DOA Estimation of Noncircular Signal Based on Sparse Representation

Wireless Pers Commun (2015) 82:2363–2375 DOI 10.1007/s11277-015-2352-z

Xuemin Yang · Guangjun Li · Zhi Zheng

Published online: 3 February 2015 © Springer Science+Business Media New York 2015

Abstract In this paper, we propose a novel method employing subspace fitting principle for DOA estimation of noncircular signal based on the sparse representation technology. The proposed method combines the signal information contained in both the covariance and elliptic covariance matrix of the received data matrix. We use the eigenvalue decomposition of the extended covariance to obtain the signal eigenvectors, and represent the steering vector on overcomplete basis subject to sparse constraint in subspace fitting method. After casting multiple dimensional optimization problem of the classical subspace fitting method as a sparse reconstruction problem, we use L1-norm penalty for sparsity, and optimization by the second order cone programming framework to obtain the DOA estimates. The proposed method can be used in arbitrary array configuration. Compared with the existing algorithms, the simulation results show that the proposed method has better performance in low SNR. Compared with L1-SVD, the proposed method also own better resolution probability.

Keywords DOA estimation · Noncircular signal · Sparse representation · Subspace ﬁtting

1 Introduction

In recent decades, the problem of estimating the direction-of-arrival (DOA) with high resolution has been widely concerned in military, sonar, radar and wireless communication. The traditional DOA estimators based on subspace method, like ROOT-MUSIC [1–3], ESPRIT

X. Yang (B) · G. Li · Z. Zheng School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China e-mail: [email protected] G. Li e-mail: [email protected] Z. Zheng e-mail: [email protected] 123 2364 X. Yang et al.

[4,5], and subspace fitting (SF) method [6], want to obtain high resolution probability, which all needs large quantity of measurements or high signal-to-noise ratio (SNR). Recently, sparse representation technique of signal has been applied in many areas, such as wireless channel estimation, cognitive radio and image processing, which also provides a new thought for DOA estimation. Several DOA estimation techniques based on sparse representation have been published in the literature [7–11]. In [7], a method called L1- SVD, which can effectively estimate DOA with single measurement. By using singular value decomposition (SVD) of received data matrix, it also works in multiple measurements case. Furthermore, the author presents an adaptive grid refinement method which is able to reduce the influence of the limitation of grid size. In [8], a mixed L2,0-norm-based joint sparse approximation technique is introduced into DOA estimation by Hyder and Mahata. In their work, the L0-norm constraint is approached by a set of convex functions, and a method called JLZA-DOA is proposed. Although JLZA-DOA method meets performance, global convergence is not guaranteed. To reduce the computational cost of the above methods, a low complexity DOA estimator based on sparse representation of array covariance matrix is proposed in [9]. The method combines Khatri–Rao product and signal sparse representation to estimate DOA by reconstructing single measurement vector, which means the computational complexity of the method is lower than L1-SVD. As the methods in [7–9] need to set the hyperparameters, Stoica et al. [10], present the sparse iterative covariance-based estimation (SPICE) approach, which can be obtained by the minimization of covariance matrix fitting criterion and can be used in both single and multiple measurements cases. It does not require selection of any hyperparameters, and it has global convergence properties. However, the algorithm based on power is limited by the grid size. In [11], Abeida et al. propose a series of user parameter-free iterative sparse asymptotic minimum variance (SAMV) approaches for array processing applications based on the asymptotically minimum variance (AMV) criterion. These approaches can effectively reduce the limitation of the grid size, and improve the performance of algorithm based on power. When the measurements are enough, SAMV is proved to coincide with the maximum likelihood (ML) estimator. Compared with the methods based on subspace, these approaches above mentioned own better performance especially in low SNR and limited measurements. Most of the researchers studying the DOA estimators are based on the assumption of complex circular signal. But, in practical communication channel there are a lot of complex noncircular signals, such as signal of BPSK, MSK, GMSK, PAM and UQPSK. Although the methods of noncircular signal take more computational cost for DOA estimation, as NC-MUSIC-like [12–16],and NC-ESPRIT [17], they can get better performance of resolution probability and noise-robust. In [18], the authors present a method called noncircular covariance matrix sparse representation (NC-CMSR). NC-CMSR realizes DOA estimation by jointly representing the covariance and elliptic covariance matrices of the array output on overcomplete dictionaries subject to sparsity constraint. The noncircular signal DOA estimators can extend the array aperture, and improve the DOA estimation performance in assumption of complex circular. Thus, in this paper we study the noncircular signal DOA estimation. As the classical SF methods need multiple dimensional optimizations with a large computational complexity, we use the sparse representation technique to solve SF method, and present a new noncircular signal DOA estimator, called NC-SFSR. This method represents the steering vectors on overcomplete dictionaries. And the problem of multiple dimensional optimizations is casted as a sparse reconstruction problem. We use the perturbance between true signal eigenvectors and estimated signal eigenvectors to estimate the hyperparameters. Then, the sparse reconstruction problem can be optimized by SOCP framework, which can 123 DOA Estimation of Noncircular Signal 2365 reduce the computational complexity of the classical SF method. Later, we compare the existing algorithms with NC-SFSR, and present the simulation results. , , [•], [•],v (•), (•), , , , , In this paper, the notations *, T H E D ec tr 0 1 2 F Im denote conjugate, transpose, conjugate transpose, expectation, variance, vectorization, trace, L0-norm, L1-norm, L2-norm, Frobenius-norm, and m×m identity matrix, respectively.

2 Data Model

We consider K far-ﬁeld stationary and uncorrelated narrowband noncircular signals impinge on the array consisting of M sensors from direction angles θk, k = 1, 2, ..., K , which are corrupted by additive circular complex Gaussian white noise. The signals are irrelevant to the noise. The array output vector at time t can be expressed as:

K x(t) = a(θk)sk (t) + n(t) k=1 = As(t) + n(t), t = 1, 2, ..., N (1) j2πd sin θ /λ j2πd − sin θ /λ T where x(t) is the receiving data of the array, a(θk) = 1, e 1 k , ..., e M 1 k is the M×1arraysteeringvector,dm is the distance between the mth sensor and the ﬁrst sensor, λ is the wavelength of the carrier. s (t) is the kth zero-mean noncircular signal, k ◦ ◦ θk is the kth direction of the arrival, θk ∈[−90 , 90 ], n(t) is Gaussian white noise with 2 zero-mean and covariance matrix σ IM . N is the number of snapshots. Equation (1) can be written in matrix form

X = AS + N (2) where

A = [a(θ1), a(θ2), ..., a(θK )] (3) A is the M × K array manifold matrix,

S = [s(1), s(2), ..., s(N)] (4)

S is the K × N noncircular signal matrix,

T s(t) = [s1(t), s2(t), ..., sK (t)] (5) s(t) is the K × 1 noncircular signal vector,

N = [n(1), n(2), ..., n(N)] (6)

N is the M × N noise matrix. For arbitrary noncircular signal, we have E SST = ρE SSH = 0 (7) where ρ = (ρ ,ρ , ..., ρ ), ≤ ρ ≤ diag 1 2 K 0 k 1(8) ◦ ◦ jϕ1 jϕ2 jϕK = diag e , e , ..., e ,ϕk ∈ 0 , 180 (9) 123 2366 X. Yang et al. and ρk is the kth noncircular rate of the noncircular signal, ϕ is the additional phase in the communication channel, called noncircular phase. Some special modulated signals, like AM, MASK and BPSK, whose noncircular rate equal 1, are the maximum noncircular rate signal. In this work, we pay attention to the maximum noncircular rate signal. According to the noncircularity of the received signal, we can combine the received data matrix and its complex conjugate counterpart into a matrix X Y = (10) X∗ and the extended data covariance matrix can be expressed as A A H R = E YYH = R + σ 2I Y A∗∗ s A∗∗ 2M H 2 B(θ; )Rs B(θ; ) + σ I2M (11) where H Rs = E SS (12) A(θ) B(θ; ) = (13) A(θ)∗∗ As SF method is based on the eigenvalue structure of covariance matrix, here the eigen- decomposition of RY is given by = H + H RY Es sEs En nEn (14) where the columns of Es are the eigenvectors corresponding to the K largest eigenvalues which constitute the diagonal matrix s , and the columns of En are the eigenvectors corresponding to the 2M − K smallest eigenvalues which constitute the diagonal matrix n. Es and B span the subspace, which are orthogonal to the noise subspace spanned by the matrix En. Then, there exists a nonsingular K × K matrix T satisfying the following relation

Es = B(θ; )T (15) The estimation of the eigenvectors of the extended covariance is usually obtained by eigen- decomposing the sample covariance matrix as

N 1 Rˆ = y(t)yH (t) Y N t=1 = ˆ ˆ ˆ H + ˆ ˆ ˆ H Es sEs En nEn (16) ˆ Because of the existence of noise, there are some perturbations between Es and Es ,andwe can get the following expression ˆ Es = B(θ; )T + ε (17) where ε is the perturbation matrix. Thereby, we can use the least square ﬁtting criterion to minimize ε,thatis

ˆ ˆ 2 θSF = arg min Es − B(θ; )T (18) θ, F 123 DOA Estimation of Noncircular Signal 2367 where B(θ; ) is the general array manifold matrix parameterized by θ and .Wetrulycare about θ in (18), and T is just an auxiliary parameter. Through ﬁxing B(θ; ), we can obtain the least square solution of T, and substitute it back into (18). Then the subspace ﬁtting optimization problem becomes

ˆ ⊥ ˆ ˆ H θSF = arg min tr P (θ;)EsE (19) θ, B s ⊥ (θ; ) where PB(θ;) is the orthogonal projection matrix of B . To solve the problem above mentioned, the traditional methods for solving the classical SF method are based on non- linear multiple dimensional optimization, which need global extremal multiple dimensional searching with great computational cost. Some famous multiple dimensional search algorithms, such as the alternating projection algorithm [19], the method of DOA estimation [20], the iterative quadric form maximal likelihood algorithm [21] and the Gaussian-Newton algorithm [22], have been proposed to estimate the true DOAs. In next section, we will introduce sparse representation technique into SF method.

3 Noncircular Signal DOA Estimation via Sparse Representation

3.1 Sparse Recovery Problem Formulation for DOA Estimation

Referring to (17), we realize that it is similar to (12)in[7]. But the difference of them is that there are two unknown parameters the DOA and noncircular phase in B. If we directly introduce the overcomplete representation B in terms of all possible samples of spatial angle and noncircular phase, the computational cost would be very huge. Since the noncircular phase matrix contained in the bottom half of B, we partition Es in (15) into two blocks Es1 and Es2, both of which are M × K matrices. (15) can be rewritten as Es1 A = ∗ ∗ T (20) Es2 A we can have the expressions of Es1 and Es2

Es1 = AT (21) ∗ ˜ Es2 = A T (22) where T˜ = ∗T is also a K × K matrix. To cast the SF problem as a sparse representation problem, we now introduce overcomplete representation A and A∗ in terms of all possible directions. Let θ˜ ∈ , is the discrete angle set that covers the possible spatial scope of the incident signals, Nθ is the sample number of the spatial discrete angle. Usually, Nθ is much greater than the number of sensors M and the number of source K . We construct two matrices composed of steering vectors corresponding to each potential angle as their columns ˜ ˜ ˜ ˜ A = a θ1 , a θ2 , ..., a θNθ (23) ˜ ∗ ∗ ˜ ∗ ˜ ∗ ˜ A = a θ1 , a θ2 , ..., a θNθ (24)

In this framework, A˜ and A˜ ∗ are known, which do not depend on the actual direction of arrival. 123 2368 X. Yang et al.

Then, Es1 and Es2 can be expressed as

˜ Es1 = ACT (25) ˜ ∗ ˜ Es2 = A CT (26) where C is Nθ ×K sparse matrix which only contains two elements (0 and 1). All the columns of C is same, and the nonzeroes are corresponding to the true angles of the arrival in A˜ and A˜ ∗.Wedeﬁne

1 = CT (27) ˜ 2 = CT (28) where 1 and 2 have the same sparse structure, which means the distribution of the nonzeroes is identical. We can rewrite (21)and(22)as

˜ Es1 = A1 (29) ˜ ∗ Es2 = A 2 (30)

A straightforward way for reconstructing the sparse matrices 1 and 2 according to (29) and (30).

v ( ) . .v ( ) = v ( ˜ ) min ec 1 0 s t ec Es1 ec A 1 (31) v ( ) . .v ( ) = v ( ˜ ∗ ) min ec 2 0 s t ec Es2 ec A 2 (32) which are difﬁcult combinatorial optimization problem. The conventional way is to replace the L0-norm penalty with L1-norm penalty. Such a penalty conversion describes the problem in (31)and(32) into a convex form, which can be efﬁciently solved by the prevalent optimization toolboxes [23,24]. Based on the above statement, and row-sparse matrices 1 and 2, we need to compute L2-norm of all columns of a particular spatial index of 1 and 2,thatistosay ( 2) ψ , = 1,i (1), 1,i (2), ..., 1,i (K ) , i = 1, 2, ..., Nθ (33) 1 i 2 ( 2) ψ = , ( ), , ( ), ..., , ( ) , = , , ..., θ 2,i 2 i 1 2 i 2 2 i K 2 i 1 2 N (34) ( 2) ( 2) ( 2) ( 2) T ( 2) ( 2) and penalize the L1-norm of = ψ , ,ψ, ,...,ψ , and = ψ , , 1 1 1 1 2 1 Nθ 2 2 1 ( 2) ( 2) T ( 2) ( 2) ψ ,...,ψ θ × 2,2 2,Nθ in which 1 and 2 are N 1 vectors. The cost functions become

2 ( 2) . . ˆ − ˜ ≤ β2 min 1 s t Es1 A 1 1 (35) 1 F 2 ( 2) . . ˆ − ˜ ∗ ≤ β2 min s t Es2 A 2 2 (36) 2 1 F

ˆ ˆ where the parameters β1 and β2 are the ﬁtting error thresholds of Es1 and Es2deviating from ˜ ˜ ∗ A1 and A 2, respectively. 123 DOA Estimation of Noncircular Signal 2369

In order to combine the signal information contained in both the covariance and elliptic covariance matrices, we resort to the following objective function min p 1 ( 2) 2 ( 2) 2 s.t. pi ≥ , + , , i = 1, 2, ..., Nθ 1 i 2 i 2 (37) ˆ ˜ 2 Es1 − A1 ≤ β 2 1 2 ˆ ˜ ∗ 2 Es2 − A 2 ≤ β 2 2 ( 2) ( 2) ( 2) ( 2) where 1,i and 2,i denote the amplitudes of the ith element of 1 and 2 , respec- ˆ tively. And the largest K peaks of 1 is corresponding to the estimated directions θk.By introducing the auxiliary variable g, and auxiliary vectors r1, r2 and p,(37) can be described into the canonical SOCP form min g g,p,r1,r2 ( ) ( ) s.t. p ≤ g, 2 ≤ r , 2 ≤ r , 1 1 1 2 2 2 + 2 ≤ , = , , ..., r1,i r 2,i pi i 1 2 Nθ (38) 2 ˆ ˜ 2 Es1 − A1 ≤ β 2 1 2 ˆ ˜ ∗ 2 Es2 − A 2 ≤ β 2 2 where T r1 =[r1,1, r1,2, ..., r1,Nθ ] (39) T r2 =[r2,1, r2,2, ..., r2,Nθ ] (40) T p =[p1, p2, ..., pNθ ] (41) For the numerical solution of (38), we use a package for optimization over self-dual homo- geneous cones, called SeDuMi [25].

3.2 Solution of the Proposed Method

Before solving (38), we should select suitable perturbation parameters β1 and β2. For taking the suitable perturbation parameters, we analyze the statistical relations between the true signal eigenvectors and estimated signal eigenvectors, as follows. According to the literatures [26,27], the sample eigenvectors are asymptotically complex normal distribution, whose mean and variance can be given by

E[eˆk]=ek (42) λ M λ H k j H D[eˆk]=E eˆk − E[eˆk] eˆk − E[eˆk] = e j e (43) N λ − λ 2 j j=k k j where λk is kth true eigenvalue, ek and eˆi are true signal eigenvectors and estimated signal eigenvectors, respectively. According to (42)and(43), the variance of the kth estimated signal eigenvectors can be rewritten as [ˆ ]= ˆ − ˆ − H = ε¯ ε¯ H D ek E ek ek ek ek E k k (44) 123 2370 X. Yang et al. where ε¯kis the perturbation vector between the true signal eigenvectors and estimated signal eigenvectors. Let us deﬁne D = D eˆ = E εεH (45) which is the variance vector of the estimated signal eigenvectors. As mentioned in [18], the perturbation parameter β can be given by β = μ × 2 E D 2 (46) where μ is the weighted factor. Substituting β1 and β2 into (38) yield the practically usable optimization function for DOA estimation of noncircular signals.

3.3 Algorithm Procedure and Complexity Analysis

Now, we can summarize the proposed approach as follows:

N ˆ 1 H Step 1. Compute the extended sample covariance RY = y(t)y (t), y(t) is the N t=1 extended received data at time t. ˆ ˆ ˆ Step 2. Eigendecompose RY , and obtain the estimated signal eigenvectors Es1 and Es2. Step 3. Compute the variance of the estimated signal eigenvectors, and select the parameters β1 and β2. Step 4. Substitute β1 and β2 into (38), and optimize it by using the software tool SeDuMi.

Then, we analyze the computational complexity of the proposed algorithm NC-SFSR. The computational complexity mainly contains two parts. Aside from O (M)2 N + (M)3 is brought by estimating the extended sample covariance matrix and the eigen value decomposition, the computational complexity of solving (38)isO (KNθ )3 . Generally speaking,Nθ M, the computational complexity of NC-SFSR stays the same with that of L1-SVD, while it is much higher than those of subspace-based methods which are O (M)2 N + (M)3 .

4 Simulation Results and Analysis

In this section, we present several simulation examples to illustrate the performance of the proposed algorithm. Since the dm is arbitrary, our proposed method can be used in arbitrary array configuration. We assumed that the array is uniform linear array (UAL) with 2 M = 8, dm = mλ/2. The SNR is defined as 10 log(1/σ ). In the first example, we compare the performances of the NC-SFSR with the NC-ROOT- MUSIC [13], NC-ESPRIT [17] and L1-SVD with two uncorrelated BPSK signal from the direction −20.3◦ and 41.7◦ impinging on the ULA whose noncircular rate are 40◦ and 60◦. ◦ The grid is uniform with 1 sampling Nθ = 180 for the NC-SFSR and L1-SVD. The number of snapshots is 100. Each simulated point is obtained as an average of 100 independent Monte-Carlo simulation runs. Figure 1 shows the root-mean-square errors (RMSEs) of the estimated DOA for the NC-SFSR, NC-ROOT-MUSIC, NC-ESPRIT and L1-SVD versus the SNR. Obviously, the NC-SFSR provides better performance than the NC-ESPRIT and L1- SVD. Moreover, the estimated accuracy of the NC-SFSR approaches the NC-ROOT-MUSIC. In the second example, we compare the spectra of NC-SFSR to those of NC-ROOT- MUSIC and L1-SVD. The simulated signal is BPSK and its DOA and noncircular rate are 123 DOA Estimation of Noncircular Signal 2371

1 10 NC-SFSR NC-ESPRIT NC-ROOT-MUSIC

0 L1-SVD 10

-1 10 RMSE(Deg)

-2 10 -10 -5 0 5 10 15 20 SNR(dB)

Fig. 1 RMSE of DOA for the NC-SFSR, NC-ROOT-MUSIC, NC-ESPRIT and L1-SVD versus the SNR

-10

-20

-30

-40

-50 spatial spectra(dB) NC-SFSR -60 NC-ROOT-MUSIC L1-SVD -70 40 42 44 46 48 50 DOA(Deg) ◦ Fig. 2 Spatial spectra for the NC-SFSR, NC-ROOT-MUSIC and L1-SVD when the grid is 0.5

45.7◦ and 20◦, respectively. The number of snapshots is 100. Each simulated point is obtained as an average of 100 independent Monte-Carlo simulation runs with SNR 10dB. Figures 2 and 3 display the spatial spectra when the grids are 0.5◦ and 0.1◦, respectively. The grid is smaller, the accuracy and the resolution probability are better. In the third example, we illustrate the influence of the source separation on the performance of the NC-SFSR and L1-SVD. We firstly fix one DOA of the BPSK signal at −21.6◦,and another DOA of the BPSK signal is the function of the angular separation. The noncircular rates both are 60◦. The number of snapshots is 200. Each simulated point is obtained as an average of 100 independent Monte-Carlo simulation runs with SNR 10,dB. The grid is 1◦ for the NC-SFSR and L1-SVD. In Fig. 4, we present the plot of bias versus angular separation. Figure 4 shows the NC-SFSR owns smaller bias for low separations, but the bias becomes same when two sources are more than about 15◦ apart. 123 2372 X. Yang et al.

-10

-20

-30

-40

-50 spatial spectra(dB) NC-SFSR -60 NC-ROOT-MUSIC L1-SVD -70 40 42 44 46 48 50 DOA(Deg) ◦ Fig. 3 Spatial spectra for the NC-SFSR, NC-ROOT-MUSIC and L1-SVD when the grid is 0.1

4 NC-SFSR 3.5 L1-SVD 3

2.5

bias(Deg) 1.5

0.5

0 5 10 15 20 25 30 35 40 source separation(Deg)

Fig. 4 Bias of two source separation for the NC-SFSR and L1-SVD

In the fourth example, we examine the performance of the NC-SFSR, NC-ROOT-MUSIC, NC-ESPRIT and L1-SVD versus the number of the snapshots. The parameters of the simulated source in this example are same with those of the ﬁrst example. The SNR is 10dB. Each simulated point is obtained as an average of 100 independent Monte-Carlo simulation runs. From Fig. 5, it can be observed that our algorithm excels the L1-SVD and NC-ESPRIT, also approaches to the NC-ROOT-MUSIC. In the ﬁfth example, we investigate the performance of the NC-SFSR, NC-ROOT-MUSIC and L1-SVD when multiple uncorrelated noncircular signals coexist simultaneously. Assume that there are seven BPSK signals impinging on the ULA with eight sensors, whose directions are −61◦, −41◦, −21◦, 1◦, 21◦, 41◦ and 61◦, respectively. All the noncircular rate is 60◦.The number of snapshots is 200. The SNR is 10dB. Figure 6 presents the estimated spatial spectra 123 DOA Estimation of Noncircular Signal 2373

0 10 NC-SFSR NC-ESPRIT NC-ROOT-MUSIC L1-SVD

-1 10 RMSE(Deg)

-2 10 200 400 600 800 1000 number of snapshots

Fig. 5 RMSE of DOA for the NC-SFSR, NC-ROOT-MUSIC, NC-ESPRIT and L1-SVD versus the number of snapshots

-10

-20

-30

-40 spatial spectra(dB) -50 NC-SFSR NC-ROOT-MUSIC L1-SVD -60 -100 -50 0 50 100 DOA(Deg)

Fig. 6 Spatial spectra for the NC-SFSR, NC-ROOT-MUSIC and L1-SVD with seven signals as seven noncircular signals coexist simultaneously. As we can see, the NC-SFSR has better performance when the number of sources gets close to the number of sensors.

5 Conclusions

In this paper, we have introduced a new DOA estimator for noncircular signal by employing the sparse representation technique, which is based on the SF method. We use L1-norm penalty to solve the sparse reconstruction problem, which is optimized by SOCP framework. Finally, we examined various aspects of our approach, such as RMSE, bias, the number of snapshots, and the number of resolvable sources, by doing simulations. This method can be used in multiple measurements, and arbitrary array conﬁguration. Simulation results indicate 123 2374 X. Yang et al. that our approach exhibits better performance than L1-SVD, and can even approach the NC- ROOT-MUSIC algorithm in low SNR.

Acknowledgments This research was supported by the National Natural Science Foundation of China under Grant No. 61301155 and 61176025, and the Fundamental Research Funds for the Central Universities Project No. ZYGX2012J003, for which the authors would like to express their thanks. The authors also wish to thank the anonymous reviewers for their helpful and constructive comments and suggestions.

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Xuemin Yang was born in Sichuan, China, on 10 October 1986. He received the M.S. degree in Signal and Information Processing from Chongqing University, Chongqing, China, in 2012 and is currently studying towards the Ph.D. degree in Communication and Information systems at University of Electronic Science and Technology of China. His research interests are focused on array signal processing and wireless communication with compressive sensing.

Guangjun Li was born in 1950. He is currently a full professor in School of Communication and Information Engineering, University of Electronic Science and Technology of China. His research interests mainly include communication signal processing and wireless personal communication.

Zhi Zheng was born in Sichuan, China, on 5 April 1980. He received the M.S. degree in Circuit and Systems from University of Electronic Science and Technology of China, Chengdu, China, in 2007 and Ph.D. degree in Communication and Information systems, at the same university in 2011. He is currently an associate professor in School of Com- munication and Information Engineering, University of Electronic Sci- ence and Technology of China. His research interests are focused on array signal processing, smart antenna and wireless communication.

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