Vo1.16 No.2 JOURNAL OF ELECTRONICS April 1999

M U L T I U S E R D E T E C T I O N A N D D I V E R S I T Y R E C E P T I O N F O R A S Y N C H R O N O U S C D M A M O B I L E C O M M U N I C A T I O N

Wang Yan Cheng Shixin

(National Commu,ication Research Lab, Southeast, Uniw~rsity, Nanjing 210096)

A b s t r a c t In CDMA mobile communication systems, multiple access interference can be can-

celed by multiuser detection technique. The Degradation by chamml fading can be reduced by

diversity reception, This paper investigates a family of nmltiuser receivers that combined decor-

relating detection, antelma diversity and RAKE multipath diw~rsity. The performance of the

multiuser receivers is analyzed. The results demonstrate a significant increase in the performance

of the receivers by using multiuser detection and diversity reception.

K e y w o r d s Multiuser detection; I)iversity reception; Asynchronous CDMA channel

I. Introduction

The major advantages of CDMA systems are high capacity and high quality of services

(QoS). Conventional DS/CDMA systems treat tile signals from other users as Multiple

Access Interference (MAI). With the increasing tmml)er of users, tile performances degrade

rapidly. Tile problems due to MAI could not be solved by conventional correlation CDMA

receivers. Another problem is near-far effect. Even when tile desired transmitter is close

to the receiver, it may be subject to a deep fading causing the interfering signals from the

distant t ransmitter to be received with a large power. The current solution to the near-far

problem is power control.

In mobile communication systems, Base Station (BS) must detect all the signals from

different Mobile Stations(MS). In the reverse link, BS can reduce the MAI by multiuser

detections. It is verified by theory and simulation tha.t the performance can be improved if

multiuser detections are used.

In mobile communications, diversity reception is one of the most powerful techniques

used to combat the fading effects of tile channels. CDMA systems exploit the RAKE re-

ception and antmma diversity to alleviate the fading effects. In this paper, we analyze a

family of multiuser receiw.'rs with antenna diversity and multipath diversity. We only con-

sider decorrelator for simplicity[d. From analysis, it is shown that the performance can be

improved if we use multiuser detections and diversity reception in fading channels.

II. System Model

We consider an asynchronous multiple-access chamml shared by K users. The impulse

response of the k-th user's channel is

L-1

t ) = - l/B,,,) (1) / = 0

118 JOURNAL OF ELECTRONICS Vol.16

Where B~ is the coherent bandwidth of the channel, Ck,l(t), k = 1 , . . . ,K; l = 1 , . . . , L - 1 is the amplitude of k-th user l-th channel. It follows Rayleigh distribution. It is assumed

that the channel varies slowly, we can get the accurate estimation of the channels. For

data symbol duration is much longer than the nmltipath delay spread, any intersymbol

interference can be neglected. Each MS modulates the signal by BPSK. The received signal

of BS is

Z(t) = S(t, b) + n(t) (2a) + o c K L - 1

S( t ,b )= ~ E b k ( i ) E C k d ( i ) x / ~ k S k ( t - i T - f k - I / B w ) (2b) i = - - o o k : l / : 0

Where Sk(t) is the spreading chip sequence of k-th user with support in [0, T), T is the

information bit period, L is the numbers of multipath, Wk is tile received power, n(t) is

the additive white Gaussian noise, b(i) = [bl(i) , ' ." ,G(i)] T is the information bit vector.

Without loss of generality, we order the users according to their relative delays of the first

arrival 0 < ~-1 < "'" < ~-k 1

In matrix notation,

Sk(t) = [Sk(t) ,Sk(t- 1 /B~) , . . . , S k ( t - ( L - 1)/B~)] T "2

Ck (t) = [ G , o (t), Ck, (t), • • •, G,L- (t)] T

In receiver, the output of despread can be expressed as

yi(t) = R( -1) .C( i+l ) .W.b( i+l )+R(O) .C( i ) .W.b( i )+R(1) .C( i -1) .W.b( i -1)+n( i ) (3)

where y(i) = [Yl,o(i),""', YI,L-1 (i), Y2,o(i),""", YK,L-1 (i)] T, W = diag( Iv/Y~-l, ~ , . . - , v/WK),

c (i)

C 2 ( i ) C(i) =

c A - ( / )

R(/) , l = - 1 , 0, 1 is the cross-correlation matrices of normalized signature waveforms. We

can get it from

f ( i + I ) T + T , , ,

Rm,~(1)= S m ( t - ~ , ~ ) ' S ~ ( t + i T - v n ) d t , m , n = l , . . . , K (4) d i T + rm

It can be shown that R ( - 1 ) = RH(1) .

The covariance matrix of the noise vector is given by E{n*(i) • nT(j)} = a2R(i - j). The Z-transform of Eq.(3) is

Y(Z) = [RH(1)Z + R(0) + R ( 1 ) Z - ' ] . [C. W . B](Z) + N(Z) (5)

1We can get the results in the same way if the delay spread is greater than T. 2Matrix superscripts T, * and H denote transpose, conjugate, and conjugate transpose,

respectively.

No.2 MULTIUSER D E T E C T I O N AND DIVERSITY R E C E P T I O N 119

Where [C. W . B](Z) is tile Z-transform of C(i) • W . b(i).

III . S t r u c t u r e a n d P e r f o r m a n c e A n a l y s i s o f t h e R e c e i v e r

In Ref.[2], the author analyze a family of receivers that use the structure of multiuser

de tec t ion /RAKE diversity combination. In Ref.[2], the multiuser detector is K L inputs and

K L outputs. The complexity is proportional to KL. It is hm'd to realize if L or K is large.

In this paper, we perform the combining prior to nmltiuser detection. The complexity of

multiuser detector is proportional to K and have nothing to do with L. The realization is

simpler than that in Ref.[2].

1. Divers i ty combiner-deeorrelator Fig.1 shows tilt s tructure of the receiver with single antenna.

Fig. l Receiver with diversity-combiner and decorrelator

If the channel varies slowly, we can accurately estimate the channel. The output of the

Maximal Ratio Combiner (MRC) is

c " . Y ( z ) = c H • [RH(~)Z + R(0) + R(1)Z-~I. C. [W. B](Z) + C " . X ( Z ) (6)

For most of the CDMA systems, tile spreading sequen(:es arc' linear independent. The cross-

correlation matrices are nonsingular. Let.

G f ( Z ) = {C tl . [R t I (1 )Z + n ( 0 ) + R(1 )Z-1 ] • C} -1 (7)

The output of decorrelat, or can be expressed as

X I ( Z ) = [W. B](Z) + a f ( z ) , c H . N ( Z ) (8)

+co . z - m , If N I ( Z ) = Gf (Z) . C H- N ( Z ) , G f ( Z ) = E,,~ -ec D f ( m ) tile decorrelator 's output

of k-th user is

SS,k = V /~k • ba- + 7,,S,,: (9)

Where N$ (Z) is the Z- t ransform of a filtered Gaussian noise vector sequence with covariance

matrix a ~. G s ( Z ) , ns,k is the zero-Inean Gaussian variable with covariance cr 2. [Ds(0)],.a:.

If the channel is fixed, the condition error probability of k-th user is

120 JOURNAL OF ELECTRONICS Vo1.16

( v/-W-7 (10) P/,k = Pr(nLk > Y@kk)= Q \G2x/[DI(O)]k k

Where Q(x) = f:co 1/x/27. e-'Y'/2cl'y. Now we consider the structure of [D I (0)]kk- Let Gp(Z) = R g (1)Z + R(0) + R(1)Z -1,

then [Di(0)]kk = 1 j:,,[C H " Gv(ejw). C~k~dW" If G'l(eJw ) represents the algebraic com-

plement of Gl(e jw) with k-th column and k-th row, G'}(e jw) is the matrix that delete

Gi(e jw) in row fi'om Lk to L(k + 1) and column from Lk to L(k + 1).

[c H " Gp(ej~). C~,_k~ = IG}(eJ~)l = IG~(eJ~)l I _ Gq(eJ~). 1 IGs(eJ~)I IGAeJw)l (Ck) H'Ck (Ck) H'Ck

~ 2 1/2 1 2~T a2x/[Ds(0)]k k = Wk" (Ck,t] C . ~ G~(dW)dw (11)

From Ref.[3] and Eq.(l l ) , we can get the Bit Error Rate (BER) of k-th user under

Rayleigh fading.:

i L-I~ El [ "T! (12) G

Wk m[(ck l)2] T[l ~_ L-1N • ' " Y ' (13) ' T t

i#t

2. Effec ts of i m p e r f e c t R A K E d ive r s i ty

In practice, the number of the received paths of RAKE receivers is smaller than the

number of resolvable paths L. We consider single antenna.

In conventional analysis, the RAKE receiver performance degradation due to MAI has

been treated as Gaussian noise. Tim assumption is accurate if K and L are large [4]. K(L - L1) is large enough in practice to estimate the paths that are not received by RAKE receivers

as Gaussian noise• Compared with full RAKE receivers, the imperfect RAKE receptions

introduce MAI. The noise and interference increase the input of decorrelator:

K L--1 2

D, : 57 Z ~{E[(C~,')~] W~} (14) k = l I : l l

Where J is the spreading gain. E(x) is the mean of x. The BER of k-th user is

1 -}~ P~' = ~ ~ " i+~, /=0

(15)

L - 1

Wk' E[(Ck,z) 2] 91 = E @t (16)

i#t

No.2 MULTIUSER DETECTION AND DIVERSITY R E C E P T I O N 121

I V . N u m e r i c a l R e s u l t s

To illustrate the performance of the proposed multiuser receivers. We consider a

DS/CDMA system with 1.25MHz bandwidth[q. The multipath intensity profile is given

by

v ( r ) = (PT /T , , , ) . e ~/T.,. (17)

Where PT is the total average received power and T, , is the multipath delay spread.

We choose Gold sequence of period 127 as spreading sequence. Ti(i = 1 , . . . , K ) are

given by nT~., where T~. is the chip duration, n is uniformly distrihuted in [0,120). In the

simulation, it is assumed that all the 1~\, are equal.

Fig.2 shows fuli RAKE reception with K=8 , J=127, L=4. It can be seen that under

full RAKE reception, MAI can be removed by nmltiuser detection and diversity reception.

The performance improves greatly.

10=1

10-: g ~: !0 -~ .£

10- ~

10 -~

10-~

10-7

'°:I - -~ ,qNR- 16dE~

~ i0_~ I / / ~ ~ ' i

I 0 - ' | I

1 a 5 6 7 10 15 20 25 SNR(dP,) Active users K

Fig.2 BER with SNR Fig.3 BER with active users

Fig.3 provides tile performance of the full RAKE reception with different user number

for the case of SNR=16dB. With tile increasing rmmber of active users, the performances of

conventional receiver degrade rapidly, but tile perfornlances of tile receiver with lnultiuser

detection and diversity reception change a little. Under the multiuser environments, the

receivers with multiuser detection and diversity reception have much higher performance

than the conventional receivers. The more the number of active users is, the more the

improvement we can get,. For the channel with L=4 and K=8 , BER curves are presented

in Fig.4 under imperfect diversity condition. It is presumed that the receiver detects the

first two paths of 4 resolvable paths. If imperfect RAKE reception is used, the residual MAI

from the paths that are not utilized in the diversity combiifing affects tire performance of

the receiver with multiuser detection and RAKE diversity reception. From Eq.(16), we get

If l/Vk/cr 2 -+ oo, tire right side of Eq.(18) tends to be a constant. The BER tends to

be a constant, too. Increasing SNR without any limitation can not improve the system

performance.

122 JOURNAL OF ELECTRONICS Vol.16

Fig.2 and Fig.4 demonstrate that tile performance degrade greatly due to imperfect

RAKE reception. We use antenna diversity to improve the performance of imperfect RAKE

reception. In Fig.4, two antennas are used. It is shown that the system performance is

improved if antenna diversity is used. The reason is that the first two paths are the two

strongest ones in four received paths. There is no MAI between four received paths of two

antennas due to multiuser detection. 3

iO-i

q~ ~. I0 -'~

.2

t 0 _ 4

10-~ L0

2

3

| I I 12 [.l 16 18

SNR(dB)

Fig.4 BER with SNR under imperfect RAKE diversity

V. Conc lus ion

In multiuser CDMA systems, the system performance can be improved greatly by using

nmltiuser detection and diversity reception. Although the system complexity increases due

to multiuser detection and antenna diversity, the system performance is improved greatly.

In integrated traffic wireless communication system, using CDMA system with multiuser

detection and diversity reception is one of our choices.

R e f e r e n c e s

[1] R. Lupas, et al., Near-far resistance of multiuser detectors in asynchronous channels, IEEE Trans. on

C o m m . , 38(1990)4,496-507.

[2] Z. Zonar, Multiuser detection and diversity combining for wireless CDMA system, Wireless and Mobile

Communications, J. Holtzman and D. Goodman, Eds. Boston: Kluwer, 1994, 51-65.

[3] J. Proakis, Digital Communications, 1st ed. New York: McGraw-Hill, 1983, Chapter 7.

[4] T. Eng, et al., Coherent DS-CDMA performance in Nakagami multipath fading, IEEE 2)'ans. on

C o m m . , 43(1995)2/3/4, 1134-1143.

[5] W. Lee, Overview of cellular CDMA, I E E E r~ans, on VT, 140(1991)2, 291-302.

3In practice, RAKE receiver searches the strongest path. The results are similar to those

of this paper. Because the strongest path varies with time, it is hard to give an exact

presentation.