Sensitivity of MIMO STAP Radar with Waveform Diversity

Transcription

1 Chinese Journal of Aeronauics 3(010) Chinese Journal of Aeronauics Sensiiviy of MIMO SAP Radar wih Waveform Diversiy Sun Jinping a, *, Wang Guohua b, Liu Desheng c a School of Elecronics and Informaion Engineering, Beijing Universiy of Aeronauics and Asronauics, Beijing , China b School of Elecrical and Elecronic Engineering, Nanyang echnological Universiy, Singapore , Singapore c School of Auomaion Science and Elecrical Engineering, Beijing Universiy of Aeronauics and Asronauics, Beijing , China Received 6 Ocober 009; acceped 1 January 010 Absrac Space-ime adapive processing (SAP) is an effecive mehod adoped in airborne radar o suppress ground cluer. Muliple-inpu muliple-oupu (MIMO) radar is a new radar concep and has superioriy over convenional radars. Recen proposals have been applying SAP in MIMO configuraion o he improvemen of he performance of convenional radars. As waveforms ransmied by MIMO radar can be correlaed or uncorrelaed wih each oher, his aricle develops a unified signal model incorporaing waveforms for SAP in MIMO radar wih waveform diversiy. hrough his framework, SAP performances are expressed as funcions of he waveform covariance marix (WCM). hen, effecs of waveforms can be invesigaed. he sensiiviy, i.e., he maximum range deecable, is shown o be proporional o he maximum eigenvalue of WCM. Boh heoreical sudies and numerical simulaion examples illusrae he waveform effecs on he sensiiviy of MIMO SAP radar, based on which we can make beer rade-off beween waveforms o achieve opimal sysem performance. Keywords: radar; MIMO; space-ime adapive processing; waveform diversiy; sensiiviy; waveform covariance marix 1. Inroducion1 In recen years muliple-inpu muliple-oupu (MIMO) radar has shown superioriy over convenional radar due o is abiliy of ransmiing muliple correlaed or uncorrelaed waveforms via is anennas. More recenly, he sudy of MIMO radar has been exended o space-ime adapive processing (SAP) for moving arge indicaion (MI) [1-6]. Convenional SAP sysems can effecively suppress he ground cluer of inheren wo-dimensional naure [7-8]. By applying SAP o a MIMO radar configuraion, we can poenially increase he SAP abiliy o discriminae cluer as well as improve he arge deecion and esimaion performances. In Refs.[1]-[6], he waveforms ransmied by separae ransmiers are assumed o be orhogonal wih each oher. hus i is possible for receiver o separae he signals from differen ransmiing anennas and uilize all degrees of freedom. From a general poin of view, one disinc propery *Corresponding auhor. el.: address: sunjinping@buaa.edu.cn Foundaion iems: Naional Naural Science Foundaion of China ( ); Naional Basic Research Program of China ( ) Elsevier Ld. Open access under CC BY-NC-ND license. doi: /S (09) of MIMO radar is waveform diversiy. In many applicaions, more general waveforms, i.e., correlaed waveforms may be occupied by MIMO radar oher han orhogonal waveforms. For example, by using parially correlaed waveforms, he beam-shape of ransmiing waveform can be opimized according o differen purposes of applicaion. Many aricles are relaed o he design of hese kinds of waveforms for MIMO radar based on differen crieria [9-15]. o he bes of our knowledge, when i comes o he parially correlaed waveforms, he performance of MIMO SAP radar is no analyzed ye. Furhermore, o analyze he performance of MIMO SAP wih waveform diversiy can provide us more insigh ino MIMO radar and show boh he advanages and disadvanages of cerain waveforms. I can hen guide us o selec proper waveforms for he applicaion of MIMO radar in cerain pracical operaion, and show us how he radar performance is growing from he convenional coheren waveforms o orhogonal waveforms. In his aricle, we sar by consrucing a signal model based on waveform diversiy, i.e., ransmied waveforms are no consrained o be orhogonal. Performance merics are hen formulaed and expressed as funcions of he waveforms. Wih ha, waveform effecs on SAP performance can be sudied from several perspecives. hen, he sensiiviy, i.e., he maxi-

2 550 Sun Jinping e al. / Chinese Journal of Aeronauics 3(010) No.5 mum range deecable, which is a meric of grea imporance for radar applicaion, is analyzed. hough some aricles poined ou ha he MIMO radar will suffer from loss of ransmiing power compared wih single-inpu muliple-oupu (SIMO) radar [4], his aricle provides a general approach o evaluae he sensiiviy of MIMO SAP radar wih waveform diversiy. I is achieved by invesigaing he effecive ransmiing-receiving (R) gain and processing gain according o differen waveforms. he sensiiviy of MIMO SAP radar wih waveform diversiy is shown o be deermined by eigenvalue disribuion of he waveform covariance marix (WCM) or waveform correlaion marix called in Ref.[15]. Along wih i, we also compare he sensiiviy of MIMO SAP applying orhogonal waveforms wih convenional SIMO SAP.. Configuraions and Signal Model he MIMO radar sysem geomery is shown in Fig.1. In his aricle we use he same convenions as in Ref.[7]. he radar plaform ravels a velociy v p in he posiive direcion of he x axis. he aliude of he array phase cener is h over he Oxy plane. he surface of he earh is assumed o be fla for he ineresed area of observaion. here are N omnidirecional ransmiing elemens uniformly spaced a disance d x, and M receiving elemens a disance d Rx. As illusraed in Fig.1, he ransmiing anennas are collocaed wih he receiving anennas, meaning ha his sysem has a monosaic MIMO radar configuraion. hus, all he elemens in he ransmiing-receiving arrays view he arge wih he same azimuh and elevaion angles. he elevaion angle and azimuh angle are illusraed in Fig.1. A each ransmier, a coheren processing inerval (CPI) consiss of a sequence of L waveforms. Le s n C NS1 be he discree baseband waveform ransmied a he nh ransmiing elemen in each pulse repeiion inerval (PRI). hen, in each PRI, he ransmiing waveform se is denoed by S=[s 1 s s N ] NN C S. We also define he covariance marix of ransmiing waveforms as R S =SS /N S C NN. Orhogonal waveforms are defined as hose saisfying Fig.1 MIMO SAP sysem geomery. R S =I N, where I N is an ideniy marix of size NN; coheren waveforms are defined as hose saisfying R S =1 NN, where 1 NN is an N-dimension marix wih each elemen equal o one; waveforms oher han orhogonal waveforms and coheren waveforms are defined as parially correlaed waveforms. We assume ha he ransmiing waveforms mee he narrowband assumpion. hus he Doppler effec wihin he waveforms can be negleced. he pulse repeiion inerval is r and he waveform duraion is p. Afer down-conversion, he echo for he lh PRI a he mh receiver from possible moving arge and all cluer paches a he range ring of ineres are N j fs, [( k 1) ( m 1)] j fd, l 1 ym ske e k1 N j fs,c[( k1) ( m1)] j fd,c ( l1) ( ) s ke e d (1) 0 k1 where is he arge reflecion coefficien; f s, = d Rx sin( )cos( )/ and f d, = v r r / are normalized arge spaial and emporal frequencies, respecively, is he wavelengh corresponding o he carrier frequency, he arge azimuh angle, he arge elevaion angle, v r he relaive velociy beween he arge and plaform; f s,c = d Rx sin()cos()/ and f d,c = sin()cos()v p r / are normalized spaial and emporal frequencies associaed wih he cluer of azimuh angle and elevaion angle, respecively; =d x /d Rx ; () is he signal ampliude from he cluer of angle. We also se = v p r /d Rx. We can define a general ransmiing seering vecor and a receiving seering vecor by v x ( ) [1 e jfs e jfs N1 N1 C () v Rx ( ) [1 e jfs e jfsm1 M1 C (3) Define a Doppler vecor as jf d jl1f d L1 u ( )=[1 e e ] C (4) o obain he sufficien saisics for SAP signal processing, we can employ =S R 1/ S as he filer bank in he receivers. I is common o diagonally load R S before evaluaing he inverse, in case R S is singular in pracical applicaions [11]. hus he arge echoes, he jamming signals and he cluer echoes are compressed by afer filering. hen he sacked daa of arge from angle is 1/ ( ) sack Rx( ) x( ) S u v v R NML1 v C (5) where x=sack(x) defines a vecor x formed by sacking he columns of he marix X, v is he arge space-ime seering vecor, and sands for he Kronecker produc. If he iso-range ring is divided in he cross-range dimension ino N c (N c NML) cluer paches, hen he discree form of he cluer daa for he lh PRI is

3 No.5 Sun Jinping e al. / Chinese Journal of Aeronauics 3(010) N c jl1fc, i xl sack ( c, i)e vrx( c, i) i1 NM 1 vx ( c, i ) R S C (6) where f c,i =sin( c,i )cos()v p r /, c,i is he azimuh of he ih cluer pach, v Rx ( c,i )andv x ( c,i ) are obained from Eqs.()-(3) by subsiuing f s wih f s,c, respecively, ( c,i ) can be modeled as a zero-mean independen complex Gaussian random variable wih he variance i. he cluer componen of he space-ime snapsho is hen given by c=[ 0 1 L1] x x x (7) he ih cluer echoes from c,i can be sacked in he following form c, i=[ x0, i x1, i xl1, i] = 1/ iu c, i vrx c, i vx c, i RS ( ) sack ( ) ( ) = 1/ iu c, i RS vrx c, i vx c, i NML1 i c, i C ( ) {[( ) ( )] ( )} v (8) where i =( c,i ). hen we define Vc [ vc,1 vc, vc, N ] c (9) =diag( 1,,, N ) c he cluer covariance marix (CCM) can be wrien as c E( c c ) c c R V V (10) For noise componen, we assume he noise snapsho, n, is emporally and spaially de-correlaed afer compression, hen he noise covariance marix is n E n n R ( ) I NML (11) where is he noise power. For a jammer a j and j, we assume is emporal behavior as he hermal noise wih he characerisics of a poin arge in he spaial domain. We define f s,j =d Rx sin( j )cos( j )/ as he normalized spaial frequency. he spaial seering vecor associaed wih he jammer is jfs,j jfs,jm1 M 1 v Rx,j [1 e e ] C (1) he jammer samples a he lh pulse inerval have he form of j l C NS1. Based on he assumpion ha he jammer is uncorrelaed emporally, we can obain ha E(j l j l )= ()I, where is he jamming-o-noise raio and () means he value of Dirac dela funcion a. herefore, afer filering, here would be NM jamming oupus for PRI. he consequen jamming componen of spaial snapsho is in he form of xj, l sack{ vrx,j( j, j)[ jl(( l1) r )] } (13) hen he jammer space-ime snapsho is j [ j,0 j,1 j, L1] x x x (14) For each pulse, he jamming oupu covariance marix can be E( xj, lxj, l) Rx,j j j Rx,j j j [ vrx,j( j, j)( vrx,j( j, j)) ] j ( v (, )) I [ ( v (, )) ] R (15) Eq.(15) indicaes ha correlaion propery of jamming signal will no be affeced by he waveform covariance marix according o he filer bank definiion. he jamming is emporally uncorrelaed beween pulses, hus l1 l E( x x ) 0 (16) hus, he covariance marix of jamming is j E( j j ) L j R I R (17) he oal space-ime snapsho including arge, cluer, jamming and noise can be n (18) j c u where u is he undesired componen, consiss of cluer, jamming and noise. For he problem of deecing he arge in a complex environmen wih cluer, jamming and noise, he opimum space-ime filer under he maximum signal-o-inerference-plus-noise raio (SINR) crierion is found from Ref.[7]: hus we can ge RuW W v max W W W 1 1 W Ru v 1 Ru E( uu ) (19) (0) Based on he above signal model consruced, i can be seen ha unlike convenional SIMO radar, he space-ime snapshos of boh arge signal and cluer signal are affeced no only by he array manifold, bu also by he waveforms, i.e., covariance marix of waveforms. MIMO radars wih boh orhogonal waveforms and coheren waveforms can be aken as a special form of he MIMO radar wih waveform diversiy. More imporanly, many waveforms for orhogonal MIMO radar in pracice are no ideally orhogonal a all. hrough he formulas derived above, he effecs of nonideal orhogonal waveforms can also be sudied. 3. Sensiiviy of MIMO SAP Radar Sensiiviy of radar is of grea imporance because i will deermine he funcional range of he radar. Radar sensiiviy is convenionally evaluaed by radar equa-

4 55 Sun Jinping e al. / Chinese Journal of Aeronauics 3(010) No.5 ion [16]. We here rewrie he radar equaion as 4 EG GR Rmax 3 (4 ) k F( S/ N) L 0 1 s EG R 3 k0f S N 1Ls (4 ) ( / ) (1) where R max is he maximum range deecable, G R he oal ransmiing-receiving gain, E he oal energy conained in one waveform, he arge cross-secion, k Bolzmann s consan, 0 a reference emperaure, F he receiver noise figure, and L s he sysem losses. For a received signal o be deecable, i has o be larger han he receiver noise by a facor denoed here as (S/N) 1. his value of signal-o-noise raio (S/N) 1 is ha required if only one pulse is presen. From Eq.(1) we can see ha he sensiiviy of radar is proporional o he ransmiing-receiving gain given oher facors fixed. Meanwhile, in SAP radar, he maximum deecion range is proporional o he gain of spaial and emporal coheren inegraion over all elemens and pulses [7]. he gain of spaial coheren inegraion is jus G R from he ransmiing-receiving beamforming. he gain of emporal coheren inegraion over all pulses is deermined by he number of pulses. Obviously, he emporal coheren inegraion gain would be he same for differen kinds of waveforms. hus, we will focus on he gain from spaial coheren inegraion. herefore, in his secion we will sudy he sensiiviy of MIMO SAP radar wih diverse waveforms from he perspecive of waveform effecs on R gain. We also compare he sensiiviy of MIMO SAP o ha of convenional SIMO SAP Waveform effec on R gain For a given sysem wih waveform diversiy, all parameers are fixed oher han waveforms. hus, G R varies according o differen waveform ses. he following will show his consideraion. For MIMO radar, he R gain can be wrien as [17] x ( ) S x ( ) Rx ( ) Rx ( ) GR v R v v v () vx ( ) RSvx ( ) where x is he magniude of scalar x. From Eq.() we can see ha he ransmiing-receiving gain of MIMO radar is he produc of ransmiing gain and he receiving gain. For SAP radar sysems wih given anenna configuraion, G R can be opimized wih respec o R S. Because R S is posiive semi-definie, i can be decomposed by singular value decomposiion as R S =U U, where = diag ( 1,,, N ) and 1 N are he singular values of R S. hen we have vx ( ) RSvx ( ) vrx ( ) vrx ( ) GR ( ) v R v x S x x x Rx Rx vx ( ) RSvx ( ) v ( ) U Uv ( ) v ( ) v ( ) x x Rx Rx vx ( ) RSvx ( ) v ( ) U Uv ( ) v ( ) v ( ) x ( ) S x ( ) Rx ( ) Rx ( ) v R v v v (3) where x is he -norm of vecor x and inequaliy comes from he rule of Cauchy-Schwarz inequaliy. As he ransmi seering vecor has consan Euclidean norm, by applying propery of Rayleigh quoien we can ge v ( ) R v ( ) ( R ) (4) x S x max S From Eqs.(3)-(4), we can see ha he maximum R gain is proporional o he larges eigenvalue of WCM. hus, waveforms ha obain he larges eigenvalue will have he maximum R gain. he maximum value is obained in he case of coheren waveforms, i.e., oal energy of R S is concenraed in one eigenvalue. While for orhogonal signals, G R will be decreased by a facor of 10lg N, because all eigenvalues are he same. hus, R gain of orhogonal waveform is only 1/N of coheren waveforms. Meanwhile, he R gain of parially correlaed waveforms may be beer han ha of orhogonal waveform bu worse han ha of coheren waveforms. Fig. illusraes he above analysis, where we have 10 anenna elemens as boh ransmiers and receivers spaced by half wavelengh. arge azimuh is 0. Coheren waveforms, orhogonal waveforms and parially correlaed waveforms are used in his example. he parially correlaed waveforms are designed by he mehod of minimum sidelobe design described in Ref.[9]. he mainbeam is cenered a 0, and 3 db mainbeam area is se o [1, 1]. owever, as he ransmiing gain of he orhogonal waveform is uniform over all azimuh angles, he maximum R gain of orhogonal waveforms will keep unchanged no maer wha he arge azimuh is (see Fig.3(a)). For coheren or parially correlaed waveform, he maximum R gain will be affeced by he difference beween he azimuhs of ransmiing beam and arge (see Fig.3(b)). In his way, alhough orhogonal waveforms can provide much more degrees of freedom han correlaed waveforms do, i will have

5 No.5 Sun Jinping e al. / Chinese Journal of Aeronauics 3(010) arge azimuh due o he un-uniform sampling propery of he equivalen virual array, which is deermined by he eigenvalue (eigenvecor) disribuion of he waveform covariance marix. Basically, for parially correlaed waveform se, because is corresponding waveform covariance marix has more complicaed eigen-specrum, discussion on he equivalen virual array is no so clear and concise as ha for he orhogonal waveforms. herefore, he paern should be beer analyzed case-by-case o gain precise knowledge. 3.. Waveform effec on processing gain and SINR Fig. Paern for differen waveforms. In his secion, we will sudy he waveform effecs on SINR meric and processing gain. Like he SINR loss defined and evaluaed in Ref.[7], we here assess he processing gain by SINR ou ( fd, ) ( fd,) (5) SNRin where SNR in is he signal-o-noise raio (SNR) ha exiss on each receiving elemen of he virual array and is proporional o he R gain, SINR ou (f d, ) is he oupu SINR of SAP filer a normalized arge emporal frequency f d,. We ake he SNR in of orhogonal waveform as 0 db. From Eq.(5), he waveform effec can be invesigaed by holding he arge angle fixed and varying he arge Doppler frequency. hree kinds of waveforms are considered here, i.e., ideally orhogonal waveform, coheren waveform, and parially correlaed waveform as previously menioned. he sysem configuraion is as follows: N=M=5, L=10, =0, d Rx =/, =5, v p =100 m/s, v =70 m/s, =1, =0.6 m, r =1.5 ms, B=10 Mz, he cluer-o-noise raio is 30 db and he jamming-o-noise raio is 30 db. wo jammer signals come from he direcions of 40 and 30, respecively. his configuraion will be employed hroughou he following conen unless oherwise specified. he processing gain of MIMO radar has a maximum value of abou 10lg(NML)=4.0 db for all kinds of waveforms (see Fig.4). he gain of NML Fig.3 Paern when arge azimuh is differen from ha of ransmiing and receiving. lower R gain. Meanwhile, alhough orhogonal waveform se has lower R gain, i has beer ubiquious searching performance han oher waveform ses because we only need o do he digial beamforming a he receiver end o cover all azimuh regions of ineres in orhogonal waveform case. he main reason for he appearance of asymmeric paern in Fig.3(b) when he arge is away from he boresigh is ha he parially correlaed waveforms may lead o an asymmeric ransmiing paern for his Fig.4 MIMO SAP processing gain of differen waveforms (N=M=5, L=10).

6 554 Sun Jinping e al. / Chinese Journal of Aeronauics 3(010) No.5 represens coheren spaial and emporal inegraion over NM virual elemens and L pulses. his resul can be explained and furher generalized from a physical perspecive ha he processing gain for differen waveforms would be he same because he oal poenial power for coheren spaial and emporal inegraion is he same for differen waveforms. owever, he orhogonal waveform se has he bes velociy deecabiliy as i has he narrowes cluer noch, while he coheren waveform se has he wors (see also Fig.4). Based on boh G R and processing gain, we can conclude ha sensiiviy of MIMO radar wih waveform diversiy is proporional o he maximum eigenvalue of he WCM. Specifically, he sensiiviy of orhogonal waveform is only 1/N of he sensiiviy of coheren waveform; he sensiiviy of parially correlaed waveforms may be beer han ha of orhogonal waveform bu worse han ha of coheren waveform. hus MIMO radar may sacrifice he sensiiviy for beer velociy deecabiliy and beer spaial resoluion capabiliy owing o more degrees of freedom. We can also compare he sensiiviy of MIMO SAP beween orhogonal waveform and convenional SIMO SAP. As for he convenional SAP, beamforming is conduced during ransmiing. While for MIMO SAP wih orhogonal waveform, beamforming will be performed afer receiving. hus, if SIMO SAP has he same number of ransmiers as ha of MIMO SAP, i.e., he same oal ransmi power, he SNR in of SIMO SAP ( SNR MIMO radar SIMO in MIMO and SIMO as ) will be N N imes of he SNR in of MIMO SNR in. We denoe he SINR ou of MIMO SINR ou and SIMO SINR ou, he processing gain of MIMO and SIMO as MIMO and SIMO. If he pulse number is L for MIMO radar and SIMO radar, hen he comparison of sensiiviy can be illusraed by he raio beween he oupu SINRs of MIMO radar and SIMO radar as follows: MIMO MIMO ou in MIMO NML M SIMO SIMO ou SNRin SIMO N NL N SINR SNR 1 SINR (6) Compared wih SIMO SAP, he oal sensiiviy of MIMO SAP wih orhogonal waveform will decrease as long as M<N. Fig.5 shows he oupu SINRs of MIMO wih N = M =10 and SIMO wih N = 0, L = 10 for boh. In his example, he oupu SINR of MIMO is approximaely 10 db less han he oupu SINR of SIMO. herefore, in pracical operaion, he sensiiviy loss of MIMO radar wih orhogonal waveforms mus be compensaed by improving he inegraion ime for some applicaions in order o achieve equivalen performance as SIMO radar. he final sensiiviy of MIMO radar afer inegraing can be calculaed based on he available opimum inegraion ime [18]. As described in Ref.[18], he opimum inegraing ime can be seriously limied by ransmier spurious-frequency spread and arge modulaion; he advanage of inegraion may no be fully realized. hus, he sensiiviy of MIMO radar should be carefully reaed before pracical applicaion. Fig.5 Oupu SINR comparison of MIMO and convenional SIMO SAP processor (N=M=10 for MIMO, N=10 for SIMO, L=10 for boh). 4. Conclusions In his aricle, we presened a general approach o evaluae he sensiiviy of MIMO SAP radar wih waveform diversiy. he sensiiviy of MIMO SAP radar wih waveform diversiy is found o be relaed o he eigenvalue disribuion of he waveform covariance marix. Simulaion examples were provided o illusrae he analysis and conclusions. Based on he sudies and conclusions we can balance differen kinds of waveforms o achieve opimal sysem performance. References [1] Bliss D W, Forsyhe K W. Muliple-inpu muliple-oupu (MIMO) radar and imaging: degrees of freedom and resoluion. Conference Record of he hiry-sevenh Asilomar Conference on Signals, Sysems and Compuers. 003; [] Chen C Y, Vaidyanahan P P. A subspace mehod for MIMO radar space-ime adapive processing. Proceedings of ICASSP ; [3] Chen C Y, Vaidyanahan P P. Beamforming issues in modern MIMO radars wih Doppler. Conference Record of he Forieh Asilomar Conference on Signals, Sysems and Compuers. 006; [4] Chen C Y, Vaidyanahan P P. MIMO radar space ime adapive processing using prolae spheroidal wavefuncions. IEEE ransacions on Signal Processing 008; 56(): [5] Mecca V, Ramakrishnan D, Krolik J. MIMO radar space-ime adapive processing for mulipah cluer miigaion. Proceedings of Fourh IEEE Workshop on Sensor Array and Mulichannel Processing. 006; [6] Mecca V, Krolik J, Robey F. Beamspace slow-ime

7 No.5 Sun Jinping e al. / Chinese Journal of Aeronauics 3(010) MIMO radar for mulipah cluer miigaion. Proceedings of ICASSP ; [7] Ward J. Space-ime adapive processing for airborne radar. echnical Repor ADA9303, [8] Klemm R. Space-ime adapive processing: principles and applicaions. London: IEE Press, [9] Soica P, Li J, Xie Y. On probing signal design for MIMO radar. IEEE ransacions on Signal Processing 007; 55(8): [10] Anonio G S, Fuhrmann D R, Robey F C. ransmi beamforming for MIMO radar sysems using parial signal correlaion. Conference Record of he hiryeighh Asilomar Conference on Signals, Sysems and Compuers. 004; [11] Forsyhe K W, Bliss D W. Waveform correlaion and opimizaion issues for MIMO radar. Conference Record of he hiry-ninh Asilomar Conference on Signals, Sysems and Compuers. 005; [1] Friedlander B. Waveform design for MIMO radars. IEEE ransacions on Aerospace and Elecronic Sysems 007; 43(3): [13] Li J, Xu L, Soica P, e al. Range compression and waveform opimizaion for MIMO radar: a Cramer- Rao bound based sudy. IEEE ransacions on Signal Processing 008; 56(1): [14] Li J, Soica P, Zhu X. MIMO radar waveform synhesis. Proceedings of IEEE Radar Conference. 008; 1-6. [15] Fuhrmann D R, Anonio G S. ransmi beamforming for MIMO radar sysems using signal cross-correlaion. IEEE ransacions on Aerospace and Elecronic Sysems 008; 44(1): [16] Skolnik M. Radar handbook. nd ed. New York: McGraw-ill; [17] Bekkerman I, abrikian J. arge deecion and localizaion using MIMO radars and sonars. IEEE ransacions on Signal Processing 006; 54(10): [18] Flahery J M, Kadak E. Opimum radar inegraion ime. IRE ransacions on Anenna and Propagaion 1960; 8(): Biographies: Sun Jinping Born in 1975, an associae professor a School of Elecronics and Informaion Engineering of Beijing Universiy of Aeronauics and Asronauics. e is engaged in high resoluion and advance mode radar signal processing, image undersanding and paern recogniion. sunjinping@buaa.edu.cn Wang Guohua Born in e is currenly a Ph.D. candidae a School of Elecrical and Elecronic Engineering, Nanyang echnological Universiy, Singapore. is curren research ineress are in he areas of waveform design and diversiy and MIMO radar signal processing. Liu Desheng Born in e is currenly an associae professor and a Ph.D. candidae a School of Auomaion Science and Elecrical Engineering, Beijing Universiy of Aeronauics and Asronauics. is curren research ineress are in he areas of avionics and signal processing.