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January 2006. AN IMPROVED DOA ESTIMATION ALGORITHM FOR. ASYNCHRONOUS MULTIPATH CDMA SYSTEM1. Yang Wei Chen Junshi Tan Zhenhui.
Vol.23 No.1

JOURNAL OF ELECTRONICS (CHINA)

January 2006

AN IMPROVED DOA ESTIMATION ALGORITHM FOR 1 ASYNCHRONOUS MULTIPATH CDMA SYSTEM Yang Wei

Chen Junshi

Tan Zhenhui

(School of Electronics and Info. Eng., Beijing Jiaotong University, Beijing 100044, China)

Takis Mathiopoulos (Dept of Electrical and Computer Eng., Univ. of British Columbia, Vancouver, BC, V6T 1Z4, Canada) Abstract This paper proposes an improved Direction Of Arrival(DOA) estimation algorithm for asynchronous multipath Code Division Multiple Access(CDMA) system. The algorithm is based on the correlation matrices of outputs of decorrelator, which is a Multi-User Detection(MUD) approach, one of the key techniques for CDMA system. Through decorrelating processing, the desired user’s mulipath signals can be resolved and all the other resolved multipath signal interference is eliminated. So the proposed algorithm is expected to perform much better than algorithm such as that based directly on the Matched Filter(MF) bank outputs. Simulation results confirm this. While the improved algorithm performs better and better as Signal-to-Noise Ratio(SNR) increases, the performance of algorithm based directly on the MF bank outputs can not be improved. Key words Code Division Multiple Access(CDMA); Decorrelating; Direction Of Arrival(DOA) estimation; Asynchronous multipath channel

I. Introduction Direct-Sequence Code Division Multiple Access (DS-CDMA) is seen as one of the next-generation of generic signal access strategies for wireless com munications. CDMA possesses many intrinsic advantages over the early access techniques such as Time Division Multiple Access(TDMA) and Frequency Division Multiple Access(FDMA). For example, it can use RAKE receiver, a technique of combining multipath signals, to enhance the system performance. Furthermore, as in other multiple access system, the use of antenna array in CDMA is expected to improve system capacity, quality and coverage promisingly[1]. To form desired beam or provide orientation service one of the key techniques in antenna array CDMA system is the Directions Of Arrival(DOAs) or Angles Of Arrival(AOAs) estimation of the objective multipath signals. A number of DOA estimation algorithms have been proposed during the last decade[2−4]. However, in CDMA, the users operate in the same frequency and time channel, and Multiple Access Interference(MAI) arises from other users. The conventional DOA estimation algorithms such as MUSIC(MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithms need that the elements of antenna array outnumber the signal source 1

Manuscript received date: January 20, 2004; revised date: August 31, 2004. Supported by the National Natural Science Foundation of China (No. 60372014) Communication author: Yang Wei, born in 1964, male, Doctor, associate professor. School of Electronics and Information Engineering,Beijing Jiaotong University, Beijing 100044, China. [email protected]

number. However, there are generally several tens of users and several sub-paths per user within a cell for a typical CDMA system. The cross-correlation from the multipath co-channel signals causes that the conventional DOA estimation algorithms such as MUSIC and ESPRIT algorithms cannot be used directly in CDMA system. However, unlike the general antenna array system, there is abundant prior knowledge of effective signature waveforms in CDMA system. The spread code is known a priori. In CDMA system every user processes its particular spread code, therefore one can extract the desired signal one by one from each direction, which is called decorrelating processing. After decorrelating processing we can apply the conventional DOA estimation algorithms such as MUSIC and ESPRIT algorithms to estimate the DOAs of any decoupled sub-paths of desired user respectively. Some DOA estimation algorithms have been proposed to solve the similar problem, they are based on the Matched Filter(MF) bank outputs or model ISI and MAI as white Gaussian noise[5,6]. Since the effect of interference is caused by ISI or MAI, the performance of those algorithms is not very satisfactory. This paper combines the decorrelating processing, a Multi-User Detection(MUD) approach which is one of the key techniques used in CDMA system with DOA estimation problem. Through decorrelating processing, the desired user’s mulipath signals can be resolved and all the other resolved multipath signal interference can be eliminated. So the proposed MUSIC like algorithm is expected to perform much better than algorithm that based directly on the MF bank outputs.

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JOURNAL OF ELECTRONICS (CHINA), Vol.23 No.1, January 2006

Comparing with the conventional MUSIC like method, the proposed decorrelating DOA estimation algorithm processes several main advantages. Firstly, it requires only the principal eigenvector to be solved, consequently the corresponding computation is decreased. Secondly, the proposed algorithm does not need to detect the number of minimum eigenvalues and the number of signal sources because of the decorrelating process. Thirdly, the proposed algorithm needs only to search the lone maximum spectrum peak, and the corresponding search algorithm is simple and reliable. Finally, also because of the dcorrelating process, the cross-correlation interference caused by multipath propagation is decreased greatly and make the proposed algorithm much more accurate. The paper is organized as follows. In Section II, the model of an asynchronous multipath CDMA system with an antenna array is presented. In Section III, the improved DOA estimation algorithm is detailed, followed by the simulation results in Section IV. Finally, the main conclusions of this paper are given in Section V.

II. System Model Consider a DS-CDMA asynchronous frequency selective uplink channels with M-element basestation antenna array. Assume K active users in the system transmitting sequence of Binary Phase-Shift Keying (BPSK) symbols through their respective multipath channels. An N -bit transmitted signal from the k-th user is given by N −1

xk (t ) = Ak ∑ bk (n) sk (t − nTb ), k = 1,", K

(1)

n= 0

where Ak is the amplitude of the k-th user, bk (n) ∈ Ξ is the n-th transmitted bit of the k-th user with equal probability, Ξ is the symbol alphabet, sk (t ) represents the spreading waveform of the k-th user G−1

sk (t ) = Ak ∑ ckg p(t − gTc )

(2)

g =0

ckg ∈ { −1, +1}, (g =0,", G −1) is the spreading code, p (t ) the chip pulse with support Tc , Tc is the chip interval, Tb is the bit interval, processing gain G is defined as G = Tb / Tc , and the spreading wave form has normalized energy, i.e.,

Tb

∫0

2

ck (t ) = 1. It

is also assumed that each user transmits independent information bits and information bits from different users are independent.

L

hk (t ) = ∑ αk ,l (t )ak ,l (θk ,l (t ))δ (t − τ k ,l )

(3)

l =1

where L is the number of paths in each user’s channel, αk ,l and τ k ,l are, respectively, the complex attenuation and delay of the l-th path of the k-th user’s signal, and ak ,l (θk ,l (t )) = [ak ,l ,1 (θk ,l (t )) " ak ,l , M (θk ,l (t ))]T / M is the M -dimensional array response vector with DOA θk ,l (t ) corresponding to the l-th path of the k-th user’s signal. The total received composite signal at the base station antenna array is K

r (t ) = ∑ xk (t ) ∗ hk (t ) + w (t ) k =0

N −1 K

L

= ∑∑ Ak bk (n) ∑ αk ,l ak ,l ,m sk (t − nTb − τ k ,l ) n=0 k =1

l =1

+w (t )

(4)

where ∗ denotes convolution, w (t ) is the Additive White Gaussian Noise(AWGN) vector with zero mean and covariance matrix σ 2 I M , where I M is an M × M identity matrix.

III. The Proposed DOA Estimation Algorithm 1. Decorrelating scheme

For DS-CDMA system with spatial-temporal multiuser detection in multipath channels with base station antenna array, there are several possible architectures[7−9] to fully take advantage of both time and space processing. For example, three possible receiver configurations are illustrated in Fig.1(a), Fig.1(b), and Fig.1(c). The detector, illustrated in Fig.1(b) and Fig.1(c), differs from that of Fig.1(a), since the MF occurs prior to beamforming. The receiver structure shown in Fig.1(b) and Fig.1(c) is more practical in fading channel than that in Fig.1(a), since the channel estimation can be performed based on the MAI suppressed signal. This approach improves channel estimation accuracy significantly[10]. Furthermore, the ordering of Fig.1(b) and Fig.1(c) allows the application of adaptive single-user receiver type receivers in fading channels, whereas the other orderings (multipath and/or spatial combing prior to MAI suppression) often have severe convergence problem in time-varying channels[11]. For this reason, in this paper, we emphasize on the DOA estimation of multipath signals based on the decorrelating output shown as in Fig.1(b) and Fig.1(c). 2. The output of decorrelator (1) The output of MF bank

YANG et al. An Improved DOA Estimation Algorithm for Asynchronous Multipath CDMA System

Denote rm (t ) as the received signal at the m-th

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form and l-th multipath components in sensor m for time interval t ∈ [nTb ,(n + 1)Tb ) is given by yk( n,l), m = ∫

(n+1)Tb +τ k , l nΤ b +τ k ,l

rm (t ) sk (t − nTb − τ k ,l )dt (6)

Assume that the multipath spread of any user signal is limited to the most P symbol interval, where P is positive integer. That is, τ k ,l ≤ PTs , 1 ≤ k ≤ K ;1 ≤ l ≤ L (7) This means that the received signals will be pro cessed in processing windows of length N = 2 P + 1. So that in order to demodulate the n-th symbol of the k-th user, the user’s MF output corresponding to each path at each antenna element, i.e., Eq.(6) can be rewritten as yk( n,l), m =

P

K

L

∑ ∑ Ak' bk' (n + i)∑ ck' ,l' ,m R( k ,l ),(k' ,l' ),m (i)

i=− P k '=1

l '=1

+wk ,l ,m (n), l = 1,", L; m = 1,", M (8) where R( k ,l ),( k ',l '), m (i ) is the correlation among the delayed user signaling waveform in sensor m and is defined by R( k ,l ),( k' ,l' ),m (i ) = ∫

+∞

−∞

sk (t − nTb − τ k ,l ,m )

×sk' (t − nTb + iTb − τ k' ,l' , m )dt (9)

wk ,l , m (n) denotes the sampled MF outputs of noise for the k-th user’s l-th path component in sensor m at symbol interval n, and wk ,l ,m (n) = ∫

( n+1)Tb +τ k , l nTb +τ k , l

wm (t ) sk (t − nTb − τ k ,l )dt (10)

{wk ,l ,m (n)} is zero-mean complex Gaussian random sequence with covariance E{wk ,l , m (n) wk ,l' ,m' (n' ) H } = ⎧ ⎪0, if m ≠ m' or n − n' > P ⎪ ⎪ (11) ⎨ ( n−n' ) ⎪ R , otherwise ⎪ ' ' ( k , l ),( k , l ) ⎪ ⎩ Now, define the symbol vector for time interval t ∈ [nTb ,(n + 1)Tb ] as Fig.1 Receiver structure for antenna array CDMA system

antenna element. From Eq.(4), the m-th element of the received vector signal rm (t ) can be given by N −1 K

L

rm (t ) = ∑∑ Ak bk (n)∑ ck ,l , m sk (t − nTb − τ k ,l ) n=0 k =1

l =1

+wm (t ), m = 1,", M

(5)

where ck ,l , m = αk ,l ak ,l ,m is the complex gain calculated from both the complex attenuation and DOA. The MF outputs of all sensors for all users and multipath components provide sufficient statistics for detection of the data symbol. The sampled output of the filter matched to the k-th user spreading wave-

T def b( n ) = ⎡⎢b1( n ) b2( n ) " bK( n ) ⎤⎥ ∈ Ξ K ⎣ ⎦ Thus, a concatenation of received symbols over a processing window can be denoted by T def b = ⎡⎢(b ( n− p ) )T " (b ( n ) )T " (b ( n+ p ) )T ⎥⎤ ∈ Ξ NK ⎣ ⎦ Analogously, define the following vector of MF output samples in sensor m for symbol interval n as T yk( n,m) = ⎡⎢ yk( n,1,) m yk( n,2,) m " yk( n, L) ,m ⎤⎥ ∈ C L (12) ⎣ ⎦ ( n) ( n) T ( n) T (n) T ⎤ T ⎡ ym = ⎢( y1,m ) ( y2, m ) " ( y K , m ) ⎥ ∈ C KL (13) ⎣ ⎦ Their concatenation over the processing window is T ym = ⎡⎢( ym( n− p ) )T " ( ym( n ) )T " ( ym( n+ p ) )T ⎤⎥ ∈ C NKL ⎣ ⎦ (14)

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JOURNAL OF ELECTRONICS (CHINA), Vol.23 No.1, January 2006

The MF output samples for sensor m in a whole can be expressed in matrix notation as ym = Rm C m Dm b + wm (15) where, the cross-correlation matrix Rm is given by ⎛ Rm (0) Rm (−1) Rm (−2) " 0k ⎞⎟ ⎜⎜ ⎟ ⎜ Rm (1) Rm (0) Rm (−1) " 0k ⎟⎟ NKL×NKL Rm = ⎜⎜⎜ ⎟⎟⎟ ∈ C # # # # ⎟⎟ ⎜⎜ ⎟ ⎜⎜ 0 " Rm (0)⎠⎟ 0k 0k ⎝ k

⎛ R1,1,m (i ) R1,2, m (i ) " R1, K , m (i ) ⎞⎟ ⎜⎜ ⎟ ⎜⎜ R2,1,m (i ) R2,2,m (i ) " R2, K , m (i ) ⎟⎟ ⎟⎟∈ C KL×KL ⎜ Rm (i ) = ⎜ ⎟⎟ ⎜⎜ # # # ⎟⎟ ⎜⎜ ⎜⎝ RK ,1,m (i ) RK ,2, m (i ) " RK , K , m (i )⎠⎟⎟ where matrix Rk ,k' ,m (i) ∈ R L×L is a correlation matrix with elements R( k ,l ),( k' ,l' ),m (i ) defined as Eq.(9). Since τ k ,l ≤ PTb and sk (t ) is zero outside [0, Tb ], it follows Rm (i ) = 0, ∀ i > P Rm (−i ) = RmT (i ) The channel matrix C m is described by C m = diag {C m( n− p ) C m( n− p+1) " C m( n+ p ) } ∈ C NKL×NK C m( n ) = diag {c1,( nm) c2,( nm) " cK( n,)m } ∈ C KL×K T ck( n,m) = ⎡⎢ck( n,1) ck( n,2) " ck( n, L) ⎤⎥ ∈ C L ⎣ ⎦ The signal amplitude matrix is expressed by Dm = diag { Am Am " Am } ∈ C NK×NK , Am = diag { A1

A2 " AK } ∈ C K×K , and wm is the noise vector at the MF outputs in sensor m. Thus the vector of concatenated MF outputs of all sensors can be given by y = RCDB + W (16) where y is defined by

and

T y = ⎢⎡ y1T y2T " ymT ⎤⎥ ∈ C MNKL ⎣ ⎦

R = diag { R1 R2 " RM } ∈ C MNKL×MNKL , C = diag {C1 C 2 " C M } ∈ C MNKL×MNKL , D = diag { D1 D2 " DM } ∈ C MNK×MNK , B = ⎡⎢bT bT " bT ⎤⎥ ∈ Ξ MNK , ⎣ ⎦ T T W = ⎡⎢ w1 w2 " w MT ⎤⎥ ∈ C MNKL . ⎣ ⎦ (2) The output of decorrelator To eliminate the multipath signal interference and decouple the information of the user’s data, the decorrelating detector applies the inverse of correlation matrix to the conventional detector output. In

this paper, the decorrelation process is viewed as multiplying the inverse of pre-calculated crosscorrelation matrix. Since the cross-correlation matrix, i.e. Rm and R in our case, are always positive definite in practice situation and their linear mapping has properties of Hemitian and positive definite[10], so their inversions always exist. For receiver structure shown in Fig.1(b) the decorrelation is based on the MF bank outputs connecting a single array element in temporal domain. Based on Eq.(15), multiplying the inverse matrix Rm−1 on the both sides yields the output of the temporal decorrelator for sensor m, given by zm = C m Dm b + Rm−1wm (17) where T zm = ⎡⎢( zm( n− p ) )T " ( zm( n ) )T " ( zm( n+ p ) )T ⎤⎥ ∈ C NKL (18) ⎣ ⎦ T zm( n ) = ⎡⎢( z1,( nm) )T ( z2,( nm) )T " ( z K( n,)m )T ⎤⎥ ∈ C KL ⎣ ⎦ T zk( n,m) = ⎡⎢ zk( n,1,) m zk( n,2,) m " zk( n, L) , m ⎤⎥ ∈ C L ⎣ ⎦

(19) (20)

Obviously, each element of the matrix zk( n,m) contains a single resolved multipath signal for user k in sensor m and has not interference from all the other resolvable multipath signals in sensor m. So every resolvable mutipath signal is detected independently. As for receiver structure shown in Fig.1(c), the decorrelation is based on the MF bank output connecting the whole array elements in spatial-temporal domains. Based on Eq.(16), similarly, we have Z = CDb + R−1W (21) where Z = ⎡⎢ Z1T Z 2T " Z MT ⎤⎥ ∈ C MNKL ⎣ ⎦ T

Z m = ⎡⎢( Z m( n− p ) )T " ( Z m( n ) )T " ( Z m( n+ p ) )T ⎤⎥ ∈ C NKL ⎣ ⎦ (22) (n) (n) T ( n) T (n) T ⎤ T KL ⎡ Z m = ⎢( Z1,m ) ( Z 2, m ) " ( Z K , m ) ⎥ ∈ C (23) ⎣ ⎦ (n) (n) (n) (n) ⎤ T ⎡ (24) Z k ,m = ⎢ Z k ,1,m Z k ,2,m " Z k , L ,m ⎥ ∈ C L ⎣ ⎦

Thus, every resolvable mutipath signal is detected independently. 3. DOA estimation algorithm Now we concern the DOA estimation of multipath signals of desired user, without loss of generality, the DOA of k-th user’s l-th multipath signal. Through decorrelating processing each user’s multipath signal is decoupled and can be detected independently. Thus we can apply the signal subspace algorithm to estimate the DOA of k-th user’s l-th mul-

YANG et al. An Improved DOA Estimation Algorithm for Asynchronous Multipath CDMA System

tipath signal based on the principal eigenvector of the corresponding covariance matrix. (1) Estimate of covariance matrix (a) Method 1 For receiver structure shown in Fig.1(b), to estimate the DOA of k-th user’s l-th multipath signal the covariance matrix corresponding to its decoupled array output needs to be estimated first. Actually, exact knowledge of covariance matrix is not available and must be estimated from the received data. As typical in such situations, Q independent observations or snapshots based on the corresponding measure model are utilized to form the sample estimate of the true covariance matrix. In our case, since there is multipath spread, the received signals have to be processed in processing windows of length N = 2P + 1 to demodulate the nth symbol of a user in the center of the windows. Therefore, to observe Q consecutive symbols, Q consecutive processing windows of length N = 2P + 1 with adjacent processing window sliding a symbol one another need to be open. From Eq.(20), we can estimate the temporally decoupled signal for l-th multipath of k-th user’s in q-th symbol interval in sensor m denoted by zk( m,l ,)m . Stacking the temporally decoupled signal in all sensors together for l-th multipath of k-th user’s in q-th symbol interval, we get the M ×1 vector as T (q) zk,l = ⎡⎢ zk( q,l),1 zk( q,l),2 " zk( q,l), M ⎤⎥ (25) ⎣ ⎦ Thus, the sample estimate of the true covariance matrix of the temporally decoupled signal corresponding to the l-th multipath of k-th user’s can be given by H 1 Q Rˆ k ,l = ∑ z (kq,l ) ( z (kq,l) ) (26) Q q=1 For receiver structure shown in Fig.1(c), the same as the estimate of covariance matrix of receiver structure shown in Fig.1(b), it also needs to be open for structure in Fig.1(c) to observe Q consecutive symbols Q consecutive processing windows of length N = 2P + 1 with adjacent processing window sliding a symbol one another. From Eq.(23), we can estimate the spatiallytemporally decoupled signal for l-th multipath of k-th user’s in q-th symbol interval in sensor m denoted by Z k( q,l), m . Stacking the spatially-temporally decoupled signal in all sensors together for l-th multipath of k-th user’s in q-th symbol interval, we get the M ×1 vector as T Z k( q,l) = ⎡⎢ Z k( q,l),1 Z k( q,l),2 " Z k( q,l), M ⎤⎥ (27) ⎣ ⎦

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Thus, the estimate of the true covariance matrix of the spatially-temporally decoupled signal corresponding to the l-th multipath of k-th user’s can be given by H 1 Q Rˆ k ,l = ∑ Z k( q,l ) ( Z k( q,l ) ) (28) Q q=1 (b) Method 2 In method 1, because of the multipath spread, the received signals have to be processed in processing windows of length N = 2P + 1 to demodulate the nth symbol of a user and to observe Q consecutive symbols, Q consecutive processing windows of length N = 2P + 1 with adjacent processing window sliding a symbol one another needs to be open. However, if the length of processing window is longer enough, we only need to open a single processing window. From N consecutive decoupled outputs of each multipath of each user among the window, Q consecutive symbols can be intercepted with the center point of the processing window as a reference. If the length of processing window is longer enough, this method will yield good results to estimate the corresponding covariance matrix. For receiver structure shown in Fig.1(b), from Eqs.(18), (19), and (20), we can estimate the tem porally decoupled signal for l-th multipath of k-th user’s in q-th symbol interval in sensor m denoted by zk( q,l),m . Stacking the temporally decoupled signal in all sensors together for l-th multipath of k-th user’s in q-th symbol interval, we get the M ×1 vector as T (q) = ⎡⎢ zk( q,l),1 zk( q,l),2 " zk( q,l), M ⎤⎥ (29) zk,l ⎣ ⎦ Thus the sample estimate of the true covariance matrix of the temporally decoupled signal corresponding to the l-th multipath of k-th user’s can be given by ⎧ Q−1 ⎛ Q−1 ⎞H ⎪ )⎟ (r − ) (r − ⎪ 1 ⎜ (r) (r) H ⎪ Rˆ k ,l = ⎨ zk,l 2 ⎜⎜ zk,l 2 ⎟⎟ + " + zk,l zk,l ( ) + ⎜⎝ Q⎪ ⎠⎟⎟ ⎪ ⎪ ⎩ Q−1 ⎛ Q−1 ⎞H ⎫ ⎪ (r + ) (r + )⎟ ⎪ ⎜ " + zk,l 2 ⎜⎜ zk,l 2 ⎟⎟ ⎪⎬ (30) ⎜⎝ ⎠⎟⎟ ⎪ ⎪ ⎪ ⎭ where we assume Q to be odd and r to be the reference point. For receiver structure shown in Fig.1(c), similarly, the sample estimate of the true covariance matrix of the spatially-temporally decuopled signal corresponding to the l-th multipath of k-th user’s can be given by ⎧ Q−1 ⎛ Q−1 ⎞H ⎪ )⎟ (r − ) (r − ⎪ 1 ⎜ (r) (r) H ⎪ Rˆ k ,l = ⎨ Z k ,l 2 ⎜⎜ Z k ,l 2 ⎟⎟ + " + Z k,l Z k,l ( ) + ⎜⎝ Q⎪ ⎠⎟⎟ ⎪ ⎪ ⎩

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JOURNAL OF ELECTRONICS (CHINA), Vol.23 No.1, January 2006

"+

Q−1 ⎛ Q−1 ⎞H ⎫ ⎪ ) (r + )⎟ ⎪ ⎜ ⎪ 2 2 ⎟ ⎜ Z k,l ⎟⎟ ⎬ ⎜ Z k,l (r +

(31)

⎠⎟ ⎪ ⎪ ⎪ ⎭ where we assume Q to be odd and r to be the reference point. (2) DOA estimation algorithm After the sample estimate of the true covariance matrix of l-th multipath of k-th user’s, i.e., Rˆ k ,l is obtained, the DOA of l-th multipath of k-th user’s can be estimated according to the following procedure: (a) Perform an eigendecomposition of the sample covariance matrix Rˆ k ,l , to reveal the eigenvector eˆ1, k ,l , corresponding to the largest eigenvalue of the correlation matrices Rˆ k ,l . (b) Construct the spatial spectrum function as 2 ⎤ −1 ⎡ PMU (θk ,l ) = ⎢1 − akH,l (θk ,l )eˆ1,k ,l ⎥ (32) ⎣ ⎦ where for uniformly spaced antenna array 2πd ⎡ − j 2πd sin(θk ,l ) −j ( M −1)sin( θk ,l ) ⎤ ⎥/ M akH,l (θk ,l ) = ⎢⎢1 e λ "e λ ⎥ ⎢⎣ ⎥⎦ (c) Search the peak of the spatial spectrum PMU that provides the DOA estimation corresponding to the l-th path of the k-th user’s signal. The estimation of θk ,l is given by ⎝⎜

{

2⎤ ⎡ θˆk ,l = arg max ⎢1 − akH,l (θk ,l )eˆ1,k ,l ⎥ ⎣ ⎦ θk , l

−1

}

(33)

IV. Simulation Results In this section, we present simulation results to illustrate the performance of the proposed DOA estimation algorithm for an asynchronous multipath CDMA system in which structure in Fig.1(b) is adopted. In the simulation, the effects of user number, processing gain, observation length, and array structure on the performance of the proposed algorithm are studied. We employ a 5-element uniformly linear array with the space between adjacent array elements being half a wavelength for reception of BPSK multipath signals. The channels are assumed to be Rayleigh two-path fading channels with equal average energy for each path and the relative time delays of the signals are within one symbol interval. We consider the situation that there are 3 users randomly distributed in the system, each has two sub-path signals respectively, and the desired user’s sub-path is supposed to be 27°. In the simulation, the spreading codes with processing gain of 16 were selected randomly and 20 consecutive observations or snapshots are taken to form the sample estimate of the true covariance matrix Rˆ k ,l . To evaluate the simulated performance 20 trials is averaged to pro-

duce the simulation results as shown in Figs.2, 3, 4, 5, 6 and 7. Firstly, Fig.2 shows the estimation performance of method 1 and method 2 employing the proposed algorithm versus SNR, which is evaluated by Standard Deviation(SD) of the estimation defined as below 2 1 U ˆ (34) θk ,l − θk ,l ∑ U u=1 where U is the number of independent trials, and θˆk ,l is the bearing estimation for the l-th path of k-th user’s signal. From Fig.2 we can observe that the performance of the proposed algorithm is very effective and accurate to estimate the DOAs of desired multipath signals. Besides, we can find that method 2 performs better than method 1 as expected, however, the performance difference is small. For this reason, without loss of generality, method 2 is adopted in the following discussions. Fig.3 shows the DOA estimation results employing the proposed algorithm compared with the corresponding algorithm based on MF bank outputs directly. From Fig.3, we can observe that the performance of the proposed algorithm is much more accurate to estimate the DOAs of desired multipath signals compared with algorithm based directly on MF bank outputs, because MAI can be eliminated through decorrelating processing in principal while it is unavoidable for algorithm based directly on MF bank outputs. Especially, as SNR increases the proposed algorithm perform better and better. On the contrary, the algorithm based directly on MF bank outputs can not be improved due to the corresponding MAI increasing. In Fig.4, we further investigate the performance of proposed algorithm with different user number.

SD =

Fig.2 SD performance versus SNR, with method 1 and method 2

(

)

Fig.3 SD performance comparison between matched filter bank based algorithm and proposed algorithm

Fig.4 shows that the proposed algorithm performs almost the same with different user number. The reason is the same as above.

YANG et al. An Improved DOA Estimation Algorithm for Asynchronous Multipath CDMA System

Fig.5 shows the effect of Processing Gain(PG) on the estimation performance of proposed algorithm. From Fig.5 it is noted that the estimation performance is not improved remarkably with the processing gain increasing. This means even in low processing gain the performance is already accurate enough.

Fig.4 SD performance versus SNR, with different user Number

Fig.5 SD performance versus SNR,with different processing gain

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be estimated independently and all the other resolved multipath signal interference is eliminated. Therefore, the proposed algorithm needs not require that the array elements outnumber the multipath signal number, which is required in conventional subspace like based DOA estimation algorithm. The performance of the proposed algorithm is studied in detail. Simulation results show that the proposed algorithm estimates DOAs of the multipath signals much more effective and accurate than that based directly on MF bank outputs. Besides, the proposed algorithm has some other advantages such as insensitive to user number and processing gain. All of these make the proposed algorithm an effective and accurate approach for DOA estimation of asynchronous multipath CDMA systems with antenna array.

References

Fig.6 SD performance versus SNR, with different observation length

Fig.7 SD performance versus SNR, with different antenna space

As shown in Fig.6, we have studied the effect of observation length on the estimation performance of proposed algorithm. Fig.6 indicates that the estimation performance can be improved with the observation length increasing since the effect of asynchronous channel is accounted for more comprehensively in the algorithm when the observation length increases. Finally, the effect of array structure on the estimation performance is also investigated. Fig.7 shows that the estimation performance is improved a lot if the distance between array elements was extended since the resolving ability of antenna array is increased with the distance of array element increasing. Besides, it is deserved to point out that even two or more sub-path signals of different users arrive at the antenna array with same DOAs we can also estimate them effectively by exploiting the intrinsic characteristic of CDMA signals that each user is assigned a unique spreading code.

V. Conclusions In this paper, we have proposed an improved algorithm to estimate directions of arrival of multipath signals for an asynchronous CDMA system with antenna array. By making full use of the prior knowledge and signature of the spreading sequence of CDMA system, DOAs of the multipath signals can

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