2004 Y’ International Conference on Computational Electromagnetics and Its Applications Proceedings

New Adaptive Beamforming Algorithms For Smart Antennas In DS-CDMA Mobile Communication Systems

Vu Dinh Thanh, Nguyen Le Hung The HoChiMinh City Unversity of Technology, Vietnam 268 Ly Thuong Kiet, Dkt. IO, HoChiMlnh City, Vietnam

v dthanhahcmut edu.vn

Abstract The increasing capacity and quallty demands for mobile communication services without a corresponding increase in RF spectrum allocation motivate the need for new techniques to improve spectrum utilhtioa The CDMA and SDMA (Spatial DMskn Multiple Access) technologies are two solutions that show real promlses for increasing spectrum efilciency. The paper investigated adaptive beamforming algorithms of mart antennas to implement and combine the CDMA and SDMA techniques in DS-CDMA systemr In the paper, three blind adaptive algorlthmr DR-LMS @e-Eptead Respread - Least Mean Square), DR-SMI (Despread Rsspread - Sample Matrix Invetdon) and DR-RLS @&spread Respread - Recursive h s t Square), are htmduced and simulated fn Matlab 6.1. These blind algorkthms are based on the conventionat LMS, SMI, RLS algorithms (Ill, 121, 131, [4f, IW

Keywords Sm~rt ankennos, blind adaptive algonthms,

orray mfema, Spatial Division Mdliple Access (SRM), Least Mean Square (urs)), Recursive Last Square (RLS), Sample Matt% Invenion (AMI)).

I. INTRODUCTION

The capacity and quality of DS-CDMA systems are mainly limited by Multiple Access Interference (MAI). One of many solutions to the problem is thz combination of SDMA and CDMA techniques in DS-CDMA systems where the smart antenna systems incIuding array antennas and digital signa1 processors are used

The radiation pattern of smart antennas can adapt simultaneously with the signal environment in a cell of mobile communication systems. It can steer constantly one main lobe (maximum direction of radiation) to a desired mobile u e r (or SOI: Signal of Interest) and nulls (minimum direction of radiation) to interfering users when mobile users move arbitrarily in a cell. This special characteristic reduces a considerable amount of MAI and multi- path fading in DS-CDMA systems. Therefore, the capacity and quality of the DS-CDMA systems can mcrease considerably.

II. MATHEMATICAL MODEL OF SIGNALS IN SMART ANTENNAS

Referenrc/ Element

Fig. I: Model of b e a r amqy antennn flrom [6]). In case of one mobile user in a cell, the

received signal vector at M element antennas can be expressed in the column vector form as:

or r(t) = a(9 )x, ( t ) (2) 1

with a(0 = le e::: 5lne

- j . - ( ~ - l ~ d rlna

(3) with 0 is the Direction of Amval (DoA) of

incoming signal from a mobile user. a(e) is called array response vector or steering vector. x,(t) IS the received signa1 at the i* element antenna.

In case of q mobile users m a cell, the received signal vector at M element antennas can be written as:

(in lght of sight environment)

0-7803-8562-8/04/$20.00 Q2004 IEEE . 165

or:

1-1 k-1

(in multi-path environment with LA4, signal paths for the iffi user).

n(t) is the noise signal vector at M element antennas. sI(t) is the transmitted signals from the $mobile user

Signals after the beamforming process in smart antenna can be represented as:

M y(k) = ( k ) = w X x ( k ) (6>

1.1

h the above formula, w = [w,, wz ,.... W, ] is the weighting vector of a desired user and wB = waT. The main aim of the study is to calculate the weighting vectors of users after each data frame by Adaptive Control Processors with many adaptive beamforming algorithms in order to minimize the error value between yfi} and s,@). The details of adaptive beamforming algorithms-will be discussed in the next part.

T

III. ADAPTIVE BEAMFOFWING ALGORITHMS. Most .of adaptive algorithms can be

classified in two main types: non-blind and blind algorithms.

In non-blind algorithms, Adaptive ControI Processors have to use the training signal, the known signal, to calculate and update constantly the weighting vector for each mobile user when they move within a cell. The conventional non-blind algorithms (the LMS, RLS, SMI, ...) are already known and presented in published papers [4], [5 ] .

In contrast to non-blind algorithms, the blind algorithms do not use the training signal to calculate the weighting vectors. In point of view of data processing, the main difference between the blind and non-blind algorithms is that the first one perfoms block processing while the other performs sample processing in received signals. All of the known criteria are the properties of transmitted signals from mobile users. It is also supposed in the paper that the transmitted signals are modulated by PN sequences that are mutually known between the transmitter and the receiver. This is the unique and ultimate criterion w i h the DS-CDMA systez which can be used to detect the signal from the i user. Because the F" sequences are orthogonal to each other, the Despread-Respread algorithms presented in the following are studied and become the new feasible solutions for blind detection. Three blind algorithms are presented in the paper: DR-LMS

(De-spread Re-spread - Least Mean Square), DR-RLS (De-spread Re-spread Recursive Least Square), DR- SMI (De-spread Re-spread - Sample Matrix Inversion). In point of view of data processing, the main difference between the blind and the non-blind algorithms is that the fm one performs block processing while the other performs sample processing in received signals.

The ultimatum of the blind algorithms is to use the known PN sequences to regenerate the signals, ~ ( 0 , which play the same role as the training signals, si(qf). in non-blind algorithms. From ~ ( l ) , all the weighting vectors w(T) could be deduced such that the receiving beamforming module.could select the best direction of arrivals with the lowest errors. We will co-mequently consider the following three proposed blind algorithms hifilling the previous aim :

at The DR-LMS blind algorithm can be described by the following iterative equations: X(2) = [x(l -t IK),x(2 -k K), ..., x((1 f 1)K)I

[r,cr+ W , Y I 1 2 + w, . . . . y iK l+ 1)V]' (8 )

(7) with I=O,l,. . .,L.

Yi (1) = by (ox(or =

The Despread process consists of the multiplication between the received signal yi(k) and the PN sequence ci(k) of the user number I, which gives the data output from the decisive detector.

bd = s e Re z y , ( k ) c , ( k - k i l ) 11 (9)

(1+l)X

{ [k*l+lX

The Respread step is now taken again on the received data b; and its own PN sequence c;(k) which produces the signal r@). 0

r,

where, L is the number of iterations to calculate the weight% vector, K is the size of a block of samples, k, is the delay time in samples of the F" sequence c,(k)

between the transmitter and the receiver. This Despread-Respread algorithm can be

summarised in the Fig. 2. The weighing vector in the (l+l)* iteration is related to that of the previous I * iteration and to the difference between the generated signal r,(l) and the output obtained signal y,{l): w, ( I + 1) = w1 (I)-+ p.X(Z).(ri(l) - y i ( l ) ) '

The equations (7), (X), (9), (IO) and (11) are the iterative equations forming the DR-LMS algorithm. After a certain number of iteration L, the weighting vector will converge to an optimal value. Therefore, the smaller L is, so the faster the convergence rate of algorithm.

= i d [c, (1 t 1 ~ - /c,),c, (2+ IK - ka 1, ...., c , ( (~ t [)K -k, C10)

(1 1)

166

I ci(cr,j

C d i - l a

Fig. 2: The Despi-eadRapeaddgmihn When the optimal weiglung vector, wj(L), is

attained, h e emx value between the received signal of user im, y,fi,, &a the beamfming process and the training signal, s,lkj, is minimum.

b l The DR-RLS algorithm follows the similar processing on the PN sequence ofthe iih user, as in the previous algorithm, and can be simildy described by the i l edve equations:

with I=O,L,. . .L. X(I)= [r(i+zK),x(2+IK), ..., X ( ( l + l ) K ) ] (12)

(1 31

q -'P(I - I)X(Z) I +r)-'xH (r)P(r - 1)X(2)

K(I) = (1 6)

e,(I> = r,(l)-wy(!-I)X(I) (17)

w , ( I ) = w ( I - I) + K(l)e (I) (18)

P(l) =q -'P(l- 1) -q-lK(l)XH(l)P(l - 1 ) (19) where €'(I) is the cross-relation matrix

between the input signal X [ I ) and the fraining sequence d(0, and P(0) = 6 -'.I with I is the identity MxM matrix.

The main modification of this algorithm compared to the previous one is that Ihe error vector

is the difference between the generated signal r,O) and the input signal xiQ) w ~ g h e d by ihe vector WO-1) of t h e previous iteration, as shown in (17). This is a recursive process and so is the name of the method. By iteratians, the weighing vector is always regulated fiom the error value, as given in (18). The iterations are repeated until the step Lm, where the enor vector q(l) attains an infinitesimal value.

C) The DRSMI rrlgorahnr can be expressed in iterative equations as:

ri ( l ) - L [ c , o + M - k,),c, (2t 1~ - tw>,. , . ,c, (0 + I ) K - k,)lr (23) 1 R(I) = -X(A * X H (l) K ,

K

where the expressions (24), (25), (26) are the conventional SMI algorithm. The new idea here is that the Despread-Resprertd process be applied to deduce the training sequence &r) fiom the signal ~ ( 4 .

We can easily found thal the main difference between a DS-CDMA system with smart antennas and a conventional DS-CDMA system is the existence of the receiving and the transmitting beamforming modules. These two modules perform as the fitters of received signals in spce domain.

'(24)

125)

(26)

d,(l) = -X[I)* 1 r, (I)'

w , (0 = R-'(l) * d, (0

IV. SZMULATION RESULTS AND DISCUSSIONS. Fig. 3 illustrates the special property of smart

antennas' beam patlea Here, we study the case of 4 users at diffaent DoA mgla. By Using the DS-RLS algorithm, aRer some iterations, the beam patlems of these 4 user antennas given in t h e Fig. 3 show that each beam pattern has one main lobe orienting toward the desired user and three nulls at the Directions of Arrival ofthe other users.

Fig. 3: Beam parrem of four usem (Direclions OJ Arrivulore respective& s@, 75'. 104. I ~ s D ) in he DS- COM system using mmrt mimw, culalafed by the DR-RLS a l g o r i ~ h .

Fig. 4 inhates that the convergence rates of IUS, DR-SMI, DR-RLS, DR-LMS d g o n h s are much faster than that offhe conventional LMS algorithm, so that the performance of the blrnd algorithms over the conventrod ones are demonstrated

SrNR ver51.15 ileration ofDR-SMI. DR-RLS, DR-LMS. ,

SINR ;ersus S MR versus jterahon ofRLS itemon of LMS Fig. 4: Average ShVR d u e of 4 users versus

iteratiom

SINRline of smart antennas with U, DR-SMI, DR-RLS. DR-LMS.

SINR h e in convenhonal DS- CDMA sysiems

SINR hne of dart antemas with LMS

Fig S . SLVR vuitte of mch mobile user. From the Fig. 5, rt is found that the SINR

values of four usem increase sharply when DS- CDMA sysfems use mart antennas (mth RLS, DR- SMI, DR-RLS, DR- LMS algorithms), compared to the iow SINR values of the conven?" DS-CDMA systems. This fact.strongly shows the advantage of smart antennas over the conventional ones.

The Fig 6 wd 7 show the complex ConsteUations of received signals (BPSK or DS- CDMA modulations) after being processed by convenhonal array and by smart antennas The 'k" marks are the expected positions of BPSK slgnals In conventional DS-CDMA systems, the POS~QO~S of demodulated sign& of four users are qwte far kom the expected positions while they are vmy near in DS-CDMA systems with marl antennas. It shows a considerable enhancement of demodulated signals in DS-CDMA systems wth smart antennas.

Fig 6: S i g d Constelhim of usem in DS-CDMA without smart antenms.

smart antennas.

V. CONCLUSION AND FUTURE WORK The paper introduced three novel blind

adaptive beamforming algorithms (DR-LMS, DR-RLS, DR-SMI) which are based on three conventianal non- blind ones (LMS, RLS, SMI) respectively. The simdation results were presented to show the considemble improvements in DS-CDMA systems wih smart antennas over fhe conventional ones and even though the advantages of Despread-Respread algorithms in the receiving system training. Although these three blind algorithms do not need the training signals, they require much more algorithmic and computational complexity than the conventional non-blind counterpart algorithms. This is the aim of the future works, where some new blind beamfonning algorithms with higher SINR values and less computational complexity will be M e r studied.

VI. REFERENCES [I] Seong Keun Oh, smnrr Antemar in Wiyireless Conimuniccnionr. *.pdf file 1996, School of Electronics Engineering, Korea. [2] Jonas Strandell and Mattias WennWom M.Sc. Thesis,

Adaptive anrennasysterns, EEUCSSON December 1996. (*.pdf file]. [3] Mattias Wcnnstrm, &m?imiennaIrnplemenW#n Irsues for Wireless Commmicatioa, Uppsala University, October 1999(*.pdf file)). [4] Vijaya Chandran Ramasami. ManbSMIAlgoPiUuruJb Spmial AdQpZzve 3ntet$?rc#e Rejection, March 16, 2001.

[ 5 ] Ajay Mahimkar, B h d Adaptive B c ~ o m i n g Algorilrm Using SoJwme R d o , MDIA (*.pdffile). [6] ECE354, Antcnna LectureNotes. [7] Nguyen Le Hung, An uppkcdon of"t mMmm Zo DS-CDM " W e communrcdbn ryriem, Master thesis, November 2003

('.pa file)

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