BISTATIC COHERENT MIMO CLUTTER RANK ANALYSIS

Transcription

1 3 Euopean Sgnal Pocessng Confeence (EUSIPCO BISAIC COHEEN MIMO CLUE ANK ANALYSIS Ksne Bell, * Joel Johnson, Chsophe Bae, Gaeme Smh, an Mualha angaswam * Meon, Inc, 88 Lba S, Sue 600, eson, Vgna 090, USA Dep of Eleccal an Compue Engneeng an ElecoScence Laboao, he Oho Sae Unves, Columbus, Oho, 430, USA US A Foce eseach Laboao, Sensos Decoae, Wgh-Paeson AFB, OH, USA ABSAC he an of he clue covaance n a bsac coheen mulple-npu mulple-oupu (MIMO aa ssem wh aba plana aas n boh he ansme an eceve s eamne he analss poves fuhe genealzaon of Bennan s ule esuls avalable fo lnea aas n monosac coheen MIMO an bsac space-me aapve pocessng (SAP ssems We fs een he wo-mensonal (D monosac SAP esuls of Vaaaajan an Kol (VK o monosac MIMO ssems wh plana aas We hen use he VK bsac SAP appoach an eemne conons une whch a fou-mensonal (4D bsac MIMO ssem can be moele as an equvalen D monosac MIMO ssem, an appl he D esuls he analcal epessons ae valae agans he numecall calculae an of he heoecal clue covaance Ine ems MIMO aa, SAP, bsac, monosac, clue an INODUCION Monosac coheen mulple-npu mulple oupu (MIMO aa fo goun movng age ncaon (GMI []-[3] s an eenson of monosac sngle-npu mulple oupu (SIMO space-me aapve pocessng (SAP [4]-[6], n whch mulple ansme elemens em ohogonal wavefoms ha ae pocesse sepaael a each of he eceve elemens an he scaeng esponses ae coheen acoss all ansm/eceve elemen pas Smlal, bsac coheen MIMO [7],[8] s a genealzaon of bsac SAP [9],[0], n whch he ansm an eceve elemens ae locae on spaall sepaae plafoms In coheen MIMO an SAP ssems, he clue occupes a low-mensonal subspace of he full-menson aa space he chaacescs of he clue subspace, nclung s an, have mpoan mplcaons fo he hs wo was suppoe b he US A Foce eseach Laboao une conac FA C-007 Opnons, nepeaons, conclusons, an ecommenaons ae hose of he auhos an no necessal enose b he U S Govenmen sgnal pocessng echnques use o mgae he clue as well as oveall ssem pefomance []-[3] Bennan s ule [4],[] poves a smple analcal epesson fo he clue an fo monosac SAP when he eceve elemens ae a unfoml space lnea aa (ULA algne wh he plafom veloc veco In hs case he effecve spaal samplng s n one menson (D along he aa as, an he scaee angle-ofaval (AOA an Dopple fequenc can be epesse n ems of a D spaal fequenc In [], he clue an was shown o be eemne b he pouc of he spaal apeue an spaal banwh, an Bennan s ule was eene o sub-aa geomees In [], hese D esuls wee fuhe eene o he monosac MIMO case whee he ansm aa s a lnea aa algne wh he veloc veco In monosac SAP ssems, when he eceve aa s a plana aa o a lnea aa no algne wh he veloc veco, he effecve spaal samplng s n wo mensons (D an he scaee AOA s epesene b a D spaal fequenc Clue an fo he D monosac case s analze n [0],[3] In [0], Vaaaajan an Kol (VK show ha he clue an s eemne b he sum of he apeue-banwh poucs along an ohogonal o he veloc veco In bsac SAP ssems, he poblem epans o one nvolvng a D ansm spaal fequenc n aon o he D o D eceve spaal fequenc an he effecve spaal samplng concep oes no anslae n an obvous manne In [0], une some some smplfng assumpons, he bsac SAP poblem was convee o an equvalen D monosac SAP poblem o whch he monosac esuls coul be apple In bsac MIMO ssems wh plana aas, we have D spaal fequences fo boh he eceve an ansme In hs pape, we fs een he VK D monosac SAP esuls o monosac MIMO ssems wh plana aas We hen use he VK bsac SAP appoach an eemne conons une whch a fou-mensonal (4D bsac MIMO ssem can be moele as an equvalen D monosac MIMO ssem, an appl he D esuls he analcal epessons ae valae agans he numecall calculae an of he heoecal clue covaance fo a epesenave scenao /5/$ IEEE 59

2 3 Euopean Sgnal Pocessng Confeence (EUSIPCO BISAIC COHEEN MIMO MODEL he bsac coheen MIMO moel pesene hee s he plana aa genealzaon of he lnea aa moels n [7],[8] he bsac coheen MIMO confguaon consss of one ansm ( plafom wh M ansm elemens an one eceve ( plafom wh N eceve elemens he ansm an eceve aas ae assume o be plana aas of omneconal elemens n geneal We assume he ansm elemens em ohogonal pulse Dopple wavefoms conssng of a sequence of L phase coheen pulses he sgnal obseve a each eceve elemen s pocesse b a ban of mache fles fo each of he ansme wavefoms he scaeng esponses ae assume o be coheen acoss all of he ansm/eceve elemens he hee-mensonal (3D fla-eah geome s shown n Fg he aa ssem paamees an vaous geomecal paamees ae efne n able he coonae ssem s efne so ha he ogn les ecl beneah he eceve plafom an he baselne beween he ansme an eceve les along he -as Fo a gven bsac ange B, he locus of goun clue scaees s an ellpse efne b he equaon: c, ( a b whee H H c B ( e e B ( B H H 4H a B( e B( e b a e We assume ha he euns fom he ene clue ellpse can be appomae as he sum of euns fom a lage numbe (N c of scee clue paches he h clue pach s hen moele as a pon scaee wh poson p [ ; ;0] an veloc p 0 Scaee paamees ae efne n able hese nclue plafom-efeence azmuh an elevaon angles, whch ae shown n Fg fo he eceve aa he measuemens fom a sngle clue pach can be epesse as a veco of he fom α vp, whee vp ( s he NML MIMO esponse veco fo a scaee a poson p an α s he comple clue eun he α ae assume o be zeo-mean, uncoelae anom vaables wh vaance P, gven b he aa equaon [8] he clue esponse veco c s hen he sum of nvual clue pach euns: N c c α v( p, (3 an he clue covaance s gven b: N c H H c E{ c c P v p v p (4 Fg Bsac coheen MIMO 3D fla Eah geome able Bsac coheen MIMO aa ssem paamees Paamee Defnon [uns] L Numbe of pulses [-] M Numbe elemens [-] N Numbe of elemens [-] aa opeang wavelengh [m] Pulse epeon neval [Hz] p p [ 0;0; ] plafom poson [m] p v H plafom veloc [m/s] v p plafom spee [m/s] Angle of plafom veloc δ veco w ssem -as p v [ cos δ ;sn δ ;0] plafom -as [-] [ sn δ ;cos δ ;0] ( n, n plafom -as [-] nh elemen poson w, aes [m] p [ ;0; H ] plafom poson [m] p v plafom veloc [m/s] v p plafom spee [m/s] Angle of plafom veloc δ veco w ssem -as p v [ cos δ ;sn δ ;0] plafom -as [-] [ sn δ ;cos δ ;0] ( m, m plafom -as [-] mh elemen poson w, aes [m] he MIMO esponse veco has he fom: vp v ( p v ( p v f ( p, (5 ( ( D( D whee enoes he Konece pouc he vecos v ( ( p an v ( ( p ae he N an M aa esponse vecos of he eceve an ansm aas, 50

3 3 Euopean Sgnal Pocessng Confeence (EUSIPCO Fg eceve plafom geome able Scaee paamees Paamee Defnon [uns] p [ ; ;0] Scaee poson [m] p p o scaee ange [m] ( p p o scaee un veco [-] p p o scaee ange [m] ( p p o scaee un veco [-] B f D p p φ θ φ θ Bsac ange [m] Saona scaee Dopple fequenc [Hz] azmuh angle [a] elevaon angle [a] azmuh angle [a] elevaon angle [a] especvel he epen on he scaee poson va he D spaal fequenc (wavenumbe vecos ( p ; an ( p ;, whose componens ae efne as follows: ( π ( π cosφ cosθ ( π ( π snφ cosθ (6 ( π ( π cosφ cosθ π πsnφ cos θ he nh an mh componens of he eceve an ansm aa esponse vecos, especvel, have he fom: v ( ( p ep{ j n n n (7 ( ep{ j m m v p m, (8 whee ( n, n an ( m, m ae he posons of he eceve an ansm elemens, along (-menson an ohogonal o (-menson he plafom veloc vecos he veco vd( f D( p s he L Dopple esponse veco, whch epens on he scaee poson va he Dopple fequenc, whch s gven b: f ( p D v v p p π (9 he lh componen of he Dopple esponse veco s: D( f v D p ep{ j π( l p fd( p l (0 ep { jl ( p v v If we efne D D l ( l pv; l ( l pv, ( an use he noaon { nml (( n M m L l, hen he { nml h elemen of he MIMO esponse veco can be epesse as: D vp ep{ j( { n l nml n ( D ep { j( m l m 3 Monosac Case 3 CLUE ANK ANALYSIS In he monosac case, p p an p p, heefoe he ansm an eceve spaal fequences conce, e an Fuhemoe, he elevaon angle cosθ cosθ s consan fo all an he D spaal fequenc componens have he elaonshp: cos π θ, (3 hus he clue specum s a ccle n he D spaal fequenc space, as shown n Fg 3 (an [0] Fg 3 Monosac clue specum he MIMO esponse veco n ( euces o: D vp ep{ j( { n m nml l (4 ep { j( n m hs has he fom of a spaal aa esponse veco, such as n (7 an (8, wh vual plana aa elemens a D posons (, nml,, nml ( n m l, n m Fom [0], he effecve apeue-banwh pouc s he numbe of ecangula esoluon cells eque o cove he ccula spaal specum, whee he sze of a esoluon cell s nvesel popoonal o he effecve apeue of he vual aa, as shown n Fg 3 he effecve apeue n he an -mensons s compue as he mum ffeence beween an wo vual aa 5

4 3 Euopean Sgnal Pocessng Confeence (EUSIPCO elemens n hose mensons plus : A ( n m mn ( n m ( L pv (5 A ( n m mn ( n m We hen fn he numbe of esoluon cells n he -an - mensons as follows: ( 4π cosθ cosθ N A ( π A (6 ( 4π cosθ cosθ N A π A ( If N > an N >, hen he numbe of cells aes o cove he spaal specum s NN 4, as shown n Fg 3 We a one o ge he clue an: ρ D N N 3 (7 he epessons n (5-(7 pove he MIMO genealzaon o he D SAP esuls n [0] he epessons ae slghl ffeen han n [0] ue o ang he em o he apeue epessons n (5 If N, hen he spaal specum can be covee b N esoluon cells, an smlal f N he poblem euces o he D case an he clue an s: N N ρd (8 N N he D esul fo N euces o he Bennan s ule genealzaon fo MIMO n [] 3 Bsac Case In he bsac case, he spaal fequenc elaonshps ae moe complcae an he clue specum s a D manfol n 4D (,,, space Fom (6, he ansm an eceve spaal fequences sasf: ( ( ( ( cos cos π θ, (9 π θ, (0 an he elaonshp beween he ansm an eceve spaal fequences can be wen as: c s ( π c ( s c ( π s, whee c ( cos( δ δ s ( sn( δ δ ( c ( cos δ s sn δ Subsung hese epessons no (, we oban: Each scee elemen poves an effecve connuous apeue of lengh, he spaal Nqus samplng neval [4] he noaon enoes ounng up o an nege { j D D c s D { j n ( m l s mc (3 D { j( π( mc ms l c vp ep - { nml n l m l m ep ep In hs pape, we conse suaons whee he MIMO esponse veco n (3 has he fom of (4 an he bsac ssem can be epesene b an equvalen D monosac ssem hs wll occu when he agumen n he h lne of (3 s equal o zeo, whch eques one of he followng conons o be sasfe: an heefoe c 0 an s 0 hs s smla o he quas-monosac assumpon n [0] δ ( c 0 an m 0 m, e he ansm plafom veloc s pepencula o he baselne beween he ansme an eceve, an he ansm aa s a lnea aa algne wh he veloc veco 90 D v ( l 0 l an ( m, m m( sn δ,cosδ, e he ansme s saona an he ansm aa s a lnea aa algne pepencula o he baselne beween he ansme an eceve, egaless of he 0 abal efne (when v 0 angle δ he MIMO esponse veco hen has he fom of (4 wh vual plana aa elemens a posons gven b he ems n he squae baces n he fs wo ems n (3 Unfounael, hese vual elemen posons va wh clue pach ne hough he ems c an s, whch epen on he ao Fo smplc, we use he aveage ao, whch we assume s appomael equal o one, (, an efne: av c cos ( δ δ ; s sn( δ δ (4 he vual aa elemens hen become: c - s D D, nml n l m l m D, nml n m l m, (5 s c an he effecve apeues ae foun fom: A (, nml mn (, nml nml,, nml,, (6 A (, nml mn (, nml nml,, nml,, he D clue specum efne n (9 s no longe a ccle cenee a he ogn, howeve s an oval-shape egon, as shown n Fg 4 fo he eample n Secon 4 o fn N an N, we fs eemne he specal een n he - an -mensons fom he mum an mnmum values of an n (9, an hen N an N ae gven b: ( ( mn mn N A ( π A π (7 ( ( mn mn N A ( π A π he clue an can hen be foun fom (7 o (8 he epessons n (4-(7 an (7 pove he 5

5 3 Euopean Sgnal Pocessng Confeence (EUSIPCO MIMO genealzaon o he D bsac SAP esuls n [0] he epessons ae slghl ffeen han n [0] ue o ang he em o he apeue epessons n (6, appomang he ange ao as one n (5, an n he meho fo compung he specal een n (7 4 EAMPLE We conse he followng scenao: N 0, M 5, L 6, 33 m, p /300 s, H m, v 00 m/s, δ 0, 5 m, H m, v 75 m/s, δ 90 he aa s a ULA wh spacng oae 3 wh espec o he eceve veloc veco he aa s a ULA wh spacng algne wh he ansm veloc veco We conse bsac anges fom 7 m o 5 m he eceve clue speca ae shown n Fg 4 A 5 m, he specum loos smla o he monosac case, bu as he ange eceases, he bsac geome causes he speca o become smalle, moe oval-shape, an shfe up an o he lef of he ogn he nomalze egenvalues of he clue covaance an he pece an ae shown n Fg 5 he egenvalues o no show a shap op-off hus s ha o sa wha he coec an s he pece ans ae all a he 999h pecenle (o geae of oal eneg he clue an s sgnfcanl less han NML 800, an eceases as bsac ange eceases ue o he smalle een of he spaal specum obseve n Fg 4 Fg 4 Bsac clue specum fo bsac anges vang fom 7 m o 5 m Fg 5 Nomalze egenvalues an pece clue an (vecal lnes fo bsac anges vang fom 7 m o 5 m 5 SUMMAY In hs pape, we analze he an of he clue covaance n a bsac coheen MIMO aa ssem wh aba plana aas n boh he ansme an eceve We fs eene he VK D monosac SAP esuls o monosac MIMO ssems wh plana aas, hen eemne conons une whch a 4D bsac MIMO ssem coul be moele as an equvalen D monosac MIMO ssem, an apple he D esuls he analcal epessons wee valae agans he numecall calculae an of he heoecal clue covaance fo a epesenave scenao EFEENCES [] J L an P Soca, MIMO aa wh Colocae Anennas, IEEE Sgnal Pocess Mag, vol 4, no 9, pp 06-4, Sep 007 [] C-Y Chen an P P Vaanahan, MIMO aa Space- me Aapve Pocessng Usng Polae Spheoal Wave Funcons, IEEE ans Sgnal Pocess, vol 56, no, pp , Feb 008 [3] J M Kano an D W Blss, Clue Covaance Maces fo GMI MIMO aa, n Poc 44h Asloma Conf Sgnals, Ss, Compu, Pacfc Gove, CA, pp 8-86, Nov 00 [4] J Wa, Space-me Aapve Pocessng fo Abone aa, MI Lncoln Laboao ech epo 05, DIC No ESC , Dec 994 [5] J Guec, Space-me Aapve Pocessng fo aa, Nowoo, MA: Aech House, 003 [6] Klemm, Pncples of Space-me Aapve Pocessng, 3 e, Lonon, UK: he Insuon of Engneeng an echnolog, 006 [7] J L, G Lao, an H Gffhs, Bsac MIMO aa Space-me Aapve Pocessng, n Poc IEEE aa Conf, Kansas C, MO, pp , Ma 0 [8] K L Bell, J Johnson, C J Bae, G E Smh, an M angaswam, Moelng an Smulaon fo Mulsac Coheen MIMO aa, n Poc IEEE aa Conf, Oawa, CN, Ap 03 [9] Y Zhang an B Hme, Bsac Space-me Aapve Pocessng (SAP fo Abone/Spacebone Applcaons, AFL ech epo AFL-SN-S , Ma 999 [0] V Vaaaajan an J L Kol, Jon Space-me Inepolaon fo Dsoe Lnea an Bsac Aa Geomees, IEEE ans Sgnal Pocess, vol 54, no 3, pp , Ma 006 [] L E Bennan an F M Sauahe, Subclue Vsbl Demonsaon, Aapve Sensos, Inc, Sana Monca, CA ech epo L--9-, 99 [] Q Zhang an W B Mhael, Esmaon of he Clue an n he Case of Subaang fo Space-me Aapve Pocessng, Eleconcs Lees, vol 33, no 5, pp 49-40, 7 Feb 997 [3] N A Gooman an J M Sles, On Clue an Obseve b Aba Aas, IEEE ans Sgnal Pocess, vol 55, no, pp 78-86, Jan 007 [4] H L Van ees, Opmum Aa Pocessng, New Yo, NY: Wle, 00 53