q
i m m g m
θ
µ a
w
w w
w
(9)
where
(
iq j)
jk jk N Tj q
i ) , , [1 e dsin i,q,j ...e d( 1)sin i,q,j]
( ,
θ
θ = − θ − −
a (10)
denotes spatial response of the array for user i, in the jth q path. Also in (9), w(i,jq)
(
m+1)
is the new weight computed at the(
m+1)
th iteration for useri, in the jth path. Also, the q variable scalar µ denotes 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 g(
ijq( )
m)
) (
w, denotes an unbiased estimate of the gradient of the power surface ( j
( )
m H rr ijq( )
mq i
) (
, )
(
, R w
w ′′ which is the expected output power of the array) with respect to wi(,jq)
( )
m after the mth iteration.The algorithm is “constrained” because the weight vector satisfies the constraint at each iteration, that is
(
, ,)
1) (
, ) (
,jq H ijq iq j =
i a θ
w . Rewrite the CLMS algorithm as
follows [7], [15].
( ) ( ( ) ( ( ) ) ) ( )
m N g m
m iq j
j q j i
q i j
q i j q i j
q i
, , ) ( ) ,
( , )
( , ) (
, )
(
, 1 θ
µ w a
β w
w + = + + (11)
where
( ) ( )
, .
) , ( , , ) , ( ) ,
(
, N
H j q i j q i j q i j q j i
q i
θ
θ a
a
β =I− (12)
The gradient of j
( )
mH rr ijq( )
mq i
) (
, )
(
, R w
w ′′ with respect to
( )
mj q i ) (
w, is given by [15]
( ( ) ) ( ( ) ( ) )
( )
mm m
m g
j q i r r
j q r i r H j q j i q i j
q i
) (
,
) (
, )
(
* , ) (
, )
( ,
2R w
w R w
w w
′
′
′
′
∆
−
=
∂
− ∂
=
(13)
and its computation using this expression requires knowledge of Rr′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 Rr′r′ by its noise sample
( )
iq( )
Hq
i′, m+1r′, m+1
r available at time instant
(
m+1)
, leading to(
( )( ) )
2 ,(
1)
(,)*( )
., m m y m
gwijq =− ri′q + ijq (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 standard algorithm are sensitive to the signal power, requiring 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 It should be mentioned that for the array antenna weight vector elements in the CLMS algorithm and for bigµ, will converge after a few iteration (is approximately equal to the number of beamformer weights, i.e.,m=N) [7], [15], [17].
Accordingly, the output signal from the jth beamformer (j=1,...,L) can be written as
( ) ( ) ( )
( )
( )
t I( )( )
t n( )
tI
t c t
b p t y
j j q i j q i
j q i j q i q i j q i q i q j i
q i
) ( , ,
, , , , , , , , , )
( ,
~ + +
+
−
′ −
= τ τ α
(15) where n(j)
( )
t is a zero mean Gaussian noise of variance σn2 andI~i,( )qj( )
t, the CCI, is defined as
( )
( ) ( ) ( )
(
iql)
q i
l q i q i l q i L
j l l
l q i j q q i i j
q i
t c
t b g
p t
I
, , ,
, , , , , ,
1
, , ) ( , , ,
~
τ
τ α
θ
−
×
′ −
=
∑
≠
=
(16)
and Ii,( )qj
( )
t , the MAI, is defined as( )
( ) ( ) ( )
(
kml)
k m(
k ml)
m k l m k
M
m K
q i m k k
L
l
l m k j q k i
m k j
q i
t c t
b
g y x p t
I
m
, , , , , , , ,
1 , ,
1 1
, , ) ( , ,
, ,
τ τ
α
θ
−
−
×
′ Γ
=
∑ ∑ ∑
= ≠= = (17)
where gi(,qj)
( )
θ is the magnitude response of the jth beamformer for user i,q toward the direction of arrival θ.B. Matched Filter Stage
Using beamforming will only cancel out the inter-path interference for the desired user and will reduce the MAI from the users whose signals arrive at different angles from the desired user signal (out-beam interference). Now, in the second stage of the RAKE receiver, the output signal from the jth beamformer is directly passes on to a filter matched to the
desired user’s signature sequence. The jth matched filter output corresponding to the nth bit is [9]:
( )
n p b( )
n I( )
n I( )
n n( )
nzi(,jq) i,q i,q i,q,j ~i,(qj) i,(qj) (j) + ′ + ′
+ ′
= ′ α
(18) where
( )
I( )( )
t c(
t)
dtn T
I iq iq j
nT
T n
j q i b
j q i
j q i b
j q i b
, , , )
1 (
, )
( ,
, ,
, ,
~ 1
~ τ
τ
τ
−
′ =
∫
+
+
−
(19)
( )
I( )( )
t c(
t)
dtn T
I iq iq j
nT
T n
j q i b
j q i
j q i b
j q i b
, , , )
1 (
, )
( ,
, ,
, ,
1 τ
τ
τ
−
′ =
∫
+
+
−
(20)
( )
1( )
,(
, ,)
.) 1 (
) ( )
(
, ,
, ,
dt t
c t T n
n
n iq iq j
nT
T n
j b
j
j q i b
j q i b
τ
τ
τ
−
′ =
∫
+
+
−
(21)
If we assume that the paths’ delays from all users are less than the symbol duration
(
τk,m,l <Tb)
for all users’ signals on all paths, the nth bit MAI at the output of the jth matched filter can be expressed as( ) ( ) ( )
(
iq j iql)
i i
q i l q i L
j l l
l q i j q q i i j
q i
R
n b g
p n
I
, , , , ,
, , , 1
, , ) ( , , )
( ,
~
τ τ
α θ
−
×
= ′
′
∑
≠
= (22)
and
( ) ( ) ( )
( )
ik(
iq j kml)
m k l m k M
m K
q i m k
k L
l
l m k j q k i
m k j
q i
R n b
g y x p n
I
m
, , , , , , , , 1
, ,
1 1
, , ) (
, ,
) (
, ,
τ τ α
θ
−
×
′ Γ
′ =
∑ ∑ ∑
=
≠
= =
(23)
where the autocorrelation function Ri,k
( )
τ is [9], [18]:( )
1 ,( )
,( )
., =
∫
+Tb
m k q i b k
i c t c t dt
R τ T τ (24)
If all users’ delays are multiples of the chip period, then
( )
G( ) ( )
c( ( )
c)
l G
l
m k q i k
i c l c l R l l T
R G 1 2
1
0 1
0
2 , 1 , ,
1 2
1 − −
=
∑ ∑
−=
−
=
τ τ
(25)
where the autocorrelation function Rc
( )
τ is:( )
= 1∫ ( ) (
+)
.Tb
b
c ct ct dt
R τ T τ (26) In the case of a maximal-length sequence (m-sequence) and for0≤τ ≤Tb, we have [18]:
( ) ( )
⎪⎩
⎪⎨
⎧
≥
−
≤ +
= −
.
; /
1
; / 1 1 1
c c c
c
T G
T T G
R
τ τ τ
τ (27)
C. Maximal Ratio Combining Stage
Diversity combining has been considered as an efficient way to combat multipath fading because the combined SINR is increased compared with the SINR of each diversity branch.
The optimum combiner is the MRC whose SINR is the sum of the SINR’s of each individual diversity branch [18], [19].
After the finger-matched filter, the fingers’ signals are combined according to the MRC principle in the third stage of the RAKE receiver. In this paper, we use the conventional MRC that the signal of user i,q in the jth path is combined using multiplying by the complex conjugate of αi,q,j.
The SINR in output of the RAKE receiver for user i,q is [9], [19]:
( ) ∑ ( )
=
=
L
j
(j) i,q i,q
1
SINR
SINR α α (28) where
( ) ( ) ( )
,( ) 2( )
( ) 2) 2 ( ,
2 , , ,
E
~ E E SINR
j j
q i j
q i
j q i q (j) i
i,q
n I
I
p
+ ′ + ′
′
= ′ α
α (29)
is the SINR in output of the RAKE receiver in path j for user i,q.
Also, we can be rewritten the SINR in (29) by (30), that shown at the bottom of the page [9], [20], whereΓk
(
x,y)
=E(
Γk(
x,y) )
and ⎟⎠
⎜ ⎞
⎝
= ⎛ , , 2
2,m,j E k mj
k α
α .
IV. SMARTSTEPPOWERCONTROLALGORITHM A major limiting factor for the satisfactory performance of CDMA systems is the near-far effect. Power control is an intelligent way of adjusting the transmitted powers in cellular
( )
( ) ( ) ∑ ∑ ( ) ∑ ( ) ( )
∑
=≠
= =
≠
=
+
−
′ Γ +
′ −
=
′
= M
m b
l m k j q k i i K
q i m k
k
L
l
l m k j q j i m k k
m k L
j l l
l q i j q i i i l q i j q j i q i q i
j q i q (j) i
i,q
T R N
g y
x p R
g p
p
m
1
, 0 , , 2 ,
, ,
,
1 1
2 , , ) (
, 2
, , ,
1
, , , 2 ,
, 2 , , ) (
, 2, , ,
2 , , ,
, 2
where SINR
τ τ θ
α τ
τ θ
α η
η α α
(30)
systems so that the total transmit power (TTP) is minimized, but at the same time, the user SINRs satisfies the system quality of service (QoS) requirements [21].
Depending on the location where the decision on how to adjust the transmitted powers is made, the power control algorithm can be divided into two groups: centralized and distributed techniques [1]-[6]. In centralized power control, a network center can simultaneously compute the optimal power levels for all users. However, it requires measurement of all the link gains and the communication overhead between a network center and base stations. Thus, it is difficult to realize in a large system [22]. 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 [23].
The distributed closed-loop power control problem has been investigated by many researchers from many perspectives during recent years [23]. For instance, the conventional fast closed-loop power control strategy used in practice in CDMA systems is a fixed step controller based on SINR measurements. The fixed step closed-loop power control (FSPC) algorithm is defined by [4]
(
iq inq)
n q i n
q
i p
p,′+1= ,′ +δsign γ*, −γ ,′ (31) where pin,q′ , γi*,q, and γin,q′ are the transmitter power, SINR target, and measured SINR of user i,q at time n′, respectively, and δ is the fixed step size. Also pin,q′+1 is transmitter power control (TPC) command in the feedback link of the base station to user i,q at time n′+1(all signals are in decibels). In this algorithm, the simple intuition behind this iteration is that if the current SINR γin,q′ of user i,q is less than the target SINRγi*,q, then the power of that user is increased; otherwise, it is decreased.
Also in [24], variable step closed-loop power control (VSPC) algorithm has been proposed. In this algorithm, variable step size is discrete with modeqv. It is shown that the performance of VSPC algorithm with mode qv =4is found to be worse than that of a fixed step algorithm (qv=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.
In this paper, we present the smart step closed-loop power control algorithm. We express the SSPC algorithm as follows.
[11]
( )
.sign *, , ,
* , , 1
, n
q q i i n
q q i n i
q n i
q
i p
p ′+ = ′ +δ γ −γ ′ γ −γ ′ (32) Performance of the SSPC algorithm is shown in Fig. 3. The algorithm is implemented as follows.
1) Select the initial transmitted power vector (n′=0) for all users within cell m as
[
0 ,]
0 , 2 0
, 1
0 m m... K m
m = p p p m
p , m=1,2,...,M.
2) Estimate the weight vector for all users with the CLMS algorithm using (11).
3) Calculate the SINR for all users using (28).
4) If γk*,m−γkn,′m >ε0 for each user then set n′=n′+1 and calculate the TPC for all users at time n′+1 using (32) and go back to 2), where ε0 is threshold value.
5) Finally, if γ*k,m−γkn,′m <ε0 for all users then algorithm ends.
V. THEOTHERBEAMFORMINGMETHODS A. Conjugate Gradient Adaptive Beamforming
In the CGBF method, unlike other adaptive algorithm, the number of weights is less than the number of sensors such thatS=2N−1. The algorithm is used of orthogonal principle to find optimum antenna weights. On this basis, a set of vectors wi is to select such that they are A-orthogonal, i.e., Awi,Awj =0fori≠ j. Accordingly, desired users’ signal in an arbitrary path is passed and the IPI is canceled in other paths in each RAKE finger, while the IPI in the CLMS algorithm is reduced [9]-[11].
B. 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. Switched-beam systems are technologically the simplest 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.
Fig. 3. Block diagram for the SSPC algorithm.
1) According to Fig. 4, coverage angle for all beams is 30 D and overlap between consecutive beams is20 . Thus each D base station has 36 beams.
2) According to Fig. 5, each user can use one beam for its each path to communicate with a base station at any time.
Also, one simple method to sectorize a cell is equal sectoring, in which all sectors have the same coverage angle.
In this paper, we assume three sectors for each base station with sector angle 120 for the ES method. D
VI. SIMULATIONRESULTS
We consider M =4 base stations for a four-cell CDMA system on a 2×2 grid as Fig. 6. We assume a uniform linear array of S omni-directional antennas in each base station with antenna spacingd=λ/2. Also, we assume the input data rate
Kbps 6 .
=9
Tb ; processing gain G=64 (for m-sequence code); the number of antenna weights N=3; the number of antenna sensors S=3; threshold value ε0=0.1dB; frequency-selective fading channel with L=2 resolvable propagation paths; variance of the complex Gaussian fading channel coefficient σα2 =4dB; fixed step size for SSPC, FSPC, and VSPC algorithms δ =0.01; mode qv =4 for VSPC algorithm [24]; variance of the log-normal shadow fading dBσξ2=8 ; path-loss component Lα =4; resolution
=1
R ; initial value for weight vectors in CGBF method and CLMS algorithm w
( )
0 =0; initial value for transmitted power vectors p0m=0. The SINR target value is the same for all users and is set toγ*=5(
7dB)
. It also is assumed that the distribution of users in all cells is uniform.Fig. 7 shows the comparison of the average SINR achieved over 32Ku = users versus the power control iteration index (n′) for SSPC, VSPC, and FSPC algorithms. In this simulation, the three-stage RAKE receiver uses CLMS, CGBF, SB, or ES methods in the first stage. Also, we assume that each user to have a maximum power constraint of 1watt.
Accordingly, we observe that the convergence speed of the SSPC algorithm is faster than the VSPC and FSPC algorithms.
In addition, we see that the convergence speed of the SSPC algorithm for the SB technique is faster than the CGBF, CLMS, and ES methods. Also it can be seen that the convergence speed of the SSPC algorithm for the CGBF method is faster than the CLMS method, because in CGBF method the IPI is removed, while in CLMS method is not canceled. Also observe that the average SINR level achieved is below the target SINR value for the ES method, because in this method the MAI is higher than CLMS, CGBF, and SB methods.
Fig. 8 shows the comparison of TTP usage versus the power control iteration index (n′) when there are Ku =32 users in all cells according to Fig. 7. But in this simulation, we assume that users no have maximum power constraints. Similar to Fig.
7, we observe that the ES method never can achieve the target SINR value. Also this figure shows that the SSPC algorithm offers more savings in the TTP as compared to the VSPC and FSPC algorithms. In addition, the figure shows that the TTP in the CGBF method is less than the CLMS algorithm. Also it can be seen that the TTP for the SB technique is lower than other methods, because in SB technique the MAI is lower than CGBF method.
VII. CONCLUSIONS
In this paper, we studied the RAKE receiver performance of multiple-cell DS-CDMA system with the space diversity processing, Rayleigh frequency-selective channel model, and
Fig. 4. 36 beams in each base station with switched-beam technique.
Fig. 5. Select of beam for two users in two paths with the switched-beam technique.
Fig. 6. Location plot of base stations and users in four cells.
closed-loop power control. This receiver consists of CLMS algorithm, MF, and MRC in three stages.
Accordingly, we proposed the SSPC algorithm in order to compensate the effects of the near-far problem. It has been shown that, by using antenna arrays at BSs, this algorithm will decrease the interference in all cells. 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. In addition, it can see that the TTP in the SSPC algorithm is less than the FSPC and VSPC algorithms.
On the other hand, it has been shown that the convergence speed of the SSPC algorithm is increased in comparison with the FSPC and VSPC algorithms.
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