Interference Cancellation in CDMA Systems Using Multiple Receive ...

Interference Cancellation in CDMA Systems Using Multiple Receive Antennas Tao Wu, Christian Schlegel

Dept. of Electrical Engineering University of Utah Salt Lake City, UT 84112 Phone: (801)581-5561, Fax: (801)581-5281 Email: [email protected], [email protected]

Abstract

A multiple receive antenna (MRA) system is studied for code division multiple access (CDMA) using pseudo-random spreading codes. The core component, the receiver, jointly processes the multiple antenna array signals, despreading and error control code metric generation. Interference from joint users is cancelled by the projection method, where the signals are projected away from the interfering signal space. This method requires knowledge of the array response vectors, which is acquired via blind subspace estimation techniques. It is shown that the increase in system capacity is linear to the number of receive antennas. Performance analysis and simulation results are given to substantiate these ndings.

1 Introduction Mobile wireless communication systems are rapidly evolving from second generation to third generation (3G). Code division multiple access technology has been adopted by the major 3G standards, such as cdma2000 [1] and WCDMA (Wideband CDMA) [2, 3]. An important advantage of 3G systems is the provision of high data rate, high capacity and advanced services, such as video and packet data. This requires new technologies in the receiver design. Among these technologies, multiuser detection and multiple receive antennas are under intensive research for this purpose. Multiuser detection seeks to improve performance by cancellation or joint detection of interfering signals and thus increasing the system capacity. MRA, on the other hand, increase signal dimensionality and have the potential to improve dramatically the system capacity. Therefore, they are very likely candidates in future wireless communication systems. There has been a signi cant amount of work on receivers exploring interference cancellation in one form or another. A linear receiver structure is investigated in [4], which is composed of the conventional matched lter followed by a tapped delay line. [5] proposed a successive interference cancellation method with a blind adaptive antenna. [6] shows that multiuser blind identi cation can be accomplished by exploiting the spatial 1

and temporal diversities of an antenna array system. In addition to cancellation, antenna response vector estimation techniques are also studied in [7, 8]. A summary of the application of antenna arrays to wireless communications, with focus on beamforming and directions of arrival estimation, is well documented in [9]. The capacity improvement due to the use of receive antenna arrays is analyzed in [10, 11] for uplink channels as well as downlink channels. In this paper, a linear statistical interference canceling receiver is used in conjunction with MRAs. This receiver, by exploiting the increased signal dimensionality, signi cantly improves system capacity. As a prelude of this work, we studied a dual-antenna narrowband multiple access system in [12], doubling the capacity by using dual receive antennas. We note, however, that the system performance heavily depends on the directions of arrival (DOA) of dierent users' signals. Since these directions may not change or change only slowly, the signals of the users may be highly correlated negatively aecting system performance. We introduce spread spectrum signaling additionally to using MRAs. Using pseudo-random spreading codes, system performance is increased by alleviating the dependency on the angles of arrival of the dierent signals. We show theoretically, that, for large systems, performance becomes independent of the angles of arrival. Our proposed receiver uses a pilotless array response vector estimator to nd the system parameters required by the decoder. This paper is organized as follows. Section 2 discusses the multiple antenna capacity potential. Section 3 gives a description of the system model. In Section 4, two methods are proposed for the estimation of the antenna array response vectors and Section 5 reviews the interference cancellation receiver. A performance analysis and system capacity discussion are given in Section 6. Section 7 presents simulation results, and concluding remarks are given in Section 8.

2 Potential Capacity Improvement with Multiple Receive Antennas A multiple antenna system can not only reliably separate dierent users on the same channel using linear beam steering techniques, it also increases the inherent capacity of a link [13]. In essence the capacity will depend on how well the received signal space can be spanned by the transmitted signals. The following system is considered. With M antennas and K transmit signals, (1) s (t); s(2)(t);


; s(K)(t), the received vector of mutually interfering signals is given by 2 K 6 6 X (t) = 666 k=1 4

3

h(1k) 7 h(2k) 77 (k) (1) y . . . 77 s (t) + n(t); 5 h(Mk) where h(k) = [h(1k); h(2k);


; h(Mk)]T is the antenna array response vector for signal k and is assumed to be constant during the transmission of a frame of a data. Letting H = [h(1); h(2);


; h(K)] 2 C M K be the antenna array response matrix, 2

y(t) = Hs(t) + n(t);

(2)

where s(t) = [s(1)(t); s(2)(t);


; s(K)(t)]T . Such a system is formally identical to a CDMA system, where H would contain the spreading codes. The capacity of such a vector channel is readily computed following [14] as 

 1 + C = log2 det I + 2 HH   = log2 det I + 12 QQ+ ! M X  i = log2 1 + 2 bits=channel use:  i=1

(3)

where we have used the spectral decomposition of HH+ , and i are the eigenvalues of HH+ . The spectral decomposition allows us to decouple the channel into independent channels of power i. The i being the eigenvalues of HH+ , are related to the space of H. In fact, the orthogonal eigenvectors corresponding to the nonzero eigenvalues identify a basis of H, and the eigenvalues are a measure of how much signal energy is contained in the direction of each eigenvector. As long as the number of signals K < M , the number of antennas, maximum capacity is not possible since HH+ is rank de cient, and some of the dimensions carry no signal energy. This situation may be bene cial for channel estimation procedures since the unused dimensions can be employed for this purpose. For K  M , the entire signal space can be spanned, and maximum capacity is achieved if HH+ = I , i.e., if the rows of H, (not the columns), are orthogonal [15]. In the ideal case of equal power, i.e., 1 = 2 =


= M = , the MRA channel results in M decoupled channels, !  (4) C = M log2 1 + 2 bits=channel use: It becomes quite clear that the system with M receive antennas has a potential M -fold capacity compared to the system with only a single antenna. The incoming signals need to cover the signal space completely in order to achieve the highest possible capacity. As shown below, introducing random CDMA into the MRA system has precisely this eect, i.e., we can increase the system capacity M -fold with M receive antennas using long pseudo-random spreading codes.

3 CDMA Multiple Antenna System Model Considering a CDMA multiple antenna system as shown in Figure 1, we assume M receive antennas and K separated simultaneous users. This is a coded system where 3

(1)

c_ User 1 (1) _b

Encoder 1

d_

p(t) c_

User 2 (2) b_

Antenna Array

(1)

p(-t)

(2)

(2)

Encoder 2

d_

p(-t)

p(t)

y_1

y_2

Multiuser Detector

(K)

_c User K (K) b_

p(-t)

(K)

Encoder K

_d

^(1) b_ ^(2) _b ^(K) b_

y_M

p(t) Channel Estimation

_n(t)

Figure 1: Block Diagram of CDMA Multiple Antenna System. convolutional codes are used with code rate R = 1=2 [16]. Each user spreads its coded symbols with pseudo-random sequences with processing gain N , i.e., there are N chips for each symbol. Uniform angular distribution of the positions of the transmitters is assumed, i.e., the users are randomly located around the central receive antenna array which receives the individual signals with incident angles k ; k = 1;


; K . Letting s(k)(t) be the signal of the kth user, the received signal y(t) of the multiple antenna array embedded in additive white Gaussian noise n(t) is given by the general equation (2), and we have assumed that H is constant during the time period of interest. The signal from user k is L NX ,1 X d(k)[l] c((kl,) 1)N +np(t n=0 l=1 p1 ; + p1 ; n = 0; ; N 1 N N

, lT , nTc) + n(t);

s(k)(t) =

(5)

g


, g is the discrete spreading sequence where fc((kl,) 1)N +n 2 f, for user k during the transmission of the lth symbol d(k)[l], which is assumed to be a BPSK symbol, i.e., d(k)[l] 2 f,1; +1g. p(t) is the chip waveform, and T and Tc are the symbol and chip intervals respectively. Sampling the received signal at every antenna element at the chip rate, i.e., Ts = 1=Tc, we obtain a received signal vector y m from the mth element whose length is LN for L symbols. Stacking the M received signal vectors into Y = [y1; y 2;


; y M ]T 2 C M LN , the system equation can be written as Y = HS T + N :

(6) where H is de ned in (2) and N is a white Gaussian noise matrix. S = [S1; S2;


; SK ] 2 f p1N ; , p1N gLN K , and Sk is the signal transmitted by user k, which is the data sequence dk = [d(k)[1]; d(k)[2];


; d(k)[L]] spread by the pseudo-random code matrix Ck , i.e.,

Sk = Ck dk ; 4

(7)

where

2 (k ) [1] 6 6 k=6 6 4

C

c

c(k)[2]

0 ...

3 7 7 7 7: 5

(8)

0 c(k)[L] For each element and k = 1;


; K , c(k)[i] = [c((ki,) 1)N +1; c((ki,) 1)N +2;


; c(iNk)]T is a spreading sequence of length N for the ith symbol of user k. Although this system model is used for synchronous CDMA, it can easily be extended to asynchronous CDMA as well as a multipath fading environment. In that case, S would have dierent delays in the columns which represent the signals from dierent users. Working with the synchronous system, (6) can be broken up into a symbol-by-symbol model. We can write the received signal matrix for the ith symbol as

Y [i] = HS T [i] + N [i]; (9) and de ne the corresponding Y [i], S [i] and N [i] in a symbol interval analogously to (6). And Sk [i] = c(k)[i]d(k)[i]; We further note that although the antenna response vectors h(k) are independent of each other under the assumption of uniform distribution of the DOA, the elements of h(k)

describing the signals from the dierent antennas for user k, are related. The phase shifts between them are determined by carrier frequency, antenna distances and incident angles. Assuming a linear antenna array at the receiver in which any two adjacent antennas are spaced by an identical distance L, the phase shift between two adjacent antennas is (10)
k = 2L  sin(k ); where  is the wavelength of the carrier waveform and k is the incident angle of the kth user. Thus, the kth array response vector is given by

h(k) = [ k1; k1ej
 ;


; k1ej(M ,1)
 ]T ;

(11) where k1 is the complex amplitude at the rst element in the antenna array. Here we assumed that, for a speci c user, we obtain equal absolute amplitudes from all the elements. k

k

4 Antenna Array Response Estimation Methods For joint detection we have the essential prerequisite that the pseudo-random spreading codes and all the antenna array responses are known at the receiver if system timing information is available. While the spreading codes can easily be generated at the receiver, the array responses are determined by the directions of arrival of the dierent signals, which are not available in general. We assume, however, that the DOA remain constant, i.e., the array response matrix H is xed for the duration of a transmission frame and perfect signal delay estimates are known to the receiver. 5

We now need to estimate the matrix H in (6) using the known sequences S . The knowledge of the spreading sequences can be exploited to obtain maximum likelihood estimates of the array response vectors. First, we describe a simple matched lter estimator using pilot symbols. Second a blind array response estimator is proposed based on subspace estimation. Since the projection multiuser detector proposed in Section 5 is also a subspace method, we will see that the blind subspace estimator is well incorporated into the multiuser detector.

4.1 Matched Filter Array Response Estimation

If the symbols d(k)[i] are known (either as pilot symbols or via decision feedback), we can use the matched lter outputs to acquire the array response. Assuming that vector c(k)[i] is the spreading code for user k at symbol i, i = 1;


; L, the symbol matched lter output for user k is given as

g(k)[i] = Y [i]c(k)[i];

(12)

which is a vector of length M . As long as the symbols d(k)[i] are available, the array response estimate h^ k can be computed as L ^h(k) = 1 X d(k)[i]g(k)[i]: L i=1 which is the maximum likelihood estimator for the vector h(k) [17].

(13)

4.2 Blind Subspace Array Response Estimation

Using pilot symbols wastes bandwidth. Thus a blind array response algorithm requiring no pilot symbols is proposed here. For blind estimation, we have to investigate the second order statistics of the received signal for the array response estimation. Doing this we lose the capability to nd initial phase values. However, since g(k)[i] lies in the span of h(k), a subspace estimation method based on the second-order statistics of g(k)[i] can be ( k ) employed to estimate h . We rst compute the average covariance matrix Rgg over L symbols,

Rgg = L1

L X (k) [i] (k)[i]H ; i=1

g

g

(14)

and then nd its eigenvalue decomposition [18],

Rgg = X H X =

M X i=1

i xi xiH ;

(15)

where i and xi are the eigenvalues of Rgg and the corresponding eigenvectors respectively. The diagonal matrix  = diag(1;


; M ) contains the M eigenvalues and the M  M matrix X = [x1; x2;


; xM ] has the corresponding eigenvectors as columns. 6

Since we are using pseudo-random spreading codes, the antenna response vectors of the users other than k are suppressed by (12) over L symbols. We nd that there is a unique largest eigenvalue max which corresponds to the signal direction of user k. All the other eigenvalues are very small compared to it, since they are from either the noise subspace or suppressed interfering subspaces. Thus the one-dimensional subspace estimation for user k is given by the product of the largest eigenvalue max and corresponding eigenvector xmax of Rgg . However, without knowledge of data sequence d(k), we can only recover the antenna response within an unknown phase. The array response of user k is then estimated as

h^ (k) = maxxmax;

(16)

analogously to [20]. It is the kth column of channel matrix H rotated by an arbitrary global phase k , i.e., h^ (k) = h(k)ej . Note that, as a consequence of the incident angles, the covariance matrix Rgg in (14) changes slowly. Thus the channel estimation, i.e., the computation of (16), can be done only once per frame. This helps to reduce the complexity of the receiver signi cantly. k

4.3 Adaptive Array Response Estimation Using Gradient Method Since only the largest eigenvalue and eigenvector of the correlation matrix are required for the array response estimation, we resort to nding the largest eigenvalue and eigenvector without performing a complete spectral decomposition of Rgg . For any eigenvalue i of Rgg and its eigenvector xi we have

Rgg xi = i xi:

(17)

xHi Rgg xi = xHi ixi = i:

(18)

Normalizing xHi xi = I , we obtain

Thus, through the maximization of the cost function subject to we can nd xmax as

J = xH Rgg x;

(19)

xH x = I;

(20)

xmax = arg max x (J ):

(21) In this section, an adaptive subspace estimator is derived for this maximization using a gradient method, which can be seen as a simpli ed version of the algorithm proposed in [19]. The gradient of the cost function J can be obtained as   (22) rJ = @@x xH Rgg x = 2Rgg x: 7

At time n, an unbiased estimate of the gradient is given by

rJ (n) = 2Rgg (n)x(n , 1): Therefore, the eigenvector x can be updated as

(23)

x(n) = x(n , 1) + rJ (n);

(24)

where  is a small positive constant. This algorithm is recursive in nature. For stability, we should choose the step-size parameter  within [18] 0 <  < 2 : (25) max In a situation of slowly changing array responses, the correlation matrix itself can be updated as

Rgg (n) = (1 , )Rgg (n , 1) + g (n)gH (n):

(26) where the forgetting factor  is chosen for appropriate tracking of Rgg and we have 0 <  < 1. Finally, the array response is tracked as

h^ (k) = maxx(n) = Rgg x(n):

(27)

Using this gradient adaptive algorithm, we can nd the array responses without computing the spectral decomposition.

5 Multiuser Detection Using Signal Projection For the convenience of deriving the multiuser detection algorithm in this section, we want to modify the system model (6) into a vector channel equation. First, from (6), the received signal vector at the mth antenna can be written as

ym =

K X h(mk) k + m k=1

S

n =

K X h(mk) k k + m: k=1

Cd

n

(28)

where nm is white Gaussian noise. De ne A(mk) = h(mk)Ck of dimension L  NL, we get

ym =

K X k=1

A(mk)dk + nm :

(29)

While interleaving the data sequences of K users into a single vector as

d = [d(1)[1]; d(2)[1];


; d(K)[1]; d(1)[2];


; d(K,1)[L]; d(K)[L]]T ; 8

(30)

we also interleave the matrices fA(mk); k = 1; 2;


; K g along the columns into a KL  NL channel matrix Am. Thus the received signal vector at the mth antenna is

y m = Amd + nm:

(31) With a frame of L symbols and M receive antennas, we de ne the received signal vector 2 3 2 3

y

6 6 = 66 4

y1 y2 ...

yM

7 6 7 6 7 7=6 6 5 4

A1 A2 ...

AM

7 7 7 7 5

d + n = Ad + n:

(32)

It is quite clear that, when we assume synchronous transmission, Am is block diagonal and (32) can be written as a symbol based model, where, for the ith symbol, analogously to (9) y[i] = A[i]d[i] + n[i]; (33) where 2 3 A 1[i] 6 A2[i] 777 6 6 A[i] = 64 ... 75 : (34) AM [i] In this section, we deal with the system models of (32) and (33). We assume that the spreading codes are known and an estimate of H is obtained through the channel estimation discussed in Section 3. For simplicity, assume that we are decoding the signal of user K . The goal of our detector is to cancel the interference from the other K , 1 users and decode the data sequence of the desired user K only. First, we partition the received signal into two parts: desired signal and interfering signals. Taking only the columns corresponding to user K in matrix A, we obtain matrix AK of dimension LNM  L . We de ne the remainder of A as AI , the interference of user K . The received signal vector can be rewritten as y = AK dK + AI dI + n: (35) From Section 3, AK can be obtained by matched lter estimation using pilot symbols. However, the interfering matrix AI can only be determined up to a global phase matrix ,

AI = A0I ; (36) where  = diag(ej ;


; ej , ), and A0I is the estimated multiple access matrix. The partitioned minimization [22] is achieved by estimating dI over the unconstrained domain, i.e., dI 2 R(K,1)L, and estimating only dK over the constrained domain, i.e., the code sequences of user K , denoted by Dc, d^K = arg min min ky , AK dK , AI dI k2 d 2D d 1

K 1

K

c

I

9

= arg min (dK );

d

K

(37)

2Dc

where the sequence metric (dK ) is generated as (dK ) = kM(y , AK dK )k2; and M is the projection matrix onto span fA?I g, given as

(38)

M = I , AI (AHI AI ),1 AHI :

(39) This matrix M performs a projection operation of the received signal vector onto the null space of the interfering subspace spanned by the columns in AI . Bringing (36) into (39), we get 



M = I , A0I  (A0I )H A0I  ,1 (A0I )H = I , A0I (H A0HI A0I ),1H A0HI = I , A0I (A0HI A0I ),1A0HI ;

(40)

and we can see that the unknown phases  of the interfering users has no eect on the result1.

y [i]

Projection Metric Generator

(dK [i])

User K Viterbi Decoder

b^K [i]

H Channel Estimation

Figure 2: Metric Computer for Viterbi Decoder. It is easy to see that if M is block diagonal, (dK ) can be broken into symbol metrics (dK [i]) = kM[i](y [i] , AK [i]dK [i])k2; (41) where M[i] = I , A0I [i](A0HI [i]A0I [i]),1A0HI [i]. The block diagram of such a symbol-by-symbol detector is shown in Figure 2. However, it is not easy to obtain M[i] since there is a matrix inverse involved which has to be calculated for every symbol. A symbol based RLS adaptive algorithm [23] or an iterative method [24] can be used to calculate the metric with lower computational complexity. 1 With

hindsight this is obvious since the projection operation is phase insensitive.

10

6 Performance Gain While projection operation removes all the interference from the received signal, it results in an energy loss of the desired signal. In a symbol interval, the energy after projection is given by

Vp = kM[i]AK [i]k2: (42) We compare this to the received energy of a single user/single antenna system, which is Vs = 1, and de ne the energy gain as ! E f V A pg = 10 log10 (E AfVpg) [dB]: (43) G = 10 log10 V s First, assume that the phases of the K users are uncorrelated and uniformly distributed in (0; 2]. Following [25], if Q is an orthonormal basis of the null space of AI [i], the projection matrix can be written as

M[i] = QQH

=

u X j =1

qj qj H

(44)

where fqj ; j = 1; 2;


; ug are the columns of Q and u is the dimension of Q with u = MN , K + 1. Since the projection matrix M[i] is idempotent,

Vp = AHK [i]M[i]AK[i] = AHK [i]QQH AK [i] u u X X = AHK [i] qj qj H AK [i] = qj H AK [i]AHK[i]qi: j =1

(45)

j =1

For convenience of derivation, we de ne vj = qj H AK [i]AHK [i]qi. AK [i] and qj are independent due to the pseudo-random codes, which allows us to separate the expectation over AI and AK , i.e., n

o

n

o

E Afvj g = E A qj H AK [i]AHK [i]qj = E A qj H E A fAK [i]AHK [i]gqj : (46) Recalling equation (11), we know that AK [i] consists of M repeated vector of spreadI

K

ing codes with phase shift
K between consecutive vectors. And also there is an arbitrary phase 'K of this vector. i.e., AK [i] = ej' [cK [i]; cK [i]ej
 ;


; cK [i]ej(M ,1)
 ]T . Since we have assumed that the users are uniformly distributed, the phases of different users are considered to be random and uncorrelated. Now that AK includes two independent random variables, i.e., pseudo-random spreading codes cK [i] and random channel phases
K , we have K

K

E A fAK [i]AHK[i]g = E
 fE c fAK [i]AHK [i]gg: K

K

11

K

K

(47)

The expectation over cK can be calculated as

E cK fAK [i]AHK[i]g =

1 N

2 6 6 6 6 4

IN

IN e,j
 ...

IN ej
 IN




IN ej(M ,1)



IN ej(M ,2)


K

K

...

K

...

IN e,j(M ,1)
 IN e,j(M ,2)



K

K

Since for an integer m 6= 0,

IN

K

(48)

E
 fejm
 g = 0;

(49)

E A fAK [i]AHK [i]g = N1 IMN ;

(50)

K

K

we obtain

...

3 7 7 7 7: 5

K

where IMN is an MN  MN identity matrix. We therefore have E A fvj g = N1 qj H IMN qj = N1 : Thus we obtain the expectation of Vp over A as

(51)

1 = M , K , 1: (52) N j =1 N Hence for an averaged user population, the performance gain of an M-receive antenna array is given by   K , 1 G = 10 log 10 M , N [dB]: (53) For example, if we have a spreading sequence of N = 15 chips per symbol, K = 46 users, M = 4 antennas, G evaluates to 0 dB, i.e., no degradation from the performance of a single user with a single antenna is expected.

E AfVpg =

u X

7 Simulation Results Although the energy gain represents a lower bound on the performance [26], it can be shown that this bound is tight [24], and useful as an estimate of the performance gain (or loss). This is especially the case for the simulation results with perfect channel knowledge. Figure 3 shows simulations results for the proposed receiver. The dashdotted line is that of a single user with a single antenna, which is used as a benchmark. Assuming a separation of L = =2 between the antennas of the linear array and a known incident angle of the desired user, we simulated the receiver with the parameters N = 15 and M = 4 antennas for dierent number of users K = 37; 46 and M = 49. According to (53), we can calculate the expected performance gain or loss compared to the single user single antenna curve, which are G = 2dB, 0dB and -1dB respectively. We choose an average user distribution for each simulation and it is xed for the entire frame, whose length is L = 200 symbols. 12

N=15,M=4,estimated channel and known channel

0

10

−1

10

K=49 −2

BER

10

K=37

−3

10

K=46

−4

10

−5

10

0

1

2

3

4 Eb/N0 (dB)

5

6

7

8

Figure 3: Performance with blind array response estimation vs. known array responses. The simulations with known channels agree well with the theory. But with estimated channels, there is a small degradation due to the imperfect estimation results. We can see the degradation is aected by the number of users, becoming larger with more users in the system. Figure 4 compares the performance between two systems, which have the same parameters but use dierent convolutional codes. A small code with 4 states and a large code with 256 states are applied. We can see that the larger code improves the system performance dramatically. In order to study the eect of user distribution on the system performance, we also simulate a special case in which all the users are bounded in a sector, resulting in a phase oset of  for each user. Phase and angle of arrival are related by equation (10) . The simulated bit error rate as a function of  is shown in Figure 5. The dashed line represents the average performance. The system parameters are chosen as N = 15, K = 46, M = 4, Eb=N0 = 3dB. As  approachs zero, the array responses become co-linear and BER goes to 0.5 as expected.

8 Conclusions This paper demonstrates that it is ecient to combine multiple antenna technology with CDMA, which is already industry standard, to improve system capacity and performance. It shows that system capacity can increase linearly with the number of antennas 13

N=15,K=16,M=2,estimated channel and known channel

0

10

−1

10

4 states convolutional code

−2

BER

10

−3

10

256 states convolutional code

−4

10

−5

10

0

1

2

3

4 Eb/N0 (dB)

5

6

7

8

Figure 4: Simulations for dierent convolutional codes. in the receive array. A blind array response vector estimator is used to provide the receiver with an array response estimate. Phase estimation for the target user is required for implementation. A performance lower bound is derived which agrees well with the simulations.

References [1] Telecommunications Industry Association (TIA) TR45.5.4, \The cdma2000 ITU-R RTT Candidate Submission", available from http://www.itu.int/imt/, June 1998. [2] ETSI, \The ETSI UMTS Terrestrial Radio Access (UTRA) ITU-R RTT Candidate Submission", available from http://www.itu.int/imt/, June 1998. [3] ARIB, \Japan's Proposal for Candidate Radio Transmission Technology on IMT2000: W-CDMA", available from http://www.itu.int/imt/, June 1998. [4] T. F. Wong, T. M. Lok, J. S. Lehnert and M. D. Zoltowski, \A Linear Receiver for Direct-Sequence Spread-Spectrum Multiple-Access Systems with Antenna Arrays and Blind Adaptation", IEEE Trans. on Information Theory, Vol. 44, No. 2, March 1998. 14

N=15;K=46;M=4;Eb/N0=3dB

0

10

−1

BER

10

−2

10

−3

10

−4

10

0.04

0.05

0.06

0.07

0.08 0.09 0.1 0.11 Phase offset θ of each user (rad)

0.12

0.13

0.14

Figure 5: Performance with various phase osets for each user. [5] V. Ghazi-Moghadam and M. Kaveh, \A CDMA Interference Canceling Receiver with an Adaptive Blind Array", IEEE Journal on Selected Areas in Comm., Vol. 16, No. 8, October 1998. [6] H. Liu and G. Xu, \Smart Antennas in Wireless Systems: Uplink Multiuser Blind Channel and Sequence Detection", IEEE Trans. on Communications, Vol. 45, No. 2, Feb. 1997. [7] X. Wang and H. V. Poor, \Robust Adaptive Array for Wireless Communications", IEEE Journal on Selected Areas in Comm., Vol. 16, No. 8, October 1998. [8] M. Torlak and G. Xu, \Blind Multiuser Channel Estimation in Asynchronous CDMA systems", IEEE Trans. on Signal Processing, Jan. 1997. [9] L. C. Godara \Application of Antenna Arrays to Mobile Communications, Part II: Beam-Forming and Direction-of-Arrival Considerations", Proceedings of the IEEE, Vol. 85, No. 8, August 1997. [10] A. F. Naguib, A. Paulraj, and T. Kailath, \Capacity Improvement with base-station antenna array in cellular CDMA", IEEE Trans. on Vehi. Tech., Vol. 43, August 1994. [11] J. C. Liberti and T. S. Rappaport, \Analytical Results for Capacity Improvements in CDMA", IEEE Trans. on Vehi. Tech., Vol. 43, August 1994. 15

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