Study of 2D DOA Estimation for Uniform Circular Array in Wireless Location System

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1 I.J. Computer etwork and Informaton Securty,,, 5- Publshed Onlne December n ECS ( Study of D DOA Estmaton for Unform Crcular Array n Wreless Locaton System Png TA Department of Electroncs and Informaton Engneerng, Huazhong Unversty of Sc. and Tech., Wuhan, Chna Wuhan atonal Laboratory for Optoelectroncs, Wuhan, Chna Emal: tanpng@mal.hust.edu.cn Pan WAG, Ye LUO, Yufeng ZHAG, Hong A Department of Electroncs and Informaton Engneerng, Huazhong Unversty of Sc. and Tech., Wuhan, Chna Emal: { wangpan5@3.com, luoye@mal.hust.edu.cn } Abstract n ths paper, the use of a unform crcular antenna arrays (UCA) for hgh resoluton of two dmensonal (D) drecton of arrvals (DOAs) estmaton n wreless locaton system s nvestgated. Performance of D DOA estmaton based on the real-valued untary transformaton USIC algorthm for UCA s presented, especally focusng on DOA estmaton of multple correlated sgnals. The determnaton of the number of ncdent sgnals on an antenna array s addressed n the condton of colored nose and coherent sgnal sources. Selected method for estmatng the number of these sources s formulated based on the modfed egenvectors of the covarance matrx of the receved sgnal at the antenna array. The calbraton procedure s also presented for UCA especally. Smulaton results are presented to confrm the performance analyss of algorthm, then the valdatons of Untary Transformaton USIC algorthm are performed based on the measurement data n a wreless locaton system. Index Terms Drecton of Arrval (DOA), antenna array, Unform Crcular Array (UCA), correlated sgnals, USIC, array calbraton I. ITRODUCTIO Wreless communcaton has enjoyed explosve growth over the past few decades. As demands for ncreased capacty and qualty grow, mproved methods for harnessng the mult-path channel must be developed. The use of adaptve antenna array s one area that shows promse for mprovng capacty of wreless systems and provdng mproved safety through poston locaton capactes []. Estmatng the drectons of arrval (DOAs) of electromagnetc waves mpngng on antenna arrays s an mportant ssue n array sgnal processng for wreless communcaton. It s needed n determnng the locaton of the moble wth hgh accuracy []. Dfferent drecton fndng technques and algorthms have been developed leadng to sgnfcant mprovements n DOA estmaton over the last decades [3]. Subspacebased methods provde hgh resoluton DOA estmaton []. However, to date, most of the reported algorthms are based on the unform lnear array (ULA) and the unform rectangular array (URA) archtectures, and very lttle attenton has been gven to the crcular array topologes despte of ther ablty to offer a number of advantages. Unform crcular arrays are of partcular mportant n DOA estmaton snce they can provde 3º azmuthally coverage and estmate both azmuth and elevaton angles smultaneously. In addton, due to ts crcular symmetry, UCA posses an azmuthally nvarant beam pattern, D DOA estmaton wth UCAs s therefore very useful n practcal stuatons, especally n wreless locaton [5]. In ths paper, the problem of estmatng the two dmensonal DOA usng UCA s nvestgated. Ths research ntends to analyze the performance of UCA usng Untary Transformaton USIC algorthm n coherent source sgnals envronments. As the hgh-resoluton USIC subspace-based method requres the number of drectonal sources, ts performance s dependent on perfect knowledge of these numbers. Ths problem s of nterest to a wreless locaton system whch necesstates the employment of hgh resoluton DOA estmaton method. The performance of AIC, DL and ET algorthms and ther modfed versons are dscussed. Fully realzng the potental of these systems requres effectve array calbraton. Array calbraton s necessary to compensate for varous non-deal array effects ncludng ampltude and phase msmatch, mutual couplng effects and error of element locatons. In the lterature there are generally two knds of calbraton technques. The frst type of method uses sgnals from known drectons transmtted on-ste to the antenna array beng calbrated and then analyzes the array output. Conceptually, these technques address each of the above ssues [7-]. The second type of method njects an equal phase sgnal to all of the channels of the antenna array. Whle ths does address the cablng msmatch ssues, t does not address mutual couplng effects, antenna dfferences, or uncertan sensor locatons [9]. A practcal calbraton approach for UCA s requred by real system. Fnally the valdaton of modfed USIC algorthm wth the measurement data n a wreless locaton system s presented. Ths paper s organzed as follows. Secton II contans the sgnal model for antenna array output. Secton III descrbes the basc theory of modfed D DOA estmaton algorthm based on the real-valued untary transformaton USIC algorthm for UCA, the estmatng the number of coherent sources n colored nose envronment and antenna array calbraton Copyrght ECS I.J. Computer etwork and Informaton Securty,,, 5-

2 Study of D DOA Estmaton for Unform Crcular Array n Wreless Locaton System 55 procedure are also presented n the Secton III.Secton IV presented the performance analyss and smulaton result. Secton V contans expermental results llustratng the performance of the descrbed calbraton method and Secton VI concludes the paper. II. SIGAL ODEL Consderng a unform crcular array (UCA) consstng of antenna elements, as shown n Fg., the antennas are dstrbuted unformly over a crcle wth radus R. The antenna elements operate at a frequency wth a correspondng wave length λ. The phase center of each antenna element s located n the xy-plane, at azmuth angle φ m =πm/ wth m=,. It s assumed that all antenna elements are dentcal and omn-drectonal. Suppose P narrow band far feld sgnals mpngng on the UCA of elements from drectons {θ, φ },..., {θ P, φ P }, the receved sgnal at the antenna array can be descrbed as X(n)=As(n)+n(n) () where X(n)=[x (n), x (n),..., x (n)] T s the n th snapshot of the receved sgnal at the antenna array, T denotes transpose. A=[a(θ, φ ), a(θ, φ ),, a(θ P, φ P )], P, s a fullcolumn rank matrx (>P) of array responses to ncdent sgnal from drecton {θ, φ },..., {θ P, φ P }, and steerng vector a(θ, φ )=[ a (θ, φ ), a (θ, φ ),, a P (θ, φ )] s the array response to the ncdent sgnal from drecton (θ, φ ), where =,, P, and θ and φ s the elevaton angle and azmuth angle of the th sgnal, respectvely. s(n) s the ncdent sgnal vector and n(n) s the n th snapshot of the addtve nose at the antenna array that s assumed to be a zero statonary complex Gaussan process wth varance σ n, uncorrelated wth ncdent sgnals. The covarance matrx of the array response s R xx =E[x(t)x(t) H ]=ARsA H +σ n I, where Rs=E[s(t)s H (t)] s the covarance matrx of the ncdent sgnals, I s a dentty matrx and H denotes conjugate transpose. III. BASIC THEORY OF ODIFIED ALGORITHS A. Basc theroy of modfed USIC algorthm To estmaton the DOAs of the sgnal receved at the array, the supper-resoluton algorthm USIC s often used. Ths algorthm s based on the ensemble-averaged correlaton matrx Rx for the antenna outputs. The egendecomposton of the covarance matrx R xx s R xx = = λ e e H, where e s the egenvector of Rx correspondng to the th largest egenvalue of Rx and λ > λ > > λ P > λ P+ =λ P+ = =λ =σ The USIC spectrum s computed by performng an egenvectors consst of two dsjont subspaces: sgnal and nose subspaces. The lager and the smaller egenvalues belong to sgnal subspace and nose subspaces, respectvely. In terms of the orthogonal characterstcs of egenvectors n the sgnal and nose subspaces, the USIC spectrum s typcally gven by the followng: P( θ, ϕ) = () a( θ, ϕ) V Where v and a denote the egenvectors correspondng to nose subspace and the scannng vector. If a sgnal mpngng on the UCA at the DOA (θ, φ), set the center of the UCA as reference, then the sgnal steerng vector s a(θ, φ)=[ a (θ, φ), a (θ, φ),, a (θ, φ)], where a m (θ, φ)=exp[jπ(r/λ)sn(θ)cos(πm/-φ)], If the number of antenna elements n a unform crcular array s even, then a m+/ (θ, φ) = a * m (θ, φ). And the steerng vector a(θ, φ) s easly rearranged n the conjugate centre-symmetrc manner, such as a(θ, φ)=[ a (θ, φ), a (θ, φ),,, a +/ (θ, φ),a +/ (θ, φ)]. Then the correlaton matrx R xx becomes centre- Hermtan, whch s complex-valued. The real value correlaton matrx Ř xx can be obtaned by an approprate untary transformaton Q as Ř xx =Re{Q H R xx Q} (3) Where f the s even, the untary transformaton matrx Q for the -by- matrx can be chosen as Q= I ji () I jii, and I and II are the dentty matrx and column flpped dentty matrx n the left rght drecton respectvely []. The steerng vector a (θ, φ )=Q H a(θ, φ ) s a realvalue vector, the compute complexty of egenvalue decomposton and spatal spectrum computaton s greatly reduce. In terms of hardware mplementaton, the mplementaton of real-valued matrx egenvalue decomposton s much easer than the complex conjugate symmetrc matrx case. In addton, the backward averagng effect s obtaned by selectng only the real part n (3). It s helpful to deal wth the DOA estmaton of correlated sgnals []. B. Estmatng the Source umber Based on subspace decomposton, the space spanned by the egenvectors of the correlaton matrx can be dvded nto sgnal subspace and nose subspace. For practcal reasons, the covarance matrx and ts egenvalues must be estmated from a fnte sample sze. The smaller egenvalues may be dfferent and not equal to σ, thus t s dffcult to determne by merely observng the egenvalues. Whle the performance of classc USIC algorthm depends on the estmaton on source number drectly, and both overestmaton and underestmaton wll affect the DOA estmaton. Varous statstc approaches have been proposed to estmate s, such as Akake Informaton theoretc Crtera (AIC) [], nmum Descrpton Length Crtera (DL) [] and predcted Copyrght ECS I.J. Computer etwork and Informaton Securty,,, 5-

3 5 Study of D DOA Estmaton for Unform Crcular Array n Wreless Locaton System Egen-Threshold approach (ET) []. But these approaches couldn t get a good performance n condtons wth colored nose and coherent sgnal. To elmnate the nequalty of the nose egenvalues caused by colored nose and coherent sgnals, the egenvalues of the R xx are modfed as λ = λ +b, =,,,. Where b = λ, =,, L,. j= Every correcton value s related wth ts former one and tself, so the less the nose egenvalue s, the greater the correcton value s, and the nose egenvalues become closer to one another. Then DL, AIC and ET approaches can be used to estmate the source number by solvng mnmze d Where ( d ) f log f ( d ) ( d ) + f f( d ) = λ L = d + / ( d ) ( d ) = λ = d + 3 ( d, ) f And the penalty functon d( d) for AIC f3( d, ) = d( d ) log for DL wth denotng the number of snapshot. As the DL and AIC crteron nvolves extractng the root of -d, t s dffcult to realze real tme n FPGA and DSP chps. The ET method uses a one-step predcton of the threshold for dfferentatng the smallest egenvalues from the others and only nvolves square root. Let l d + = λ, d = d then / ( ) ( ( ) ) u + t d + λ d = d + d l. / d + t( d ) The egenvalues n the nose subspace should satsfy, u λ d λ d So estmatng source number P by fndng mnmum d u whch meets λ > λ. d d C. Array Calbraton Procedure However, n a real-world, there are some reasons whch lmt the general use of antenna arrays. One of them s the precse calbraton requred such arrays when they are used for DOA estmaton, whch requre the acquston of the precse ampltude and phase relatonshps of the sgnal collected at each element. These relatons are unfortunately senstve to many potental error sources, leadng to severe performance constrants. An antenna array calbraton procedure s a crtcal stage for utlzng hgh-resoluton DOA estmaton algorthms. Consderng the specal symmetrc structure of UCA, a smple and practcal calbraton for UCA s presented n ths paper. Assume the antenna elements are omndrecton, and a calbraton sgnal transmtter antenna s placed at the center of UCA, the ampltude and phase of receved sgnals Sa(t) at each element are same n theory. Assumng no mutual couplng, ampltude and phase msmatch of array elements s taken nto account. A dstorton matrx G s generally used to encapsulate all of these non-deal effects, whch can be expressed as jϕ jϕ jϕ C = dag( ae,a e,...,a e ). The receved sgnal at the antenna array can be descrbed as X(n)=CSa(n)+n(n), and H H H H R = E( XX ) = CSaSa C + σ I = CC σ S + σ I. So H j ϕ ϕ r = x n x n = a a e σ + σ, =,, L, = ( ) ( ) ( ) Therefore, the calbraton matrx G can be obtaned by r G = [ g,,g, L,g ], g =, =,, L, r IV. SIULATIO RESULT AD PERFORACE AALYSIS In ths secton, we nvestgate the performance of the Un-tray Transformaton USIC algorthm through some smulaton experments. An -element UCA wth the half-wavelength nter-element spacng was consdered for the smulaton. Antenna elements are labeled as shown n Fg., and then the steerng vector s conjugated centresymmetrc. So the untary transformaton USIC algorthm can be used n a UCA system. Snce the estmated correlaton matrx s real value, t s smpler to mplementaton the egen-decomposton of a real value matrx than that of a complex one. The smulaton wll analyze the performance of untary transformaton USIC algorthm wth comparson wth normal USCI algorthm,when there are varaton n the Sgnal to ose Rato (SR) and the resoluton of the ncomng sgnal. A narrowband gauss dgtal sgnal s(nt s ) s consdered as sgnal of source, where n=,,, s the number of snapshot, T s s samplng perod. To evaluate the performance of DOA estmaton algorthm n hardware systems, the smulated array sgnals are generated, dgtalzed and processed as a IF samplng recever archtecture shown n fg.. If the sgnal mpngng on the UCA as a plane wave from (θ,ϕ), the tme delay between the element m the center of UCA s τ m =Rsn(θ )cos(πm/-φ )/c. Usually, the delay τ m s less than T s or not ntegral multples of T s, so a sgnal reconstructon method s consdered n modelng array recevng sgnal X(t)=[s (t)+n (t), s (t)+n (t),, s (t) +n (t)], where Sa n Copyrght ECS I.J. Computer etwork and Informaton Securty,,, 5-

4 Study of D DOA Estmaton for Unform Crcular Array n Wreless Locaton System 57 π ( f st f sτ m k) ( f t f τ k) sn sm () t = s( t m ) = + τ s( k), π k= s s m m =,,L and n m (t) s the nose on antenna element m whch s often assumed that the nose s zero mean and addtve. Colored nose can be generated by passng whte nose through a flter wth requred frequency response. A. Source umber Estmaton Based on the desgned UCA, the performances of AIC, DL and ET are compared wth basc algorthm Egen value, modfed algorthm and modfed algorthm wth untary transformaton correlaton matrx respectvely. Supposed three uncorrelated narrowband sgnals mpngng on the array from ( θ =, ϕ =3 ), ( θ =3, ϕ = ) and ( θ 3 =7, ϕ 3 = ) respectvely. The estmaton results of source number are llustrated n fg.3 and fg.. The smulaton results show that under a certan condton of some SR and snapshots, the modfed AIC, DL and ET have good performance n color nose; however, basc AIC, DL and ET fal n detecton under colored nose. In the coherent sources smulaton, three narrowband sgnals are supposed mpngng on the array from (θ=, ϕ =3 ), (θ=3, ϕ = ) and (θ3=7, ϕ 3 = ) respectvely. Sgnal 3 s the duplcaton of the sgnal wth delay tme τ=. ns and sgnal s uncorrelated wth sgnal and sgnal 3. The number of snapshot s. Estmaton results of source number wth modfed egenvalues algorthm vs. SR are presented n fg.5 (a). The source number s under estmated. Utlzng the real value correlaton matrx obtaned by a untary transformaton as (3), the estmaton results wth modfed egenvalues algorthm vs. SR are gven as fg.5 (b). It shows that the modfed AIC, DL and ET wth untary transformaton have good performance n color nose and coherent sources condton. Fgure. a UCA confguraton wth conjugate centre-symmetrc steerng vector Fgure. The flow chart of sgnals generatng basc AIC basc DL basc ET the number of snapshot (a) Basc algorthms of estmatng source number modfed AIC modfed DL modfed ET the number of snapshot (b) odfed egenvalue based algorthms Fgure 3. Estmaton result of source number wth three uncoherent sources vs. the number of snapshots, SR=3. basc AIC basc DL basc ET (a) Basc algorthms of estmatng source number modfed AIC modfed DL modfed ET (b) odfed egenvalue based algorthms Fgure. Estmaton result of source number wth three uncoherent sources vs. SR, the number of snapshots =. Copyrght ECS I.J. Computer etwork and Informaton Securty,,, 5-

5 5 Study of D DOA Estmaton for Unform Crcular Array n Wreless Locaton System AIC DL ET 3 5 (a) odfed egenvalues wthout untary transformaton AIC DL ET 3 5 (b) modfed egenvalues wth untary transformaton correlaton matrx Fgure 5. Estmaton result of source number wth three sources vs. SR, the number of snapshots =, source and source3 s coherent. as SR s more than db. Ths algorthm shows hgh resoluton capacty n hgh SR condtons. When the number of Snapshot s and SR s 3, USIC spatal spectrum s gven n the Fg. Error of elevaton angle(deg) number of snapshots Error of azmuth angle(deg) number of snapshots Fgure. Absolute error of DOA estmaton wth one source vs. the number of snapshots, SR=3dB Error of elevaton angle(deg) Fgure 7. Absolute error of DOA estmaton wth one source vs. SR, number of snapshot = Error of azmuth angle(deg) B. The umber of Snapshot and Sgnal to ose Rato In ths example, we numercally llustrate the Untary USIC algorthm for the case of a sngle source, assumng the DOA of a desred sgnal s (θ=5, ϕ= ). The nfluences of SR and the number of snapshots on the performance are nvestgated. In wreless locaton system, some targets usually move quckly, such as n a hgh speed tran and arplane, then the samplng tme,.e. the number of snapshot, s lmted. When SR s 3dB, and the number of snapshots s changed from to, the absolute error of estmated result wth deal DOA s gven n the Fg.. It shows that when snapshot number s more than 5, the error of DOA estmaton n short perod s small enough to meet the locaton accuracy. When the number of Snapshot s, the absolute error of estmated result wth deal DOA vs. SR s gven n the Fg.7. Dynamc range of the USIC spectrum can be mproved by ncreasng the SR, and t provdes better estmaton performance. oreover, the estmaton errors of elevaton and azmuth angles are both less than Fgure. Spatal spectrum of the Untary USIC algorthm, one sgnal from (5, ), SR=3dB, number of snapshot = C. Uncorrelated Sgnals and Coherent Sgnals The two drectonal sgnals are sad to be fully correlated or coherent when one s the delay and scaled verson of the other. ultpath sgnals normally result n Copyrght ECS I.J. Computer etwork and Informaton Securty,,, 5-

6 Study of D DOA Estmaton for Unform Crcular Array n Wreless Locaton System 59 partal correlaton. Correlaton between two drectonal sgnals lmts the applcablty of basc USIC algorthm, whereas the real-value untary USIC algorthm can deal wth two correlated sgnals. For example, two correlated narrowband sgnals mpngng on the antenna array from (θ =, ϕ =3 ) and (θ =3, ϕ = ) respectvely, and sgnal s the duplcaton of the sgnal wth delay tme τ=.3ns. If SR s db and snapshot s, there s only one peak n the spatal spectrum of basc USIC algorthm, as shown n Fg.9. The estmated number of source s, and the estmated DOAs (θ =9., ϕ =5. ) are ncorrect. Even f s gven as, the spatal spectrum of basc USIC algorthm s gven n Fg.. the estmated DOAs are stll ncorrect. Whle, the spatal spectrum of untary transformaton USIC algorthms s presented n Fg.. There are two sharp peaks n the spatal spectrum. The estmated DOA s dentcal to the deal DOA. It shows that untary USIC algorthms can correctly estmated DOA of two correlated sgnals. The results of DOA estmaton error vs. SR are also presented n the Fg., t shows that the DOA estmaton resoluton depends on SR, and adequate SR levels are necessary to get hgh accuracy. Fgure 9. Spatal spectrum of basc USIC algorthm, two correlated sgnals wth arrval angle of (, 3 ) and (3, ) Fgure. Spatal spectrum of untary transformaton USIC algorthm, two correlated sgnals arrval angle of (, 3 ) and (3, ) Fgure. Absolute error of DOA estmaton wth two correlated source vs. SR, Snapshot = (a) The estmated source number s (b) The source number s set to V. EXPERIET RESULT AD DISCUSSIO The performance of D DOA estmaton based on the untary USIC algorthm for UCA s valdated n a wreless locaton system, whch operates at VHF band. The desgn and mplementaton of the necessary hardware to prove the feasblty of hgh resoluton DOA estmaton was acheved. An -onopole element UCA and an -channel heterodyne array recever are mplemented, and the sgnal processng subsystem s FPGA and DSP based. The computaton flow of the untary USIC DOA estmaton algorthm nvolves 3 man steps: () estmaton of the samplng real value correlaton matrx wth untary transformaton; () egenvalue decomposton (EVD) of the correlaton matrx; (3) estmate based on the modfed egenvalues algorthm; () the computaton of USIC spectrum and search peaks n the -dmenson spatal spectrum. The frst step s mplemented n a FPGA chp, and then the EVD Copyrght ECS I.J. Computer etwork and Informaton Securty,,, 5-

7 Study of D DOA Estmaton for Unform Crcular Array n Wreless Locaton System computaton, the number source estmaton and peak search process are processed n a DSP chp. The DOA estmaton performance for one source s tested n a open area wth the wreless locaton system. The deal DOA of the source s (θ =57.5, ϕ =7.99 ). The estmated DOA n DSP wth snapshot s (θ=5, ϕ =7.5 ). Fg. s the spatal spectrum based on the estmated correlaton matrx calculated n the FPGA. The measured data valdate the performance of Untary Transformaton USIC algorthm, whle the DOA accuracy and resoluton s hghly depended on the envronments and channel calbraton. A calbraton approach that sgnfcantly mproves the performance of the estmates s undergong. Fgure. Spatal spectrum of untary USIC algorthm based on measured data wth snapshot, one source from ( θ=57.5, ϕ=7.99 ). VI. COCLUSIO Ths paper has deal wth some facets of two dmenson DOA estmaton n UCA. Ths paper has ntroduced the D untary transformaton USIC algorthm n UCA. And modfed egenvalues based algorthm to estmate sgnal number s present and analyss. In ths paper, we have shown the nfluence of colored nose and coherent sources, SR and snapshot number on the D DOA estmaton of UCA by means of smulatons; we also verfed the results by measurements data. It turns out that, Therefore, detal nvestgaton to verfy the performance by smulaton whch takes nto account mutual couple and other error and by means of measurements are stll n progress. ACKOWLEDGET Ths work was supported n part by fund of atonal Key technology R&D program (BAC3B ) and atonal atural Scence Foundaton of Chna (9755) REFERECES [] A. Pages-Zzamora, J. Vdal, Evaluaton of the mprovement n the poston estmate accuracy of UTS mobles wth hybrd poston technques, n IEEE VTC,vol., pp, 3-35, [] kos Delganns, Spros Louvros, Hybrd TOA-AOA locaton technques n GS etwork, Wreless Pers Commun., Vol.5, pages:3-3 [3] H.KRI and. VIBERG, Two decades of array sgnal processng research : the parametrc approach, IEEE Sgnal processng ag., vol.3, no., pp.7-9, 99 [] R.O. Schmdt, ultple emtter locaton and sgnal parameter estmaton, IEEE Trans. Antenna Propagaton, vol. 3, o.3: 7-, arch 9 [5] Yufeng Zhang, Zhongfu Ye, Chao Lu, An effcent DOA estmaton method n multpath envronment, Sgnal Processng 9 (): [] Km,. (), "Hardware mplementaton of sgnal processng n smart antenna systems for hgh speed wreless communcaton", Department of Electrcal and Computer Engneerng, Yokohama atonal Unversty, Yokohama, PhD thess. [7] Kapl R. Dandekar, Hao Lng and Guanghan Xu, Smart antenna array calbraton procedure ncludng ampltude and phase msmatch and mutual couplng effects, IEEE Internatonal Conference on Personal wreless communcatons,, Dec. 7-, pp [] Y. Chen, A. Chang, and H. Lee, Array Calbraton ethods for Sensor Poston and Pontng Errors, crowave and Optcal Technology Letters, vol., pp. 3-37,. [9] R. Ertel, Z. Hu, and J. Reed, Antenna Array Hardware Ampltude and Phase Compensaton Usng Baseband Antenna Array Outputs, 999 IEEE Vehcular Technology Conference Proceedngs, vol. 3, pp , 999. [] K. Huarng and C. Yeh, A untary transformaton method for angles of arrval estmaton, IEEE Tran. Acoustc, Speech, Sgnal Processng, vol. 39. o.. pp , Aprl. 99. []. Wax, T. Kalath. Detecton of sgnals by nformaton theoretc crtera. IEEE Trans. on Acoustcs, Speech and Sgnal Processng,95, 33(): [] W. G. Chen, K.. Wong, J. P. Relly. Detecton of the number of sgnals: a predcted egen-threshold approach. IEEE Trans.on Sgnal Processng, 99, 39(5): 9. Png TA receved the B.S and Ph.D degrees n electrcal engneerng from Huazhong Unversty of Scence and Technology, wuhan, Chna, n 99 and, respectvely, and the.s. degree n rado physcs from Chnese Academy of Scences n. She s currently a lecturer wth the department of Electroncs and Informaton Engneerng, Huazhong Unversty of Scence and Technology, and Wuhan atonal Laboratory for Optoelectroncs, Wuhan, Chna. Her areas of research nclude array sgnal processng, wreless locaton and computatonal electromagnetcs. Copyrght ECS I.J. Computer etwork and Informaton Securty,,, 5-