Source Localization with Distributal Electromagnetic Component Sellsor Array Processing - Abstract coilceut of ~ector-sensorarralvronssiug tvhere the complete .. electromagnetic iuforniation of the signnl is inenrural a d I.lye pmpose an n p p m c h to achieve high-perfoimance /mal- pmd. The>-apply the Poj-iting relatiomhip I r t r e e n i x t z o n 0.f mdtaple sozmes using n. small aperture anrry o.f t l r electric and niaguetic nrasnrenrats to enable estimasptially-dzstributcri electric and magnetic conipnent sen- tion of tlr DOA of multiple sigial s o u m s using a single sors. The n p p m c h Zr; based on exploiting o.f nil nunilable wxtol-siixr. Directioirfinding with a vector s i m r (Sir electmiiingnetic in,foniirdiorz along uZt/i the time rlelny irz- perC.&RT antema mrav) \vas demoustratecl in [7]. Since it fonimtion. LXng siiiiulnted dnta. %:edemonstmte thnt this clw6 !lot rely on qxtial diversity, a DOA estimator wing n p p m c h outpe7:fomis both rc single uertm-sensov m d scolnra *ingle vector s e n a r shonld exhibit consistent performaim sensor nrmys in nccz~incyo.f di,tio,i-o.f-al7-i~,r'l (00.3) es- over its operating frequencj- bawl ancl sllould easil2- xnrk tin1rrtWn. \Tit11 wide-band signals[l]. \ \ h e n operating as an arraj- of vector ,wnsors. the electromagnetic arid tinis-delay measureiwnts can I x siinoltaimiisly urecl to estimate the D 0 . k 1 Introduction This allows the use of smaller aperturearrays whilc mainThe problem of estimating electminagiietic wave parameters taiuiilg gml performauce over a wide frequency bandtridth. wing seiimr arrays has attracted significant attention over Howei-er?emplTiig m i array of vector scnsors may be erl a r s nuiiilrr of receivers is necessary. For iocent years and lead to the dei:elopii=nt a numkr of high pensive I-wle resolution algorithms, such as LIUSIC. ESPRIT and \\9F. example. a %\:&or snmrs array \vi11 require an I%chamiel These algoritlims have f o c u , , on direction-of-arrival esti- receiL-er. This paper propo%s a simple and ellective alternative mation i n sucli arcas as n~iidcsscoinmimications and radar. for achieving DOR estimation perforinaiice IL-ith small hlmt existing arra?-procesiug niethods rel5- on tlle spaapertuuparraj-s. The appiloach u=s an arm)- of qmtially c l i s tial diversit? of tllc mnsor arraj- to estimate the DOA. A dranback of this approach is that the performance accuracy tributal scalar ntagmtic ancl electric sensors. \Ve .shall call the ~ ~ p o p array o ~ l as distributed electmniagiletic c o i n p b i u e s highly clepenclent GU the size ofthe arra:-'s eierfrzuent array (DEhlCA). I t is assumed that the array of .scalar cal apeitrur. In many applications: tlw arra? is exlxctcd to r s in aggegate. nieasure q x r a t e over a wide frequency range. To avoid ambipitics maguetic a d electric m ~ ~ shouldl in the array nmnifold: t.lle pliysical size of such h l d b a l K ~ at lead all the 3D electric and mapietic coinimnents of the array is constrailled Ip the highest operating fkquenc?. ancl electroinagnet.ic maw. The p m l d DEIICA ill aiford tho the nundxr of snsors. Poorer performaiioe at lower freclueir follox\-ingthree advaitages: Firstly, the fnll electric and magcies rvill E s d t due to their larger wavelengths: especiallj- netic field components measure bj. the maguetic awl electric mwmrs: tlwrehy ellectuating derivation of the murocs' diroo when small ~iumberof n?cciver chanmls is available. The tiom1 information. s e c O ~ d l ytheir , s p t i a l distribution will castl?- approacl~to alleviate t.liis problem is t o aim for larger allow eA%r.actiou of 'additional m i m s ' diredional informa..unmulhi,vwion3" array ,wnrtry 13)- increasing the n m d x r way of t l r clilferential-delay nwxmucmelts. Finally. of receiver chmnmls. Anotlier va:- to overcunie this problem tiou structure v i l l significantly m u o n i i e the number DEhlCA's is to use multiple sets of senmr arrays where each set is OF timized to operate ol-er a smaller Ibadn.iclth. This nlay not of imivers i i d c d to simultaneously utilize the timodel%?IE feasible in while- or fast-denloviuent. sensor mrav . a i d - aid conzplete electromagnetic information for DOA estimaczztions. Hence: there is a netd to develop DO,\ estimation tion' methods that c m a small-aperture array that nchieve , d . _ . I performance ovev a wide operating f r q u c n q . 2 Measurement Model The DO.& estinmtor's performance cau lx improvecl by usiu,v Imlarhatiowsensitii~cmnsor am?- to cxploit thc p A d o p t i ~ qthe conv-ntions ill [l]. tlw nlcasu~otnc~lt model of Iarization diversit)- of the signals 13-: estimating their signal tlle vector setlmr is 6ir.en by polarization parameters aloiig a i t h their DOA [2] [3] [4]. In Ydt) 4 4 a reccnt development. Xehorai and Paldi [I] introduml the vctws(t) CH(t) ! ( I ) Y H ( t ) = h:;) C.hI.S. ,See i > iritb DSO National Lahoratories. 20 Scieuce Park Drive. Singalare 118230. Tel: 065-GS712.123. Fax: 06iFCrS72.135G. \'here Eniail:s~l,onsnicBd~.~,~.~~ A. Kielarai is n-itb the LIiUiwrsity of Illirois. Cllieago. L!SA. Tel: (312j%?77& Fax:(112)111-002L Etrail: ,,cIurniOece.aic.edu. 0-7803-7946-2/03/$17.00 02003 E E E 177 [ 3 ] [ 0 + --U: uy [ ] is the unit direction vector from s e m r to source and t+, 3 Cramer -0 Bound and are the 3. y and 3 mnipoimds. The matrices V . \Ve U= the CramerRao bimd (CRB) to examine the perQ and vector w are giwn by formance gain achievable b?. ow approach. CJdng the nota- sin81 -cos& sin& tions, statistical amnnptions and results in [I] [SI,the CRB (3) is givenby 0 U 1% . . . . where 01; 62. 83 a d 04 are the azimuth, elevation, e l l i p ' s where P = E (s(t)s"(t))? U = P(A"AP + orientation a d ecentricit3- angle. Extending from (1) a d aswming that the signal sources u21)-'AHAP. Il = I - A(AnA)-'A", D = are nnrmwbnnd, me can write the measurement model of [By), .D:~I.. D ~. .JD ~ I ]D , ~ X-I a;;$'~ and 0 = the distributed component sensor array in a multiple source em4romnent as [SI .. .ddIT] and where o2 is the noise power and N . [ , ] = 2a(,$kJ)sk(t) , " k=1 + 1, [ n(*) Y(i) . . =, is the nnmher of independent snapshots. In order to c i r ( 5 ) cnnivent the intrinsic singnlaritiesdue to the reference-dinate 3-stem: the mean square augnlar error (LIME) was propozed in [I] and is given by HYJ] where = [/??I, Or), 6r'. deudesthe directiod and 4 Numerical Example polarization parameters of the kih sounr si,+al. r(B1.02) is a diapnal matrix dnse n"diapnal entrj- is given l q B y nsing a numerical example, we shall demonstrate the [r(B1,8&, = n , ( H 1 . 8 z ) e j W ~ r "xhere , r, is the differential w a t e r efticaq of the distribnted electromagnetic m m p delaj- of the signal source I&etrvem the nih m n p u e n t and nent s n s o r arra5- (DEhICA) prooessing when it is compared the phase center and a,(&,&) is the RsponJe of the nth with salar-arraj- processing that relies on an elgtric-only, mmponent slly3r; uC is the carrier frequenq and R is a diverslj- polarized and -polarized antenna array. Since selection matrix elenieuts of 1 and 0. For example, when the motivation of this development is the design of a smallo r t b p n d triads of mapettic ancl electric seaylrs alp nsed. aperture seusor array: we shall make the comparison b d R = 16. If an additional x electriccomponent sefwor is 4. on the principle of %qndaperture, equal number of channels". We assnine a six-channel receiver and use a six element the sslection matrix becomes uniform circular arraj- in this analpis. This will allow the comprisou betweeu the performance of a vectocsensor as o= 1 0 0 0 0 0 r6 well as a six element diversely and cs-polarized array with the p r o p a d DEhICX. The diversel~--polarizedarrq- nsed in From (5), o k r v e that the electromagwtic sources dire0 this stndy is an array of x ! y and =-electric component sentional information are all e m l d d e d in sors. The difference between the diversely-polarized and the p r o p a d sensor array is that the former uses only electric component sensors while the latter usss hoth electric and magnetic component sensors to form a six-element sen.mr This allorvs the dillerrdial dela)- masureiwnts resulting array with a &-channel receimr. The three sensor arrays from divem placemnt of the component senmrs and elare depicted in Figiue 1. Note that the interelement spa0 tromagnetic field measurements to be jointlj- exploited in ing is fixed at A,, = A. where c is the specd of light 2f"estimating the source parameters. Given both the complete a i d fmax is the maximum operating frequency. electromagnetic and spatial information, g o d pxamcter e s An example of the DOA estimation performance as a timation with a smaller apertiue array can be e e e d over function of freqwgc?. is shown in Figure 2. We considered a wide frequenq range. It sfices to point out that the two nnmrrelated sources with e(')= [lo:10",45°.0Q]Tand distributed-mqmuent fellrsors array mcdel in (5) general- e(?),= [5.. 9". -45", -5"IT. The signal-tenoiue ratio is fixed izes the vectorsensor array [SI. at IOrlB. Therein the intereleluent spacing of the uniform We can express ( 5 ) compxtly in matrix form as L v e dat O k r v e from the fignre that circular array is f the distributed EM sensor array has consistent performance y ( t ) =As@) n(t) (7) over a a i d e operating bandwidth. In addition, it achieved four orders of magnitude of gain in aocoraq of DOA estimaurhelpA = a ( O ( ' ) ) . .a(6cdJ)]and s ( t )= [SI( t )...sd(t)IT. tion over the x electric arraj-and one order of ma,pitiide over [ 3 &. + 1 . 178 ' I in-{nr<j Figure 1: Array C k m e t l ) - of Distributed Eh1 Cwulnneot Seneor x-electrie (mpolaiized) array and electric-only cliveiwly lmlarired array. E,(H,). E, ( H y ) a i d E,(H:) ale the electiic Figlire 2: c;RB ~ r sF ~ e q ~ ~ e e e+: y . DEhlC.4. o : Dix-ersely ID (eiagnet.ic) eonqmncnt BCIIY)IS. hrized dipole array. -: Vector leu~y)r. Scalar array of " , 0 diiertional S ~ J O I S . x : Scalar srmy of x-electric sensor (dipole). Army. the electric-only. diversel>--polarizcdlarra>- at = 0.3. This result clearly denmnstrates the gain obtainable fmin tlie full exploitation of the spatial ancl ele3romagiIetic information alforclecl k DEhICA. Figwc 3 plots the DOA estimation pcrforniaixr as a f i n r tion of tlie azimuthal angle of sparation Ixtwecn i i m r r c lated two ~ l u p c e shn-ing IOrIB SKR. The uorinalizecl o p r atiiig frquencx is 6xed at = 0.3. The graph shows that. the propml DELICA kzonstrates significant performance gain especiallj~for cla?el?;spacecl SOIII'C~S. This feature is p.u.ticnlarl: useful ill applications wit Ii short integration time or at IOK signal-tc-noise ratio. f 5 _ _ Concluding Renlarks \Ve have presentecl a new approach for the localization of electioinagnetic soiiires thmngh the joint exploitat.ion of spatid diversit)- and eledromaggaetic information using ~~atiall?.~li~trihiitecl electric ancl magnetic coinpone+ ,en- mrs. Perforinancc aiial:-.;is via numerical examples illas t r a t d the potential gaiii of the piolmscd. approach over tlie =:alar and diverse?\- polarized arraj. The analpis indicatd that the didribated conipooeut Eh1 mum array shoeld allow tlie we of sniall arraj- alm-tiires diile maintaining cl++ sirecl resolution and performance accnracy over a tvicle operatiiig bandaidth. 179 Figure 3: CRB v s A n p l a r Separation Ekctmluagnctic Source Localization," IEEE Tram. on S i a l Pmeessiu~,VoI.42, N o 2 pp.376398, Feb. 1994. (a shorter vemion of this payer has also appeared in Pme 25th Aailomar G n f . S i a b Syst. Gmput.: Nov. 1991, pp. 566572) [Z] E.R. Ferrara Jr. and T.M. Parks, "Direction fiuding with an array of anteaoa having dive= polarization". IEEE Trans. Antennas Pmpagat., vol. AP-31, pp.231-236. Mar. 1983. [3] R. Schmidt. '.A Sigual Subspace Appmach to Multiple Emitter Location and Spectral Estimation; '' Pb.D. dkisertation, Stanford Unk-eersity, C.A., Nov. 1981. [4] 1. Ziskind and hl.\Vax: "hlaxhnum Likelihood Localization of Diverraly Polarized Sources by Simulated healing;.'; IEEE Trans. A u h n a s and Pmpagatiou, Vol. 38, pp. 1111-1114, July 1990. 1.51 J. Li. "Direction and Pohrization Estimation Using Arm!-s with Small Loopi and Short Dipoles: IEEE Tram. Antemar and Propagation, Vol. 11,No. 3. pp. 379487. hlareh 1993. [S] C.M.S. % and A. Nehorai. "Distributed Electmniagudie Component Susor ArraJ-". 7th Annual Adaptive S a w r AF ray Pioeer;sing Worksbop, M a d 1999. Full version in pmpa ratan. [7] G.F. Hatke, "Perfominnee Analysis of the SuperCAIlT Autcnna Array". Project Peport AST--22: Lhmlu Laboratory, hlassachcsetts Institute of techno lo^, 23 Mareh 1992. 180

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