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160 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 59, NO. 1, JANUARY 2011

“Vector Cross-Product Direction-Finding” With anElectromagnetic Vector-Sensor of Six Orthogonally

Oriented But Spatially Noncollocating Dipoles/LoopsKainam Thomas Wong, Senior Member, IEEE, and Xin Yuan, Student Member, IEEE

Abstract—Direction-finding capability has recently been ad-vanced by synergies between the customary approach of inter-ferometry and the new approach of “vector cross product” basedPoynting-vector estimator. The latter approach measures theincident electromagnetic wavefield for each of its six electromag-netic components, all at one point in space, to allow a vectorcross-product between the measured electric-field vector and themeasured magnetic-field vector. This would lead to the estimationof each incident source’s Poynting-vector, which (after propernorm-normalization) would then reveal the corresponding Carte-sian direction-cosines, and thus the azimuth-elevation arrivalangles. Such a “vector cross product” algorithm has been predi-cated on the measurement of all six electromagnetic components atone same spatial location. This physically requires an electromag-netic vector-sensor, i.e., three identical but orthogonally orientedelectrically short dipoles, plus three identical but orthogonallyoriented magnetically small loops—all spatially collocated in apoint-like geometry. Such a complicated “vector-antenna” wouldrequire exceptionally effective electromagnetic isolation among itssix component-antennas. To minimize mutual coupling across thesecollocated antennas, considerable antennas-complexity and hard-ware cost could be required. Instead, this paper shows how to applythe “vector cross-product” direction-of-arrival estimator, even ifthe three dipoles and the three loops are located separately (insteadof collocating in a point-like geometry). This new scheme has greatpractical value, in reducing mutual coupling, in simplifying theantennas hardware, and in sparsely extending the spatial apertureto refine the direction-finding accuracy by orders of magnitude.

Index Terms—Antenna array mutual coupling, antenna arrays,aperture antennas, array signal processing, direction of arrivalestimation, diversity methods, nonuniformly spaced arrays,polarization.

I. INTRODUCTION

A. The Six-Component Electromagnetic Vector Sensor (EMVS)for Direction Finding

A SIX-COMPONENT electromagnetic vector-sensor con-sists of three identical, but orthogonally oriented, elec-

trically short dipoles, plus three identical but orthogonally ori-

Manuscript received March 15, 2010; accepted September 17, 2010. Date ofpublication October 07, 2010; date of current version December 17, 2010. Theassociate editor coordinating the review of this manuscript and approving it forpublication was Dr. Philipe Ciblat. This work was supported by the Hong KongPolytechnic University’s Internal Competitive Research Grant #G-YG38.

The authors are with the Department of Electronic and Information Engi-neering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong(e-mail: [email protected]).

Color versions of one or more figures in this paper are available online athttp://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSP.2010.2084085

ented magnetically small loops—all spatially collocated in apoint-like geometry. This electromagnetic vector-sensor aimsto distinctly measure all three Cartesian components of the in-cident electric field and all three Cartesian components of theincident magnetic field, as a 6 1 vector, at one spatial loca-tion and at one time-instant.

Such an electromagnetic vector-sensor’s array manifold maybe idealized, by overlooking all mutual coupling among its sixcollocated constituent antennas. This idealized array manifoldwould be a concatenation of the 3 1 electric-field vector withthe 3 1 magnetic-field vector , to be [4]

(1)

where denotes the incident source’s elevation-anglemeasured from the positive axis, symbolizes theazimuth-angle measured from the positive axis,refers to the auxiliary polarization angle, and rep-resents the polarization phase difference. Note that de-pends only on the arrival-angles, whereas depends only on thepolarization-parameters. Also, .

By measuring the incident electromagnetic wavefield explic-itly in terms of its six individual electromagnetic components,the electromagnetic vector-sensor physically gathers the fulldata necessary to estimate the Poynting-vector , via a simplevector-cross-product between the measured electric-fieldvector and the measured magnetic-field vector. This esti-mated Poynting-vector, when normalized with respect to itsFrobenius norm , gives the incident source’s Cartesian di-rection-cosines (and hence the incident source’s elevation-angleand azimuth-angle). Mathematically

(2)

1053-587X/$26.00 © 2010 IEEE

WONG AND YUAN: VECTOR CROSS-PRODUCT DIRECTION-FINDING 161

where the superscript denotes complex conjugation, sym-bolizes the vector cross-product operator, with , and rep-resenting the impinging source’s direction-cosines respectivelyalong the axis, the axis, and the axis.

The unique array-manifold in (1) has been much exploitedby various eigenstructure-based direction-finding schemes [3],[5]–[16], [19], [21]–[37], [40]–[45], [47].

Many are the advantages offered by this six-component elec-tromagnetic vector-sensor to arrival-angle estimation:

1) In a multisource scenario, each source’s three Cartesian di-rection-cosine estimates (and thus each source’s azimuth-angle estimate and elevation-angle estimate) can be auto-matically paired without further postprocessing.

2) Like other diversely polarized antenna-arrays, the electro-magnetic vector-sensor can resolve incident sources on ac-count of the sources’ polarization-difference, in addition totheir azimuth/elevation angular differences.

3) The “vector-cross-product” approach of direction-findingin (2) can complement the customary interferometry ap-proach of DOA-estimation, which is based on the spatialphase-delay across displaced antennas. Creative synergybetween these two approaches has produced several novelcapabilities:

a) The direction-of-arrival estimation accuracy can beimproved by orders of magnitude, by extending thespatial aperture, without incurring ambiguity in the di-rection-of-arrival estimates and without requiring ad-ditional antennas [13], [14].

b) The directions-of-arrival may be estimated withoutprior knowledge/estimation of the nominal/actualgeometric array-grid and without any calibration-source, thereby easing “real-world” deployment [12].

c) No prior coarse estimate is needed to initiate theMUltiple SIgnal Classification (MUSIC) iterativeparameter-estimation routine. Instead, MUSIC cannow “self-initiates” its iteration [15].

d) Blind geolocation, beamforming, and interference-re-jection are possible for frequency-hopping sourcesof unknown and arbitrary hop-sequences and direc-tions-of-arrival [16].

B. An Electromagnetic Vector-Sensor of SpatiallyNoncollocating Component-Antennas

Unrealistically presumed by the algorithms cited inSection I-A, however, is negligible mutual coupling acrossthe six collocated antennas that constitute the electromagneticvector-sensor. Mutual coupling could be reduced but never en-tirely avoided, and only by intricate electromagnetic isolation,that would categorically complicate the antenna implementationand would thus sky-rocket the hardware cost [46]. Instead, thisproposed scheme bypasses this mutual coupling problem, byspatially displacing the six component-antennas and showinghow to modify the “vector-cross-product” Poynting-vectorestimator accordingly. That is, this proposed method willretain all advantages mentioned in Section I-A of collocatedvector-sensor direction-finding, despite spatially separating

the six component-antennas here. Furthermore, additionaladvantages become available, as explained here.

4) As the six constituent antennas now span an extended spa-tial aperture (instead of collocating at one point), the re-sulting antennas have improved azimuth-elevation spatialresolution. That is, the present scheme spatially extends thegeometric aperture, without additional antenna.

5) As aforementioned, spatially separation of the six com-ponent-antennas reduces their mutual coupling, therebysaving the cost to implement electromagnetic isolation.

The key question now is: Across the spatially displacedcomponent-antennas, spatial phase shifts exist, invalidating thearray manifold of (1) and nullifying the vector cross-productPoynting-vector estimation in (2). To these problems, this paperwill advance a class of array-configurations to spatially spacethe six constituent antennas of the now-spread electromagneticvector-sensor, such that the vector cross-product estimatorwould still work—and would work better, indeed.12

II. ARRAY MANIFOLD FOR THE NEW ELECTROMAGNETIC

VECTOR-SENSOR WITH NONCOLLOCATED

COMPONENT-ANTENNAS

The following notation will be used: The symbol refersto the dipole oriented along the axis, similarly for and .The symbol corresponds to the loop oriented along theaxis, analogously for and . The symbols sig-nify, respectively, the elevation-angle, the azimuth-angle, andthe distance of relative to . Similarly, defines thedistance of from .

This work will show the following:The “vector-cross-product” estimator remains applicable for anelectromagnetic vector-sensor of spatially noncollocated com-ponent-antennas, if3

A) The , , and axis oriented dipoles are all placed ona straight line, with a spacing between the first twodipoles, and a spacing between the last two dipoles.

B) The -, , and axis oriented loops are placed in an orderopposite to that in , on another straight line in parallelto the first straight line,4 with a spacing between thefirst two loops, and a spacing between the last twoloops.

1[17] has previously shown how the vector-cross-product DOA-estimator re-mains fully applicable, for a dipole-triad that is displaced from a loop-triad.However, the three dipoles there remain spatially collocated among themselves;and so do the three loops among themselves. Hence, mutual coupling, thoughreduced in [17], remains very substantial. In contrast, the present scheme allowseach of six constituent antennas to occupy its distinct location, away from allother five component-antennas.

2Estimation accuracy bounds are derived in [20] for a spatially extended elec-tromagnetic vector-sensor under certain specific array-configurations; however,no algorithm is presented therein. [38], [39] advance hardware implementationsof a spatially extended electromagnetic vector-sensor, but again no algorithm.Original to the present work is the modification of the vector cross-product es-timator to adopt to a spatially extended electromagnetic vector-sensor.

3These constitute a sufficient condition, maybe not a necessary condition.4If �� , the aforementioned two array-axes will be parallel to the �-�

Cartesian plane. If �� additionally, the two lines are parallel to the � axis;if �� instead, the two lines lie in parallel to � axis.


Fig. 1. Six permutations to place the six orthogonally dipoles/triads on twoparallel lines, which may lie arbitrarily in three-dimensional space as shown inFig. 2.

For the spatially non-collocating electromagnetic vector-sensor aforementioned, the array manifold is no longer(1), but (3), shown at the bottom of the page. In which,

, andsymbolizes the element-wise multiplication between two

vectors.The spatial support-region is hemispherical, with the hemi-

spherical base perpendicular to the two array-axes, as in Fig. 2.5

In (3), the th element of represents the th compo-nent-antenna’s spatial phase-factor, whereas the th element of

gives the th component-antenna’s gain/phase/polarization re-sponse. Note the antisymmetry in the exponents of and ,versus the exponents of and . This will be critical to thesuccess of the proposed scheme.

5In the special case of the two parallel lines parallel to the � axis, the spatialsupport-region for the estimates would be either the right or the left hemisphere.If the two parallel lines are parallel to the � axis, the spatial support-regionwould be either the front or the back hemisphere. If parallel to the � axis, thespatial support-region for the estimates would be either the upper or the lowerhemisphere.

Fig. 2. Spatial geometry, showing for the dipoles/loops permutation case (1) inFig. 1.

III. A NEW “VECTOR-CROSS-PRODUCT” DIRECTION-FINDING

ALGORITHM

In all eigen-based “vector-cross-product” direction-findingschemes cited in Section II, an intermediate algorithmic stepwould estimate each incident source’s steering vector, but cor-rect to only within an unknown complex-value scalar .6 Thatis, available (in each algorithm for each incident emitter)7 is theestimate , from which and are to be estimated. (Thisapproximation becomes a equality in noiseless or asymptoticcases.) The question now is whether suffices to estimate

and unambiguously, where denotes the spatially extended(3), instead of the collocated (1).

The answer is “yes”; and the following shows why and how.Cross-multiply and to give

(4)

6For example, see step �� in Section IV-A, which reviews the key algo-rithmic steps in the Uni-Vector-Sensor ESPRIT method of [6].

7This does NOT presume only a single incident source. Multiple, possiblycross-correlated/broadband/time-varying sources can be handled. For details,please refer to those references directly.

(3)


Next, normalize (4) according to its Frobenius norm

To ease subsequent exposition, assume momentarily that thetwo array-axes are parallel to one of the Cartesian axis.

A. If the Two Array-Axes are Parallel to the Axis

This special case has and ; hence, degradesto

Consider the following two disjoint cases, separately.1) Suppose : Consequentially, the axis

direction-cosine . Hence

(5)

where denotes the angle of the ensuing entity, and sym-bolizes the th element of the square-bracketed vector.

The above equation leads to these estimates of the three Carte-sian direction-cosines

(6)

In the above, is set to , not to , to retain thesign of . Similar considerations apply for and . Theoperand, under noiseless or asymptotic conditions, would nec-essarily be real-value for each inverse-trigonometric operatorabove. These operands could become complex-value with noise,hence the real-value operators above.

However, the complex-phases in (5) can afford also fine esti-mates of the axis direction-cosine:

(7)

(8)

These finer-resolution estimates are obtainable, due to thenonzero interantenna spacings of and , on accountof the sparse array-spacing principle. These more accurateestimates are available here for only the axis direction-cosine,because both and are aligned along the axis.Therefore, the interantenna spacings are sparse along only the

axis, but not along the axis nor along the axis.

As lengthens beyond , more than one value mayexist of that satisfy (7). Hence, this more accuratecould be cyclically ambiguous, in contrast to , which isunambiguous but coarser in estimation accuracy. Similar con-siderations hold for . These several complementary esti-mates of in (6), (7), and (8)), they could be synergized byusing to disambiguate and , to produce anestimate that is both fine in estimation resolution and unam-biguous:

(9)

where

for

where refers to the smallest integer not less than , andrefers to the largest integer not exceeding .

However, for , the spatial aperture is not muchextended; hence, simply set .

Last

2) Suppose : Consequentially,. This gives

with remains as in (7), as in (8), and as in (9).


B. If the Two Array-Axes Are Parallel to the Axis

This special case has and ; therefore,degrades to

Separately consider the following two disjoint cases.1) Suppose : Hence the axis direction-cosine

. Hence

(10)

(11)

(12)

(13)

if , where

for

However, for , simply set .Also from (10)

2) Suppose : This implies that the axis direc-tion-cosine . Therefore

with remains as in (11), as in (12), and as in (13).

C. If the Two Array-Axes Are Parallel to the Axis

This particular case has . degrades to

(14)

Separately consider the following two disjoint cases.1) Suppose : This would imply that the axis

direction-cosine . Therefore

From the above equation

(15)

(16)

(17)

for where

for


However, for , simply set .Also from (14),

ifif

2) Suppose : This implies that . Therefore

As a result,

ifif

with remains as in (15), as in (16), and asin (17).

D. If the Two Array-Axes Are Arbitrarily Oriented

In the general case that the two parallel array-axes are arbi-trarily oriented, a new coordinates could be definedsuch that the two array-axes would fit with one of the specialcases in Sections III-A–III-C. In reference to these ,the directional cosines are estimated. Then thefollowing rotational transformation through the Euler angles

(see [1, Fig. 3 and p. 147]) would give the Carte-sian directional cosines in the Cartesian coordinates

.

IV. A FULL ALGORITHM TO ILLUSTRATE HOW TO APPLY THE

NEW TECHNIQUE IN SECTION III

The new “vector-cross-product” direction-finding techniqueproposed in Section III may be applied to any eigen-based

parameter-estimation algorithm that can estimate a source’ssteering vector (to at least within a possibly unknown com-plex-value scalar).

To illustrate how so, this section will consider the “uni-vector-sensor ESPRIT” algorithm of [6], which is originally developedfor an electromagnetic vector-sensor of collocated component-antennas. This section will instead show how the technique inSection III can modify [6] for a spatially spread vector-sensoras defined in the boxed description in Section II.

A. Review of Data Model and Algorithm of [6] for aCollocated Electromagnetic Vector-Sensor

Multiple completely polarized transverse electromagneticwaves, having traveled through an homogeneous isotropicmedium, impinge upon a single electromagnetic vector-sensor,with spatially collocated component-antennas, all at the originof the Cartesian coordinates. The th such wavefront is associ-ated with the steering vector , defined analogously as in (1).Let the th incoming signal to have power , but to betemporally monochromatic at a frequency (distinct from allother incident sources’ frequencies) with an initial phase of .With such incident sources, the 6 1 data-vector collectedat time equals , where

symbolizes the additive noise at the electromagneticvector-sensor.8

The Uni-Vector-Sensor ESPRIT algorithm [6] would formthese two time-delayed data-subsets out of the aforementionedcollected data: and

, where represents a constant time-delay betweenthe two sets of time samples.

The following will summarize the algorithmic steps of theUni-Vector-Sensor ESPRIT algorithm. For the motivations un-derlying these algorithmic steps, please refer to the lengthy ex-position in [6] itself.

{1.} Form the data-matricesand

.9 Then, form the 6 6 data-cor-relation matrices and , wherethe superscript denotes the Hermitian operator.

{2.} Apply ESPRIT to the matrix-pencil , as fol-lows, to estimate all impinging sources’ steering-vec-tors:

{2a.} Let denote the signal-subspace eigen-vector matrix whose columns are the 6 1signal-subspace eigenvectors associated with the

largest eigenvalues of . Let denote thecorresponding signal-subspace eigenvector matrixfor .

{2b.}Define the matrix

8The technique proposed in Section III may be readily applied to other datamodels, and not restricted to the one reviewed here of [6]. This present datamodel serves only as an illustrative example.

9The two datasets � and � are interrelated by the temporal “invariances”of �� , thereby allowing the use of the parameter-esti-mation method of Estimation of Signal Parameters Via Rotational InvarianceTechniques (“ESPRIT”) [2].


Fig. 3. The Cartesian coordinates �� are rotated through the Euler an-gles �� , to give a second set of Cartesian coordinates �� . (Thisdiagram is based on a similar diagram in Wikipedia’s entry on “Euler angles”.)

where the th eigenvalue of equalsand the corresponding

right-eigenvector constitutes the th column of .{2c.}The impinging sources’ steering-vectors of (1)

may be estimated, to within a complex-value mul-tiplicative scalar, as

These unknown complex-value multiplicative scalarsarise from the eigen-decomposition of .

{3.} Apply the vector-cross-product of (2) to the th source’sabove-estimated steering-vectors, as follows, to obtainthe three corresponding Cartesian direction-cosineestimates:

The th source’s azimuth-elevation direction-of-arrivalcan then be estimated as

and the corresponding polarization parameters can thenbe estimated as

(18)

(19)

where

(20)

B. Applying Section III’s Proposed Method, to theUni-Vector-Sensor ESPRIT Algorithm of [6], But Now With theComponent-Antennas Spatially Spread as in Section II

Suppose now the spatially spread electromagnetic vector-sensor of Section II is now deployed, instead of a spatially col-located electromagnetic vector-sensor.

The 6 1 data-vector collected at time would now equal, instead. From this,

Section IV-A’s algorithmic steps , andcan still follow here, but now with a tilde atop all symbols.

However, as for of the precedingSection IV-A, replace them by their counterpart estima-tion-formulas newly defined in Sections III-A–1, III-A–2,III-B–1, III-B–2, III-C–1, or III-C–2.10

V. MONTE CARLO SIMULATION FOR THE ALGORITHM

OBTAINED FROM MODIFYING [6] BY THE TECHNIQUE

PROPOSED IN SECTION III

The proposed scheme’s direction-finding efficacy and ex-tended-aperture capability are demonstrated by Monte Carlosimulations.

Fig. 4 shows a two-source scenario, whereas Fig. 5 showsa three-source scenario.11 Each graph plots the compositemean-square-error of each incident source’s three Cartesiandirection-cosine estimates, versus the inter-antenna spacingparameter . Each data-point on each graph consistsof 1000 statistically independent Monte Carlo trials. Theseestimate uses 400 temporal snapshots. All sources have unitypower. Each source’s signal-to-noise ratio equals 30 dB.The “spatially spread” electromagnetic vector-sensor con-forms to a rectangular grid and lies at some nonzero angleto all three Cartesian axes. Specifically, referring to the arraygeometric symbols defined in Fig. 2:

,with defined to equal the minimum of .

Figs. 4 and 5 clearly demonstrate the proposed scheme’s suc-cess in resolving the incident sources, even if the electromag-netic vector-sensor’s six component-antennas are spaced veryfar apart. In fact, this spatial non-collocation leads to orders-of-magnitude improvement in estimation accuracy, even as mutualcoupling is reduced. Moreover, the estimation is very close tothe Cramér-Rao lower bound (derived in the Appendix) as theinter-antenna spacing increases above a few wavelengths.

VI. CONCLUSION

Many direction-finding advantages are offered by the recentsynergy between interferometry and “vector cross-product”Poynting-vector estimation. However, the practicality of thissynergy is limited by the mutual coupling across the six com-ponent-antennas comprising the electromagnetic vector-sensor.To alleviate this mutual-coupling problem, and thus to simplifythe antenna implementation and to reduce hardware cost,this paper show a way how to achieve “vector cross-product”

10For polarization estimation, (18)–(20) remain applicable, except that (20)needs to have its �� replaced by �� , and to have its �� replaced by�� .

11The estimation bias is about an order-of-magnitude smaller than the corre-sponding estimation standard deviation.


Fig. 4. The composite mean-square-error of the Cartesian direction-cosinesestimates, for two incident sources, at digital frequencies � � �� and� � ��, respectively, with �� and �� .

Fig. 5. The composite mean-square-error of the Cartesian direction-cosinesestimates, for three incident sources, at digital frequencies � � �� , and � � ��, respectively, with �� , and�� . The same “spatially spread”electromagnetic vector-sensor configuration is used here as in Fig. 4.

Poynting-vector estimation while spacing the six compo-nent-antennas far from each other. This spatial noncollocationextends the spatial aperture, to improve direction-finding accu-racy by orders of magnitude, at lower hardware cost.

APPENDIX

DERIVATION OF THE CRAMÉR-RAO BOUND

To avoid unnecessary distraction, simple assumptions will bemade of the signal statistical model in Section IV-A: One single

pure-tone’s frequency and known initial phase are presumed asknown constants. The data sampling instants occur at ,where refers to the time-sampling period, and denotesa 6 1 vector of additive zero-mean spatio-temporally uncor-related Gaussian noise, with an unknown covariance-matrix of

, which is deterministic, 6 6, diagonal with all diagonal el-ements equal to , which represents the known noise-varianceat each component-antenna.

With number of time-samples, the data-set is andequals

where sym-bolizes the Kronecker product, represents a noisevector with a spatio-temporal covariance matrix of

, and denotes an identity matrix. Therefore,, i.e., a Gaussian vector with mean and covariance .

Collect all deterministic unknown entities into avector, . The re-sulting Fisher Information Matrix (FIM), , wouldhave its th entry equal to [18, eq. (8.34)])

where denotes the real-value part of the entity inside ,and represents the trace operator.

Any unbiased estimation of the directions-of-arrival wouldhave these Cramér-Rao lower bounds

These equations may be easily evaluated by MATLAB’s sym-bolic toolbox, to obtain the Cramér-Rao bound curves in Figs. 4and 5.

For a general -source scenario, the Fisher Information Ma-trix would be in size, to be specified bynumber of distinct scalar equations (after accounting for sym-metry in the matrix). As illustration the following equationspresent the 10 equations for the Fisher Information Matrix’s16 elements in the single-source case, for the specific case of

. The equations would become excessivelylengthy to state here for the general array manifold of (3). De-fine the elements of the single-source Fisher Information Matrixas follows:


Using symbolic programming by MATLAB and Mathe-matica


where

The Cramér-Rao bounds would be excessively lengthy tostate here for the spatially spread electromagnetic vector-sensor,even for the single-source case. These expressions are verylong, because the Fisher Information matrix needs be inverted

to produce the Cramér-Rao bounds. However, for(i.e., the six component-antennas are spatially collocated), theCramér-Rao bounds equal (see the equation at the top of thepage).

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Kainam Thomas Wong (S’85–M’86–SM’01)received the B.S.E. degree in chemical engineeringfrom the University of California, Los Angeles, in1985, the B.S.E.E. degree from the University ofColorado, Boulder, in 1987, the M.S.E.E. degreefrom Michigan State University, East Lansing, in1990, and the Ph.D. degree in electrical engineeringfrom Purdue University, West Lafayette, IN, in 1996.

He was a manufacturing engineer at the GeneralMotors Technical Center, Warren, MI, from 1990to 1991, and a Senior Professional Staff Member

with the Johns Hopkins University Applied Physics Laboratory, Laurel, MD,from 1996 to 1998. Between 1998 and 2006, he had been a faculty memberat Nanyang Technological University (Singapore), the Chinese University ofHong Kong, and the University of Waterloo (Canada). He was conferred thePremier’s Research Excellence Award by the Canadian province of Ontarioin 2003. Since 2006, he has been with the Hong Kong Polytechnic Universityas an Associate Professor. His research interest includes sensor-array signalprocessing and signal processing for communications.

Dr. Wong has/had been an Associate Editor for Circuits, Systems, and SignalProcessing, the IEEE SIGNAL PROCESSING LETTERS, the IEEE TRANSACTIONS

ON SIGNAL PROCESSING, and the IEEE TRANSACTIONS ON VEHICULAR

TECHNOLOGY.

Xin Yuan (S’09) received the B.Eng. degree inelectronic information engineering in 2007 and theM.Eng. degree in information and communicationengineering in 2009, both from Xidian University,Xi’an, Shaanxi, China.

He is currently working toward the Ph.D. degree atthe Hong Kong Polytechnic University. His researchinterest lies in space-time signal processing.

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