5766 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 3, JUNE 2019

Assistant Vehicle Localization Based on ThreeCollaborative Base Stations via SBL-Based

Robust DOA EstimationHuafei Wang , Liangtian Wan , Member, IEEE, Mianxiong Dong , Member, IEEE,

Kaoru Ota , Member, IEEE, and Xianpeng Wang , Member, IEEE

Abstract—As a promising research area in Internet of Things(IoT), Internet of Vehicles (IoV) has attracted much attention inwireless communication and network. In general, vehicle local-ization can be achieved by the global positioning systems (GPSs).However, in some special scenarios, such as cloud cover, tunnelsor some places where the GPS signals are weak, GPS cannotperform well. The continuous and accurate localization servicescannot be guaranteed. In order to improve the accuracy of vehi-cle localization, an assistant vehicle localization method based ondirection-of-arrival (DOA) estimation is proposed in this paper.The assistant vehicle localization system is composed of three basestations (BSs) equipped with a multiple input multiple output(MIMO) array. The locations of vehicles can be estimated if thepositions of the three BSs and the DOAs of vehicles estimated bythe BSs are known. However, the DOA estimated accuracy maybedegrade dramatically when the electromagnetic environment iscomplex. In the proposed method, a sparse Bayesian learning(SBL)-based robust DOA estimation approach is first proposed toachieve the off-grid DOA estimation of the target vehicles underthe condition of nonuniform noise, where the covariance matrixof nonuniform noise is estimated by a least squares (LSs) proce-dure, and a grid refinement procedure implemented by findingthe roots of a polynomial is performed to refine the grid points toreduce the off-grid error. Then, according to the DOA estimationresults, the target vehicle is cross-located once by each two BSsin the localization system. Finally, robust localization can be real-ized based on the results of three-time cross-location. Plenty ofsimulation results demonstrate the effectiveness and superiorityof the proposed method.

Manuscript received January 15, 2019; revised March 9, 2019; acceptedMarch 11, 2019. Date of publication March 18, 2019; date of current ver-sion June 19, 2019. This work was supported in part by the National NaturalScience Foundation of China under Grant 61701144 and Grant 61801076, inpart by the Young Elite Scientists Sponsorship Program by CAST under Grant2018QNRC001, in part by the Program of Hainan Association for Science andTechnology Plans to Youth Research and Development Innovation under GrantQCXM201706, in part by the Scientific Research Projects of University inHainan Province under Grant Hnky2018ZD-4, in part by the Major Scienceand Technology Project of Hainan Province under Grant ZDKJ2016015, inpart by the Scientific Research Setup Fund of Hainan University under GrantKYQD(ZR)1731, in part by Japan Society for the Promotion of ScienceKAKENHI under Grant JP16K00117, and in part by KDDI Foundation.(Corresponding author: Xianpeng Wang.)

H. Wang and X. Wang are with the State Key Laboratory ofMarine Resource Utilization in South China Sea, College of InformationScience and Technology, Hainan University, Haikou 570228, China (e-mail:wong9525@163.com; wxpeng1986@126.com).

L. Wan is with the Key Laboratory for Ubiquitous Network and ServiceSoftware of Liaoning Province, School of Software, Dalian University ofTechnology, Dalian 116620, China (e-mail: wanliangtian@dlut.edu.cn).

M. Dong and K. Ota are with the Department of Information and ElectronicEngineering, Muroran Institute of Technology, Muroran 050-8585, Japan(e-mail: mx.dong@csse.muroran-it.ac.jp; ota@csse.muroran-it.ac.jp).

Digital Object Identifier 10.1109/JIOT.2019.2905788

Index Terms—Base station (BS), direction-of-arrival (DOA)estimation, nonuniform noise, off-grid error, sparse Bayesianlearning (SBL), vehicle localization.

I. INTRODUCTION

W ITH the rapid development of economy and automaticdriving technology, the number of mobile devices such

as autonomous vehicles [1], [2] has increased dramatically inInternet of Things (IoT). The vehicle localization is becomingmore and more important for Internet of Vehicles (IoV) [3], [4]since the data transmission is based on accurate locationinformation of vehicles. Generally, vehicle localization can beaccurately achieved by the cooperation between global posi-tioning systems (GPSs) and motion sensors on the vehicles inmost scenarios when the GPS is available [5]. However, GPSis not always available anywhere. Therefore, it is particularlyimportant to exploit an assistant localization system, whichmay be composed of radars or sensors [6], [7], to achievevehicle localization. The received signal strength indication(RSSI) technique has been adopted widely [8]–[10] to achievetarget vehicle localization. However, most of the RSSI-basedalgorithms need to know the spatial fading characteristics ofsignals [11]–[13], which is difficult to obtain accurately dueto the complexity of wireless channel. In addition, some timedifference of arrival (TDOA)-based algorithms [14], [15] arearisen, but their performance is highly sensitive to time dif-ference measurement, which makes it hard to achieve highaccuracy vehicle localization. Aiming at this, the direction-of-arrival (DOA)-based target localization methods [16], [17]become a good choice. Compare with the RSSI and TDOA,the DOA-based localization methods are just dependent on theaccuracy of DOA estimation, which is easily obtained by theplenty exist DOA estimation algorithms.

For DOA estimation, a lot of excellent methods havebeen proposed based on the subspace technique, such asmultiple signal classification (MUSIC) [18], [19] algorithmand estimation of signal parameters via rotational invariancetechniques (ESPRIT) [20]. Further, some reduced-complexity(RC) methods, such as root-MUSIC [21], RC-MUSIC [22],and RC-ESPRIT [23], are reported for reducing the computa-tional complexity of the subspace-based algorithms. However,only when the signal-to-noise ratio (SNR) and snapshot

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WANG et al.: ASSISTANT VEHICLE LOCALIZATION BASED ON THREE COLLABORATIVE BSs VIA SBL-BASED ROBUST DOA ESTIMATION 5767

number are large enough, these subspace-based algorithmscan achieve the required DOA estimation performance. Whenthe SNR is low and/or the snapshot number is limited,their performance may decrease significantly. To overcomethese limitations, the sparse signal representation (SSR) tech-nique has emerged as a new DOA estimation technique.Based on the advantages of SSR technique, amounts of SSR-based methods have been presented for DOA estimation,including l1-norm optimization-based algorithm [24], [25] andsparse Bayesian learning (SBL)-based algorithm [26], [27].Compared with the l1-norm optimization-based algorithm,the SBL-based methods are paid more attention by scholarsbecause of their small estimation error and better estimationperformance [28].

However, it is known that the SBL-based methods usuallyobtain the sparsity of the signal by discretizing the spatialrange, which will form a uniform discrete grid, and thenDOA estimation can be realized by using the maximum like-lihood (ML) criterion or the maximum posterior probabilitycriterion. However, without a suitable discrete grid, which isdifficult to select in practice, it is hard for SBL-based methodto achieve the satisfied DOA estimation performance [29]. Adense enough grid will lead to heavy computation complex-ity. It is unavailable for all true DOAs to exactly locate onthe discrete grid points, and then the off-grid error must existbetween the true DOA and its nearest grid point. Aiming atsolving the off-grid DOA estimation problem, a sparse totalleast squares (STLSs) solution is proposed in [30], where theoff-grid gap is supposed to follow a Gaussian prior distribu-tion, and the error is approximated by the first order Taylorexpansion of the true DOA at the grid point closest to it.In addition, a new method called off-grid sparse Bayesianinference (OGSBI) [31], in which the off-grid error is sup-posed to obey a uniform distribution within the grid interval,is proposed to achieve the off-grid DOA estimation by lin-ear approximation. Furthermore, a block-SBL method [32],where the noise variance does not need to be estimated, ispresented to realize the off-grid DOA estimation by utilizingthe covariance matrix of received data. However, both of thesetwo methods in [31] and [32] achieve the satisfied off-gridDOA estimation performance at the expense of computationalcomplexity, and their performances are still unsatisfied undera very coarse grid condition. Therefore, in order to achievesatisfied performance with relatively low computational com-plexity and a coarse grid, the root SBL algorithm for off-gridDOA estimation (ROGSBL) is reported in [33], in which thespatial grid is refined by solving a polynomial. Nevertheless,the process of solving polynomial in [33] is still computation-ally inefficient. Hence, to further improve the efficiency ofthe grid updating procedure, an enhanced SBL method [34]is proposed to realize the off-grid DOA estimation, where thegrid point is dynamically updated by a forgotten factor model.

On the other hand, all the algorithms mentioned above foroff-grid DOA estimation are based on the assumption that thenoise is uniform Gaussian white noise which is unrealisticto meet in practice due to the nonuniform sensor responseand nonideal receiving channel [35], [36]. Aiming at deal-ing with the nonuniform noise, a large number of ML-based

algorithms [37]–[40] have been proposed in the past fewdecades. Particularly, the stochastic ML method presentedin [40] can effectively eliminate the influence of nonuni-form noise by accurately estimating the covariance matrix ofnonuniform noise based on a modified inverse iteration algo-rithm. However, the requirement of ML algorithm for jointsearch makes it unfavorable for practical application. On theother hand, the SSR-based algorithms [41]–[44] for DOA esti-mation under nonuniform noise condition also attract greatattention. By utilizing the modified inverse iteration algorithmin [40] to estimate the covariance of nonuniform noise, animproved SBL-based algorithm is presented in [41] to realizeDOA estimation with nonuniform noise. Besides, consideringthe second-order statistical information of the received signal,several covariance matrix-based methods [42], [43] are investi-gated to achieve DOA estimation in nonuniform noise, and thehigh precision DOA estimation can be achieved in [43] basedon an adaptive procedure [29]. However, the performance ofthe method proposed in [43] may suffer from aperture lossand can be further improved. Moreover, by adopting the leastsquares (LSs) strategy, an SBL-based method [44], which issuitable for nonuniform noise is proposed to achieve DOAestimation. It is not difficult to find that all the algorithmsmentioned above either consider the presence of nonuniformnoise or the off-grid error. However, in order to improve theDOA estimation accuracy in complexly practical environment,the coexisting of nonuniform noise and off-grid error have tobe tackled efficiently.

In this paper, an assistant vehicle localization method basedon an SBL-based robust DOA estimation approach in the coex-istence of nonuniform noise and off-grid error is proposed,where the assistant vehicle localization system is composed ofthree collaborative base stations (BSs) equipped with multipleinput multiple output (MIMO) array. In the proposed DOAestimation method, the received data of BS is first compressedby a transformation matrix. Then a sparse model is estab-lished for off-grid DOA estimation, where the variance of echosignal is estimated by expectation maximization (EM) algo-rithm. The noise power, which is always nonuniform noiseafter dimensional reduction, is estimated by an LS strategy,and the discrete grid point is refined by the EM algorithmwhich is performed by solving a polynomial. Finally, the off-grid DOA estimation can be realized by performing a 1-Dspectrum search of the echo signal on the refined discrete grid.Extensive simulation results indicate that the proposed methodcan maintain superior localization performance based on theexcellent performance of the proposed robust DOA estima-tion approach under the coexistence of nonuniform noise andoff-grid error, especially under the condition of a very coarsegrid.

The main contributions of this paper are summarized asfollows.

1) A vehicle localization system consisting of three col-laborative BSs equipped with MIMO array is presented.Each two of the three BSs can cross-locate the targetvehicle once, and three results of cross-location can beobtained. The final localization result is obtained by theaverage of three cross-location results, which enables

5768 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 3, JUNE 2019

the proposed method to achieve more stable localizationperformance.

2) The collaborative BS is composed of MIMO arraywhich can expand array aperture effectively, and thespatial diversity makes radar signal processing achievemore degree of freedom (DOF). These advantages makeMIMO array obtain higher spatial angle resolution forDOA estimation, improve the accuracy of angle estima-tion effectively, and increase the maximum number ofdiscernible targets significantly.

3) An SBL-based robust DOA estimation approach isproposed under the coexistence of nonuniform noise andoff-grid error. The LS strategy is adopted to estimate thevariance of nonuniform noise, and a grid refinement isperformed by finding roots of a polynomial to update thediscrete grid. Thus, the DOA estimation approach caneffectively handle the influence of nonuniform noise andoff-grid error simultaneously. As a result, the proposedDOA estimation approach can maintain more accurateand stable localization performance under the coexis-tence of nonuniform noise and off-grid error. On theother hand, compare with the subspace-based method,the proposed SBL-based approach is less sensitive toSNR and snapshot number, and can maintain superiorperformance of DOA estimation under small SNR or/andlow snapshot number.

4) The grid refinement procedure in the proposed DOAestimation approach can effectively reduce the off-grid error, especially in the very coarse grid case.Without affecting the performance of DOA estimation,the coarser the grid partitions, the faster the DOA esti-mation speed achieves. In addition, by selecting anappropriate number of “active” grid points, the DOAestimation speed can be improved further. Plenty ofsimulations are conducted to verify the superiority andeffectiveness of the proposed approach.

The definition of some important notations used in thispaper are given in the following Table I.

II. LOCALIZATION SYSTEM AND DATA MODEL

As shown in Fig. 1, consider an assistant vehicle localiza-tion system with three collaborative BSs consisting of a largenumber of antennas, where the BS is equipped with MIMOarray. This is reasonable since a large number of antennas canbe used for constructing the MIMO array. All the three BSs areconfigured and work in the same way. The BS estimates theDOA of the target vehicle, and each two BSs cross-locate thetarget vehicle based on the DOA estimation results. The accu-rate localization can be ultimately achieved through the threeresults from cross-localization. Each BS consists of transmit-ting array and receiving array, and the transmitting array andreceiving array are colocated, which means that the DOA ofa vehicle is identical for the transmitting array and receivingarray. Both transmitting array and receiving array are uniformlinear array (ULA), and the distance between adjacent anten-nas is half-wavelength. Suppose that the transmitting array and

TABLE ISOME IMPORTANT NOTATIONS

Fig. 1. Vehicle localization system with three collaborative BSs.

receiving array are composed of M and N antennas, respec-tively. There exist K target vehicles in the same plane range,θk represents the DOA of the kth target where k = 1, 2, . . . , K.The transmitting array of BS emits M orthogonal waveformsand the receiving array collects the echo signal reflected bythe target vehicles. Then the echo signal received by receivingarray of the BS at the t-th snapshot can be expressed as [18]

x(t) =K∑

k=1

sk(t)ar(θk)aTt (θk)��� + n(t) (1)

where sk(t) = ξk(t)ej2π fk(t) represents the echo signal reflectedby the kth target vehicle, ξk(t) and fk(t) stand for thereflection coefficient and the Doppler frequency, respectively.��� = [ω1, ω2, . . . , ωM]T is the complex code matrix of Morthogonal waveforms emitted by transmitting array, whereωm(m = 1, 2, . . . .M) represents the complex code vectortransmitted by the mth transmitting antenna. When i = j, thewaveforms satisfy ωH

i ωj = 1, and when i �= j, they satisfy

WANG et al.: ASSISTANT VEHICLE LOCALIZATION BASED ON THREE COLLABORATIVE BSs VIA SBL-BASED ROBUST DOA ESTIMATION 5769

ωHi ωj = 0. n(t) represents the unknown nonuniform Gaussian

white noise vector and its covariance can be expressed asQ = E{n(t)n(t)H} = diag{σ 2

1 , σ 22 , . . . , σ 2

N}, where σ 2n is the

variance of noise received by the nth receiving antenna andσ 2

1 �= σ 22 �= · · · �= σ 2

N . at(θk) and ar(θk), respectively,represent the transmit steering vector and receive steeringvector with at(θk) = [1, e−jπsinθk , . . . , e−jπ(M−1)sinθk ]T andar(θk) = [1, e−jπsinθk , . . . , e−jπ(N−1)sinθk ]T . After matching fil-tering, the output data at the receiving array of the BS can beexpressed as

x(t) = As(t) + n(t) (2)

where x(t) ∈ CMN×1 is the output data vector at the t-

th snapshot. A = [at(θ1) ⊗ ar(θ1), . . . , at(θK) ⊗ ar(θK)]represents the transmit-receive joint steering matrix. Ands(t) = [s1(t), s2(t), . . . , sK(t)]T is the echo signal vector. n(t)denotes the noise vector after matched filtering, which is stillnonuniform noise. The covariance matrix of n(t) is shown as

Q = E{n(t)n(t)H} = IM ⊗ Q. (3)

Collecting T snapshots, the output data in (2) can beformulated as the matrix form as follows:

X = AS + N (4)

where X = [x(1), x(2), . . . , x(T)], S = [s(1), s(2), . . . , s(T)],and N = [n(1), n(2), . . . , n(T)].

By observing the structure of the joint steering matrix A, itcan be found that the joint steering vector at(θk) ⊗ ar(θk) ∈C

MN×1. However, there are only P = M+N−1 unique entriesin it, which means that there exist some redundant entries init. Considering the existence of redundant entries in the jointsteering vector, it can be rewritten as

at(θk) ⊗ ar(θk) = J × b(θk) (5)

where b(θk) = [1, e−jπsinθk , . . . , e−jπ(P−1)sinθk ]T is the newsteering vector, and J ∈ C

MN×P is expressed as

J =

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1 0 · · · 0 0 · · · 00 1 · · · 0 0 · · · 0...

.... . .

......

. . ....

0 0 · · · 1 0 · · · 0

0 1 0 · · · 0 · · · 00 0 1 · · · 0 · · · 0...

......

. . ....

. . ....

0 0 0 · · · 1 · · · 0

......

......

......

...

0 · · · 0 1 0 · · · 00 · · · 0 0 1 · · · 0...

. . ....

......

. . ....

0 · · · 0 0 0 · · · 1

⎤

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

. (6)

Hence, the data model in (4) can be rewritten as

X = JBS + N (7)

where B = [b(θ1), b(θ2), . . . , b(θK)] is the new steeringmatrix without redundant entries. It should be noticed that itis inappropriate to directly multiply JH with (7) to reducethe dimension, which will transform the noise into colornoise [34]. On the other hand, we can find that

JHJ = diag

⎛

⎜⎝1, 2, . . . , min(M, N), . . . , min(M, N)︸ ︷︷ ︸|M − N| + 1

, . . . , 2, 1

⎞

⎟⎠

(8)

which is a full rank matrix. Hence, in order to remove theredundant entries and achieve the purpose of dimensionalityreduction, the following transformation matrix is constructed:

D = (JHJ

)−1JH . (9)

By multiplying the transformation matrix D with the datamodel in (7), we have

Y = DJBS + DN = BS + E (10)

where Y = [y(1), y(2), . . . , y(T)]. E = DN is still theunknown nonuniform noise, and its covariance matrix isshown as

Q = E{(Dn(t))(Dn(t))H} = diag

{σ 2

1 , σ 22 , . . . , σ 2

P

}(11)

where σ 2p (p = 1, 2, . . . , P) can be regarded as the converted

noise power. Obviously, whether the received noise at thereceiving array is uniform or nonuniform, the converted noisemust be nonuniform noise.

Generally, according to the sparse representation strategy,the plane range from −90◦ to 90◦ where target vehicle islocated is uniformly fixed into K parts with K � P > K.Then a discrete grid will be formed in the plane and a completedirection set ϑϑϑ = [ϑ1, ϑ2, . . . , ϑK] can be obtained. Obviously,if the complete direction set is dense enough, the vehicles aresparse on it. Then the sparse signal model of (10) can beexpressed as

Y = BS + E (12)

where B = [b(ϑ1), b(ϑ2), . . . , b(ϑK)] ∈ CP×K

is the overcomplete dictionary with b(ϑk) =[1, e−jπsinϑk , . . . , e−jπ(P−1)sinϑk ]T(k = 1, 2, . . . , K). And S =[s(1), s(2), . . . , s(T)], where s(t) = [s1(t), s2(t), . . . , sK(t)]T

is a K sparse signal vector. According to the sparse signalmodel in (12), the DOA estimation of vehicles can beachieved by estimating the parameters of the sparse signalvector.

III. SBL-BASED ROBUST DOA ESTIMATION

A. Sparse Bayesian Framework

Based on the statistical SBL strategy [26], each column ofthe sparse matrix S is supposed to follow the independentcomplex Gaussian distribution in this paper, i.e.,

s(t) ∼ CN (0,ϒϒϒ) (13)

where CN (0,ϒϒϒ) represents the complex Gaussian distribu-tion with zero mean and variance ϒϒϒ = diag(γγγ ). γγγ =

5770 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 3, JUNE 2019

[γ1, γ2, . . . , γK]T is known as the hyper-parameter set, andγk denotes the variance of echo signal from the direction ϑk.Since S contains the echo signal of T snapshots, its probabilitydensity distribution can be calculated as

p(S|γγγ ) =

T∏

t=1

CN (s(t)|0,ϒϒϒ). (14)

In addition, the entries of γγγ are assumed to follow theindependent Gamma distribution, i.e., γk ∼ �(α, β), withk = 1, 2, . . . , K. Then the probability density distribution ofϒϒϒ can be obtained as

p(ϒϒϒ) =K∏

k=1

�(γk|α, β

)(15)

where �(γk|α, β) = �(γk)−1βαγ α−1

ke−βγk with �(γk) =∫∞

0 tγk−1e−tdt. Generally, α and β are two constants closeto zero [26].

According to the above assumptions and Bayesian principle,it is easy to deduce that the received data Y also follows thecomplex Gaussian distribution. Hence, the probability densityfunction of Y is

p(Y|S, Q

) =T∏

t=1

CN (y(t)|Bs(t), Q)

= |πQ|−Texp{−tr

[(Y − BS

)HQ

−1(Y − BS

)]}.

(16)

Then by utilizing the Bayesian derivation, the posteriorprobability density of S can be calculated as

p(S|Y;γγγ , Q

) = p(Y|S; Q

)p(S|γγγ )

∫p(Y|S; Q

)p(S|γγγ )dS

= |π���|−Texp{−tr

[(S − μμμ

)H���−1(S − μμμ

)]}

(17)

where μμμ and ���, respectively, represent the mean and covari-ance, which are calculated as

μμμ = ϒϒϒBH(

Q + BϒϒϒBH)−1

Y (18)

��� = ϒϒϒ − ϒϒϒBH(

Q + BϒϒϒBH)−1

Bϒϒϒ. (19)

In order to estimate μμμ and ���, the hyper-parameter γγγ andthe nonuniform noise covariance matrix Q should be estimatedfirst. The posterior probability density distribution of Y withrespect to γγγ and Q can be calculated as follows:

p(Y|γγγ , Q

) =∫

p(Y|S, Q

)p(S|γγγ )dS

= |π���Y |−Texp{−tr

(YH���−1

Y Y)}

(20)

where ���Y = Q+BϒϒϒBH

. Obviously, it is a type-II ML problemfor the estimation of γγγ and Q. By taking the logarithm of(20) and neglecting the constant terms, the objective likelihoodfunction for estimating hyper-parameter γγγ is shown as follows:

L(γγγ , Q) = ln|���Y | + tr

(���−1

Y R)

(21)

where R = (1/T)YYH is a substitute for R =E[y(t)yH(t)], because the ideal R is unrealistic to obtain inpractice.

B. Estimation of Echo Signal and Nonuniform Noise Power

To estimate the hyper-parameter γγγ , we just have to mini-mize the objective likelihood function in (21). Generally, theEM algorithm is adopted to optimize the objective likelihoodfunction and achieve the estimation of γγγ . Hence, accord-ing to the strategy of EM algorithm, the partial derivativeof (21) with respect to γγγ is taken and we set it to bezero, i.e.,

∂L(γγγ , Q)

∂γγγ= 0. (22)

Then, by solving (22), the updating formula for γγγ can bederived as γ

(i)k

= (1/T)‖(μμμ(i))k·‖22 + (���(i))k,k. However, in

the process of convergence, most elements of γγγ tend to bezero due to its sparsity, which may lead to the calculationsingularity. Therefore, in order to avoid this phenomenon, theupdating formula for γγγ is revised as [28]

γ(i)k

= 1

T‖(μμμ(i)

)

k·‖22/

⎡

⎣1 −(���(i)

)k,k

γ(i)k

⎤

⎦+ τ (23)

where k = 1, 2 . . . , K. (·)k and (·)k,k represents the kth entry

of a vector and (k, k)th entry of a matrix, respectively. γ(i)k

,μμμ(i) and ���(i) denote the estimated results of γk, μμμ and ���

in the ith iteration, respectively, where μμμ(i) and ���(i) can becalculated by (18) and (19). τ is a small positive constant,such as τ = 10−10 [28].

On the other hand, Q can also be estimated theoreti-cally by optimizing the objective likelihood function in (21).However, it seems impossible to obtain the analytical esti-mation of Q by optimizing the objective likelihood functionin (21) through the partial derivative due to the nonuni-formity of Q [28]. Therefore, LS procedure is adopted toestimate the nonuniform noise covariance matrix Q. Aftereach iteration, the crude estimation of K DOAs, which isdenoted as ϑϑϑ = [ϑ1, ϑ2, . . . , ϑK], can be obtained by the1-D spectrum search, and the corresponding steering matrix isBK = [b(ϑ1), b(ϑ2), . . . , b(ϑK)]. Based on the theory in [44]and the knowledge of subspace technique, the subspace formedby the columns of R−Q and BK are the same subspace, whichmeans

R − Q = BKH (24)

where R = E[y(t)yH(t)], and H is a full rank matrix. Thep(p = 1, 2, . . . , P)th column of R − Q can be represented byup = vp − σ 2

p ep, where vp denotes the pth column of R andep is a column vector with only the pth element is 1 and theother elements are 0. Then, the error between column vectorsof R − Q and BKH can be calculated by

g(p) = ‖up − BKhp‖22 (25)

where hp represents the pth column of H. By utilizing theLS procedure to solve the (25), the LS solution of hp can

WANG et al.: ASSISTANT VEHICLE LOCALIZATION BASED ON THREE COLLABORATIVE BSs VIA SBL-BASED ROBUST DOA ESTIMATION 5771

be obtained as hp = (BHK BK)−1B

HK up. Then, the objective

function for estimating noise variance can be derived bysubstituting hp back into g(p) as follows:

�(σ 2

p

)=

P∑

p=1

‖up − BKhp‖22 =

P∑

p=1

uHp ���up (26)

where ��� = IP −BK(BHK BK)−1B

HK . Then, the updating formula

for the nonuniform noise covariance matrix Q is derived bytaking the partial derivation of �(σ 2

p ) with respect to σ 2p , i.e.,

∂�(σ 2p )/∂σ 2

p = 0. Thus, the updating formula for σ 2p can be

derived as

σ 2p = eT

p���vp − vHp ���ep

2eTp���ep

. (27)

Until now, the variance of echo signal and nonuniform noisecan be estimated by (23) and (27), respectively. Based on thesparsity of S, the DOA estimation can be realized throughthe 1-D spectrum search now. However, the obtained accuracyof DOA estimation is still seriously affected by the off-griderror. Especially, when the discrete grid is very coarse, theperformance will be seriously degraded. Aiming at solving thisproblem, the off-grid DOA estimation with a coarse grid willbe achieved by a grid refinement procedure in the followingsection.

C. Off-Grid DOA Estimation

Similar to the procedure in [33], the EM algorithm is used torefine the grid points. In E-step, the mathematical expectationof (16) is first calculated as follows:

Ep(S|Y;γγγ ,Q

){ln(p(Y|S, Q

))}

= −T∑

t=1

‖Q− 1

2(yt − Bμμμt

)‖22 − Ttr

((Q

− 12 B)���

(Q

− 12 B)H)

(28)

where yt and μμμt represent the t-th column of Y and μμμ, respec-tively. Then, in M-step, the mathematical expectation [i.e.,(28)] of (16) is maximized. Let ϕk � e−jπ sin ϑk , and thenwe set the partial derivative of (28) with respect to ϕk to be0, i.e.,

(b′k

)H(

bk

T∑

t=1

(|μμμt,k|2 + εk,k

)

+ T∑

i �=k

εi,kbi −T∑

t=1

μμμ∗t,k

yt−k

⎞

⎠ = 0 (29)

where bk = Q−(1/2)

bk and b′k = dbk/dϕk. bk denotes

the kth column of B. yt−k = yt − ∑i �=k μμμt,kbi with yt =

Q−(1/2)

yt. μμμt,k denotes the (t, k)th element of μμμ, and εi,k isthe (i, k)th element of ���. Then, by defining the followingequation:

�(k)�

T∑

t=1

(|μμμt,k|2 + εk,k

)(30)

Algorithm 1 SBL-Based Robust DOA Estimation Approach1: Input: The received data X;2: Construct the transformation matrix D according to

Eq. (9);3: Obtain Y according to Eq. (10);4: Initialization: Q, γγγ ;5: while ∼ Converge do6: Update μμμ and ��� by Eq. (18) and Eq. (19);7: Update γγγ according to Eq. (23);8: Update Q according to Eq. (27);9: Refine ϑϑϑ according to Eq. (32), Eq. (33) and Eq. (34)

10: end while11: Output: ϑϑϑ and μμμ;12: Achieve off-grid DOA estimation through 1D spectrum

search on new ϑϑϑ .

�(k)� T

∑

i �=k

εi,kbi −T∑

t=1

μμμ∗t,k

yt−k. (31)

Equation (29) can be transformed into a polynomial form as

[ϕk, 1, ϕ−1

k, . . . , ϕ

−(P−2)

k

]

⎡

⎢⎢⎢⎢⎢⎢⎢⎣

P(P−1)2 �

(k)

�

(k)

2

2�

(k)

3...

(P − 1)�

(k)

P

⎤

⎥⎥⎥⎥⎥⎥⎥⎦

= 0 (32)

where �(k)p denotes the pth entry of �(k). Since |ϕk| = 1, the

root with absolute value nearest to 1 in the P − 1 roots ischosen to refine the grid point after solving the polynomial.The chosen root is represented by ϕk∗ , and then the kth newgrid point can be calculated by

ϑ refk∗ = arcsin

(− λ

2πd· angle

(ϕk∗))

. (33)

Actually, when the true DOAs of vehicles overlap withthe original grid points, the refinement procedure wouldinevitably reduce the accuracy of DOA estimation. Therefore,in order to avoid this negative impact, a further threshold isset to determine whether to refine the grid points or not asfollows:

ϑk∗−1 + ϑk∗

2≤ ϑ ref

k∗ ≤ ϑk∗ + ϑk∗+1

2. (34)

Now, an SBL-based robust DOA estimation approach underthe coexistence of nonuniform noise and off-grid error hasbeen proposed. The estimation of variance of echo signal andnonuniform noise can be obtained by an iterate procedure. Theproposed method is summed up in Algorithm 1.

Remark 1: In step 4, Q is initialized as Q = (σ 2)(0)IP with

(σ 2)(0) = |tr{(IP−BBH)R}/(P−K)|, where IP denotes a P×P

unit matrix. γγγ is initialized as (γk)(0) = (1/T)‖(μμμ(0))k·‖2

2 with

μμμ(0) = BH(BB

H)−1Y.

Remark 2: The proposed robust DOA estimation methodcan maintain superior performance in the case of the coexis-tence of nonuniform noise and off-grid error, mainly caused

5772 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 3, JUNE 2019

Fig. 2. Simplified diagram for vehicle localization with three collabora-tive BSs.

by steps 8 and 9. In step 8, the variance of nonuniform noisecan be accurately estimated. In step 9, the off-grid error canbe minimized effectively. Actually, the refinement procedurein step 9 does not need to be implemented for every grid pointin each iteration. In order to speed up the DOA estimation ofthe proposed algorithm, a proper number of active grid pointsare selected to be refined [33]. Define f = ‖μμμt‖F , and thenthe active grid points are determined according to the indexof the first η maxima value of f , where 1 ≤ η ≤ P. Usually,η is set to be η ≥ K. When the number of signal is unknown,η = P is recommended.

IV. VEHICLE LOCALIZATION BASED ON

DOA ESTIMATION

For the sake of simplicity, the BSs in Fig. 1 are simplified tothe bold red line as shown in Fig. 2, and the central antenna ofBS is set as the reference point. The coordinates of referencepoints A1, A2, and A3 corresponding to the three collaborativeBSs are known to be (0, a), (0, 0), and (b, 0), respectively. S isthe position of the target vehicle, and its azimuth angles relatedto A1, A2, and A3 are defined as θ1, θ2, and θ3, respectively.

According to the measured data of BS A1, A2, and A3, θ1, θ2,and θ3 can be obtained by the robust DOA estimation approachin Algorithm 1, respectively. Then the following equation canbe obtained as:

tanθ1 = a − y

x(35)

tanθ2 = y

x(36)

tanθ3 = b − x

y. (37)

Based on (35) and (36), the target vehicle can be cross-located, and the coordinate of S(x, y) can be calculated as

x1 = a

tanθ1 + tanθ2y1 = atanθ2

tanθ1 + tanθ2. (38)

Similarly, based on (36) and (37) and (35) and (37), thecoordinates of S can be obtained, respectively, as

x2 = b

1 + tanθ2tanθ3y2 = btanθ2

1 + tanθ2, tanθ3(39)

x3 = b − atanθ3

1 − tanθ1tanθ3y3 = a − btanθ1

1 − tanθ1tanθ3. (40)

Ultimately, based on the results of three cross localizationin (38)–(40), the coordinate of S(x, y) can be determined by

x = x1 + x2 + x3

3y = y1 + y2 + y3

3. (41)

Remark 3: Theoretically, we only need two of the threeBSs in Fig. 2 to determine the coordinate of S and achieve thevehicle localization, and the result calculated by (38)–(40) areequal. However, in practice, the coordinates estimated by onlytwo collaborative BSs must exist errors due to various dis-turbances, and the results of (38)–(40) cannot be completelyequal. In this paper, three collaborative BSs are used, in whicheach two BSs can estimate the coordinates of the target vehi-cle once. The finally estimated coordinates are averaged by(41), which can reduce the localization error and make thelocalization result more stable.

V. SIMULATION AND TEST RESULTS

In this section, the performance of the proposed vehiclelocalization method is mainly evaluated by the DOA esti-mation performance of the proposed robust DOA estimationmethod. The OGSBI [31], ROGSBL [33] and the enhancedSBL (ESBL) method [34] are adopted to compare with theproposed method. In addition, the Cramér–Rao bound (CRB)is utilized to evaluate the performance of these methods.Each BS in the localization system consists of M = 8transmitting antennas and N = 10 receiving antennas, andthe distance between adjacent antennas in both transmittingand receiving arrays is half-wavelength. Suppose there existK = 3 un-correlated targets in the same range, and forthe sake of generality, their DOAs are randomly generatedfrom [−30◦,−20◦], [0◦, 10◦], and [40◦, 50◦] with a resolu-tion of 0.01◦, respectively. The range from −90◦ to 90◦ isuniformly fixed by 4◦, which will form a very coarse grid.Except for special instructions, the number of active gridpoints is generally selected as η = P = M + N − 1, andthe covariance matrix of received nonuniform noise is mod-eled as Q = diag{[10, 1, 9, 7, 2, 8, 1.5, 0.5, 1, 3]}. The worstnoise power ratio (WNPR) is defined by

WNPR � σ 2max

σ 2min

(42)

where σ 2max and σ 2

min represent the maximum value and theminimum value of noise power, respectively. In order to ana-lyze the performance of these methods intuitively, the rootmean square error (RMSE) is defined by

RMSE = 1

K

K∑

k=1

√√√√1

ξ

ξ∑

i=1

(θi,k − θk

)2(43)

WANG et al.: ASSISTANT VEHICLE LOCALIZATION BASED ON THREE COLLABORATIVE BSs VIA SBL-BASED ROBUST DOA ESTIMATION 5773

Fig. 3. Power spectrum under different grid intervals.

TABLE IIDOA ESTIMATION RESULTS BY THE PROPOSED

DOA ESTIMATION APPROACH

where ξ represents the total number of Monte Carlo trials,which is set as ξ = 100 in this paper. θi,k denotes the esti-mated result of DOA for the kth target in the ith Monte Carlosimulation.

First, the power spectrum of the proposed DOA estimationmethod with different grid intervals in the case of nonuniformnoise (i.e., Q = diag{[10, 1, 9, 7, 2, 8, 1.5, 0.5, 1, 3]}) is sim-ulated. The results are given in Fig. 3, where the SNR is setas SNR = 0 dB, and the number of snapshot is T = 200.The different grid intervals are set as r = 1◦, r = 2◦, r = 4◦,and r = 6◦, respectively. As shown in Fig. 3, the power spec-trum of the proposed method has very sharp peaks, whichcan be used to estimate DOA, in the case of different gridintervals. This represents that the proposed method has theadvantages of high accuracy and high resolution under thecoexistence of nonuniform noise and off-grid error, especiallyunder a very coarse grid condition. On the other hand, theDOA estimation results of Fig. 3 are given in Table II. Itcan be seen that no matter how large the grid interval is, theproposed method can still maintain high estimation accuracy.This further illustrates that the proposed method can effec-tively reduce the influence of nonuniform noise and off-griderror, and maintain high DOA estimation accuracy.

Then, the performance of the four methods under differentSNRs are compared in the case of nonuniform noise. Fig. 4shows the change of RMSE versus SNR of four methods,which is carried out under the condition that the number of

Fig. 4. RMSE versus SNR under nonuniform noise condition.

Fig. 5. RMSE versus the number of snapshot under nonuniform noisecondition.

snapshot is T = 200. As shown in Fig. 4, with the increase ofSNR, the RMSE of OGSBI almost does not decrease, whilethat of the other three methods keep decreasing. It is obviousthat the proposed method has the lowest RMSE among the fourmethods, and the RMSE of the proposed method is closer toCRB. The main reason for this result is that the performanceof OGSBI in a very coarse grid case is mainly limited bythe off-grid error, and the increase of SNR cannot effectivelyreduce this error. On the other hand, although ROGSBL andESBL can effectively reduce the off-grid error under coarsegrid condition, they ignore the nonuniform noise.

Fig. 5 shows the RMSE versus the number of snapshot inthe nonuniform noise case, where SNR = 0 dB, T = 200.It is clear from Fig. 5 that the performance of the proposedmethod improves with the increase of the number of snapshotsand is more approach CRB. Conversely, the performance ofthe other three methods do not improve significantly with theincreasing number of snapshots. This is due to the existenceof nonuniform noise, which is neglected by the other threemethods.

Fig. 6 depicts the relationship between RMSE and WNPRwith SNR = 0 dB and T = 200, where WNPR is generatedonly by changing the maximum value of noise power. It can beobserved that the increase of WNPR does not affect RMSE of

5774 IEEE INTERNET OF THINGS JOURNAL, VOL. 6, NO. 3, JUNE 2019

Fig. 6. RMSE versus WNPR under nonuniform noise condition.

Fig. 7. RMSE versus grid interval under nonuniform noise condition.

OGSBI because the off-grid error is dominant in a very coarsegrid condition. On the other hand, the RMSE of ROGSBLand ESBL keep increasing with the increase of WNPR, whichmeans that their performance are seriously degraded. While theproposed method always keeps a lowest RMSE at all WNPRs,and its performance is slightly influenced by the nonuniformnoise. This is because the proposed method can effectivelyreduce the influence of nonuniform noise, while the other threemethods completely ignore it.

Fig. 7 is the comparison of RMSE of different methodsversus different grid intervals in nonuniform noise, where theSNR and snapshot number are, respectively, set as SNR =0 dB and T = 200. As shown in Fig. 7, the proposed methodcan achieve lower RMSE than the other three methods at allgrid interval conditions, especially in a very coarse case, whichdemonstrates that the proposed method can guarantee the DOAestimation accuracy under the coexistence of off-grid error andnonuniform noise.

Fig. 8 illustrates the RMSE versus grid interval with differ-ent number of active grid points, and Fig. 9 illustrates theaverage simulation time versus grid interval with differentnumber of active grid points, where η is selected as η = 4,η = 8, η = 12, and η = 16, respectively. Both of these tworesults are generated in the case of SNR = 0 dB and T = 200.As shown in Fig. 8, no matter how many activate grid points

Fig. 8. RMSE versus grid interval with different number of active grid points.

Fig. 9. Average simulation time versus grid interval with different activegrid points.

Fig. 10. Localization diagram for two vehicles.

are selected, the performance of the proposed method can bemaintained in almost the same excellent performance. Besides,it can be found from Fig. 9 that the average simulation timedecreases with the increase of grid intervals, and the smallerthe number of active grid points is, the less the average sim-ulation time needs. The results in Figs. 8 and 9 demonstratethat the DOA estimation speed of the proposed method can

WANG et al.: ASSISTANT VEHICLE LOCALIZATION BASED ON THREE COLLABORATIVE BSs VIA SBL-BASED ROBUST DOA ESTIMATION 5775

TABLE IIIVEHICLE LOCALIZATION RESULTS AND ERRORS BY OGSBI

TABLE IVVEHICLE LOCALIZATION RESULTS AND ERRORS BY ROGSBL

TABLE VVEHICLE LOCALIZATION RESULTS AND ERRORS BY ESBL

TABLE VIVEHICLE LOCALIZATION RESULTS AND ERRORS

BY THE PROPOSED APPROACH

be accelerated by selecting an appropriate number of activegrid points and grid interval without affecting the accuracy ofDOA estimation.

Finally, the vehicle localization performance of differentDOA estimation methods is tested based on the proposedassistant localization system, where T = 200, r = 4◦, andη = P = M + N − 1. Supposed there exist two vehiclesin the same plane range as shown in Fig. 10, their positioncoordinates are #1(200 m, 400 m) and #2(500 m, 300 m),respectively. The coordinates of reference points of three BSs

are A1(0 m, 500 m), A2(0 m, 0 m), and A3(600 m, 0 m),respectively. Theoretically, the DOAs of these two vehicleswith respect to A1, A2, and A3 are θ#1

1 = 26.56◦, θ#12 =

63.43◦, θ#13 = 45.00◦ and θ#2

1 = 21.80◦, θ#22 = 30.96◦,

θ#23 = 18.43◦. The vehicle localization results and errors ver-

sus SNR by different DOA estimation methods are given inTables III–VI, respectively. By comparing these results, it canbe obviously found that the localization error of our proposedDOA estimation method is the smallest among the fourmethods, which is consistent with the performance of DOAestimation.

VI. CONCLUSION

In this paper, an assistant vehicle localization methodbased on three collaborative BSs via a robust SBL-basedDOA estimation approach is proposed. Through EM algo-rithm and LS strategy, the power of nonuniform noise andthe discrete grid points can be accurately estimated andupdated, respectively, by the proposed robust DOA estimationapproach, which enables it to maintain superior DOA estima-tion performance under the coexistence of nonuniform noiseand off-grid error. Based on the collaborative BSs and theproposed DOA estimation approach, the vehicle localizationwith both off-grid error and nonuniform noise scenario canbe accurately achieved. Large number of simulation resultshave fully demonstrated the effectiveness and superiority ofthe proposed method. In the future, the proposed vehicle local-ization method can be combined with the GPS localization tofurther improve the localization accuracy and real-time local-ization performance. Thus, how to combine the proposed vehi-cle localization system with GPS system and how to designthe localization algorithm is the key problem to be furthersolved.

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Huafei Wang was born in 1995. He receivedthe B.S. degree from Hainan University, Haikou,China, in 2017, where he is currently pursuingthe M.S. degree in information and communicationengineering.

His current research interests include array signalprocessing and MIMO radar.

Liangtian Wan (M’15) received the B.S. andPh.D. degrees from the College of Information andCommunication Engineering, Harbin EngineeringUniversity, Harbin, China, in 2011 and 2015,respectively.

From 2015 to 2017, he was a Research Fellowwith the School of Electrical and ElectronicEngineering, Nanyang Technological University,Singapore. He is currently an Associate Professorwith the School of Software, Dalian University ofTechnology, Dalian, China. He has authored or co-

authored over 40 scientific papers in international journals and conferences.His current research interests include social network analysis and mining, bigdata, array signal processing, wireless sensor networks, and compressive sens-ing and its application.

Dr. Wan is an Associate Editor of IEEE ACCESS.

WANG et al.: ASSISTANT VEHICLE LOCALIZATION BASED ON THREE COLLABORATIVE BSs VIA SBL-BASED ROBUST DOA ESTIMATION 5777

Mianxiong Dong (GS’08–M’12) received theB.S., M.S., and Ph.D. degrees in computer scienceand engineering from the University of Aizu,Aizuwakamatsu, Japan.

He is currently an Associate Professor withthe Department of Information and ElectronicEngineering, Muroran Institute of Technology,Muroran, Japan. He was a JSPS Research Fellowwith the School of Computer Science andEngineering, University of Aizu, and a VisitingScholar with the BBCR Group, University of

Waterloo, Waterloo, ON, Canada, supported by the JSPS Excellent YoungResearcher Overseas Visit Program from 2010 to 2011. His current researchinterests include wireless networks, cloud computing, and cyber-physicalsystems.

Dr. Dong was a recipient of the Best Paper Award from IEEE HPCC 2008,IEEE ICESS 2008, ICA3PP 2014, GPC 2015, IEEE DASC 2015, IEEE VTC2016-Fall, and FCST 2017, the 2017 IET Communications Premium Award,the IEEE ComSoc CSIM Best Conference Paper Award in 2018, the IEEETCSC Early Career Award in 2016, the IEEE SCSTC Outstanding YoungResearcher Award in 2017, the 12th IEEE ComSoc Asia–Pacific YoungResearcher Award in 2017, and the Funai Research Award in 2018. He wasselected as a Foreigner Research Fellow (a total of three recipients all overJapan) by the NEC C&C Foundation in 2011. He serves as an Editor for theIEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING,IEEE COMMUNICATIONS SURVEYS AND TUTORIALS, IEEE Network, IEEEWIRELESS COMMUNICATIONS LETTERS, IEEE CLOUD COMPUTING, andIEEE ACCESS, as well as a Leading Guest Editor for the ACM Transactionson Multimedia Computing, Communications and Applications, the IEEETRANSACTIONS ON EMERGING TOPICS IN COMPUTING, and the IEEETRANSACTIONS ON COMPUTATIONAL SOCIAL SYSTEMS. He has beenserving as the Vice Chair of the IEEE Communications Society Asia–PacificRegion Information Services Committee and Meetings and ConferenceCommittee, the Leading Symposium Chair of IEEE ICC 2019, the StudentTravel Grants Chair of IEEE GLOBECOM 2019, and had served as theSymposium Chair of IEEE GLOBECOM 2016 and 2017. He is currentlya member of the Board of Governors and the Chair of Student FellowshipCommittee of IEEE Vehicular Technology Society.

Kaoru Ota (GS’10–M’11) was born inAizuwakamatsu, Japan. She received the B.S.degree in computer science and engineeringfrom the University of Aizu, Aizuwakamatsu, in2006, the M.S. degree in computer science fromOklahoma State University, Stillwater, OK, USA, in2008, and the Ph.D. degree in computer science andengineering from the University of Aizu, in 2012.

She is currently an Assistant Professor withthe Department of Information and ElectronicEngineering, Muroran Institute of Technology,

Muroran, Japan. From 2010 to 2011, she was a Visiting Scholar with theUniversity of Waterloo, Waterloo, ON, Canada. She was also a Japan Societyof the Promotion of Science Research Fellow with Kato-Nishiyama Lab,Graduate School of Information Sciences, Tohoku University, Sendai, Japan,from 2012 to 2013. Her current research interests include wireless networks,cloud computing, and cyber-physical systems.

Dr. Ota was a recipient of the Best Paper Award from ICA3PP 2014,GPC 2015, IEEE DASC 2015, IEEE VTC 2016-Fall, and FCST 2017,the 2017 IET Communications Premium Award, the IEEE ComSocCSIM Best Conference Paper Award in 2018, and the IEEE TCSC EarlyCareer Award in 2017. She is an Editor of the IEEE TRANSACTIONS ON

VEHICULAR TECHNOLOGY, IEEE COMMUNICATIONS LETTERS, Peer-to-Peer Networking and Applications (Springer), Ad Hoc & Sensor WirelessNetworks, the International Journal of Embedded Systems (Inderscience),and Smart Technologies for Emergency Response & Disaster Management(IGI Global), as well as a Guest Editor of the ACM Transactions onMultimedia Computing, Communications and Applications (leading), theIEEE INTERNET OF THINGS JOURNAL, IEEE Communications Magazine,IEEE Network, IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS,IEEE ACCESS, the IEICE TRANSACTIONS ON INFORMATION AND

SYSTEMS, and Ad Hoc & Sensor Wireless Networks (Old City Publishing).

Xianpeng Wang (M’15) was born in 1986.He received the M.S. and Ph.D. degrees fromthe College of Automation, Harbin EngineeringUniversity, Harbin, China, in 2012 and 2015,respectively.

He was a full-time Research Fellow with theSchool of Electrical and Electronic Engineering,Nanyang Technological University, Singapore, from2015 to 2016. He is currently a Professor withthe College of Information Science and Technology,Hainan University, Haikou, China. He has authored

over 50 papers published in related journals and international conference pro-ceedings. His current research interests include communication system, arraysignal processing, radar signal processing, and compressed sensing and itsapplications.

Dr. Wang has served as a Reviewer of over 20 journals.