Space-time Clutter Model and Simulation for Space-based Radar

Transcription

1 Spa-tm Cluttr Modl and Smulaton for Spa-basd Radar Shool of Eltron Engnrng, Unvrsty of Eltron Sn and Thnology of Chna, Chngdu , Chna Abstrat Th prforman of Spa-Basd Radar (SBR) to dtt ar or ground movng targts s nflund by arth luttr, so an fftv algorthm to supprssng luttr an b dsgnd f knowng th powr and dstrbuton of arth luttr. In ths papr, th luttr modl of SBR s ddud. Bsds, th arth's rotaton fft s takn nto aount and th modfaton to Dopplr frquny s drvd. Fnally, w plot luttr spa-tm sptrum and luttr angl-dopplr tras basd on th modlng. It s shown that arth's rotaton togthr wth Dopplr ambguty sgnfantly dgrad th luttr supprsson prforman of adaptv prossng algorthms. Dtald drvatons of ths rsults ar prsntd n ths papr. Kywords: Spa-basd radar, Cluttr modl, Earth's rotaton, Cluttr smulaton 1. Introduton Spa basd radar (SBR) baus of ts hght an ovr a vry larg ara on arth for ntllgn, survllan and montorng of ar, sa and ground movng targts [1-4]. On launhd nto orbt, th SBR movs around th arth whl th arth ontnus to rotat on ts own axs. By adjustng th SBR spd and orbt paramtrs t s thus possbl to san varous parts of th arth prodally and ollt data. As a rsult, targts of ntrst an b dntfd and trakd. For lookng down mod, t s ndd to mtgat th luttr prsnt n spa-basd radar rturns so as to obtan targt rang and vloty Informaton [5]. Svral paprs [6-8] hav provd that spa-tm adaptv prossng (STAP) s th bst mthod for luttr mtgaton. Spa-tm uttr smulaton and luttr haratrsts analyss s th bass for STAP [9]. Thrfor, stablshng a fasbl luttr modl for Spa-basd Radar s vry mportant for studyng th luttr haratrst and STAP thnqus. Ths papr manly dsusss th luttr modl and smulaton mthod of SBR. Frst, a brf Ston on satllt gomtry and ffts of arth's rotaton provds a bass for luttr smulaton. Nxt, w dtal dsuss th alulaton mthod of th spa-tm luttr sptrum as sn by a puls-dopplr radar from a spa platform. Fnally, w plot dffrnt spa-tm luttr sptrums and luttr angl- Dopplr tras for som dffrnt onfguratons. Som suggstons ar gvn as wll. 2. Cluttr modl for spa-basd radar 2.1. Radar-arth Gomtry An SBR loatd at an orbtal hght H abov ts nadr ponts has ts manbam fousd to a pont of ntrst on th ground loatd at rang R. Radar-arth gomtry s shown n Fgur 1. A rprsnts th SBR, and B rprsnts th nadr pont. Th pont of ntrst D s loatd at rang R from B along th grat rl that gos through B and D wth C rprsntng th ntr of th arth. rprsnts th grazng angl, R rprsnts Earth's radus, EL rprsnts lvaton angl, AZ rprsnts azmuth angl, rprsnts or angl btwn th nadr pont and th grazng pont masurd at th arth's ntr, Vp rprsnts satllt vloty vtor. Th arth or angl subtndd at th ntr of arth by th rang ar BD s gvn by R/ R (1) Journal of Convrgn Informaton Thnology(JCIT) Volum7, Numbr3, Fbruary 2012 do: /jt.vol7.ssu

2 and from trangl ACD w gt R R ( R H) 2 R ( R H)os (2) s th grazng angl s also a funton of rang. R H (3) 1 os ( sn( R/ R )) Rs th lvaton angl s gvn by EL R R R (4) 1 sn ( sn( / )) Rs From th trangl ACD w obtan th rlaton of th slant rang, grazng angl and lvaton angl /2 /2 R/ R (5) EL Fgur 1. A gomtr modl of th satllt and th ground luttr rsoluton lls 165

3 2.2. Th fft of arth's rotaton on th Dopplr Consdr a spa basd radar (SBR) at hght H abov th arth on a grat rular orbt that s nlnd at an angl (wth rspt to th quator). SBR s s movng wth vloty V /( R H) (6) p 3 2 s Kplr fator, km / s. In a rular orbt and ths ontrbuts to a rlatv vloty V V sn os (7) r p EL AZ If Dopplr shft T r rprsnts th radar rptton rat and th opratng wavlngth, thn th d 2VT p r d snel osaz (8) /2 As th SBR movs around th arth, th arth tslf s rotatng around ts own axs on a hour bass n a wst-to-ast drton. Ths ontrbuts an astward moton wth quatoral vloty of V km / s. Fgur 2 shows th satllt n arth projton profl. SPR path 2 AZ V os 2 1 Equator 1 2 Fgur 2. Satllt n arth projton profl 166

4 Lt ( 1, 1) rfr to th lattud and longtud of th SBR nadr pont B and ( 2, 2) rfr thos of th pont of ntrst D. As a rsult, th pont of ntrst D on th arth at lattud 2 rotats astward wth vloty V os 2, whh wll ontrbut to th Dopplr shft of th pont D. Rsarh [10] has provd that th modfd Dopplr frquny that onsdr th fft of Earth rotaton to b. 2VT p r 2 2 d sn EL((1 kos ) osaz k os 1 os sn AZ) /2 2VT p r A sn EL(os AZ ) (8) /2 whr os os 1 A tan 1os (9) (10) os 1 2 os and V H k (1 ) V R (11) p A rprsnts th rab magntud and rprsnts th rab angl. Th ovrall fft of th arth s rotaton on th Dopplr turns out to b two orrton fators n trms of a rab angl afftng th azmuth angl, and a rab magntud salng th Dopplr magntud of th luttr path. Both fators dpnd only on th SBR orbt nlnaton and ts lattud 1 and not on th spf loaton of th luttr path of ntrst. Equaton (8) orrsponds to th as whr th rgon of ntrst D s to th ast of th SBR path. If on th othr hand, th rgon of ntrst s to th wst of th SBR path, thn 2VT p r d A sn EL (os AZ ) (12) /2 Combnng (8) and (12) w obtan th modfd Dopplr to b. 2VT p r d A sn EL (os AZ ) (13) /2 3. Spa-tm luttr sptrum alulaton For SBR, th Earth's surfa s th major sour luttr and s th only typ of luttr to b onsdrd n ths papr. Ground luttr s dstrbutd n both angl and rang and s sprad n Dopplr frquny du to th platform moton. In ths ston, a modl s dvlopd for th ground luttr omponnt of th spa-tm snapshot for a gvn rang, and th proprts of th luttr spa-tm 167

5 ovaran matrx ar onsdrd. Fnally, w gv th mthod of mnmum varan sptrum alulaton bas on th luttr spa-tm ovaran matrx Cluttr ovaran matrx alulaton Th SBR antnna s a unformly spad lnar array antnna (ULA) onsstng of N lmnts. Th radar transmts a ohrnt burst of M pulss at a onstant PRF fr 1/ Tr, whr T r s th puls rptton ntrval (PRI). Th transmttr arrr frquny s f0 / 0, whr s th propagaton vloty. W ar now n a poston to quantfy th total luttr rturn from a gvn so-rang rng. Assumng that th th luttr path at a normalzd angl,, ts spatal N-dmnsonal strng vtor a s gvn by: T j2 j2 (2) j2 ( N1) 1 a (14) b s th M-dmnsonal Dopplr strng vtor gvn by j2 fd j2 (2) fd j2 ( M1) f d b 1 (15) T Whr fd s a normalzd Dopplr shft. V s th NM-dmnsonal spa-tm strng vtor for th th luttr path. V b a (16) dnots th Kronkr produt. Th luttr omponnt of th spa-tm snapshot s thn gvn by: X N V (17) 1 X s th NM-dmnsonal random vtor. s a omplx salar RV that aounts for th ampltud and phas of th th luttr path, V s th NM-dmnsonal spa-tm strng vtor for th th luttr path, and N s th total numbr of luttr paths n th so-rang rng. Th luttr spa-tm ovaran matrx s: R E X X H H N N E V V 1 1 N N 1 j1 E VV N 1 H j * H j j GVV (18) 168

6 whr G s luttr powr pr lmnt. G E for N (19) 2, 1,, 3.2. Mnmum varan of th luttr sptrum alulaton From th angl-dopplr strutur of ovaran matrx R, w an gt th 2-D(angl-Dopplr) powr sptrum(mnmum varan sptrum) [11]. 1 P(, f ) d H S (, f ) R S(, f ) (20) d d S(, f d ) s th NM-dmnsonal targt strng vtor spfyng th normalzd Dopplr and angl of ntrst. S S S (21) s t S s dnot th dsrd spatal strng vtor and S t th Dopplr omponnt. and T j2 fs j2 ( N1) fs Ss 1 (22) T j2 ft j2 ( N1) ft St 1 (23) whr fs dnot th spatal frquny of targt sgnal and f t th tm frquny. f s d os (24) 2V p ft os (25) f r d s spa of lmnt, s on angl. 4. Smulaton and analyss of spa-tm luttr Spa-tm luttr powr sptrum and luttr angl-dopplr ar th tools to study th haratrst of SBR s luttr and th prforman of STAP algorthms. In th followng, w wll smulat th luttr sptrum and luttr angl-dopplr of som typal onfguratons. Frst, Suppos that th spa-basd radars s low arth orbt (LEO) radar wth th hght of 500km, th orbt nlnaton angl s 65, Th longtud and lattud of th nadr pont ar (103, 35 ). Th 169

7 radar frquny s 1.15GHz, th antnna array s unform lnar array wth 16 lmnts, ah rv spatal hannl ollts 32 ohrnt puls, th PRF s 125 khz. Fgur 3(a) prsnts th spa-tm mnmum varan (MV) luttr sptrum, Fgur 3(b) prsnts th angl-dopplr tra. Not that th luttr nrgy s dstrbutd along a ln, and angl-dopplr tra s a dagonal. Du to th arth's rotaton, th ln of angl-dopplr tra on both sds s urvd. Th sptrum of SBR luttr vars wth th rang and shows non-stablty. (a) spa-tm luttr sptrum (b) angl-dopplr tra Fgur 3. Th spa-tm luttr sptrum wth PRF 125 khz If th spa-tm luttr sptrum of spa basd radar an b sam as fgur 3, th luttr supprsson usng STAP algorthms wll gt good rsults. Atually, th powr aprtur (PA) of spa basd radar s lmtd, and th targt s vry far away from th radar. Th slant rang btwn radar and targt s km wth th hght of 500km. So radar systm dsgnrs typally us a wd puls n ordr to dtt th far dstan targt. So, th PRF an t b hgh. At th sam tm th targt s spd and rang nd to b masur. But rang and Dopplr ar ambguty at targt dtton of long rang and vry fast spd as SBR applatons. Gnrally, SBR systms us mdum PRF wavforms to masur both targt rang and vloty auratly n th prsn of luttr. Suppos that th PRF s 30 khz, othrs smulaton paramtrs ar 170

8 sam as up. Fgur 4(a) prsnts th spa-tm mnmum varan (MV) luttr sptrum wth PRF 30kHz, Fgur 4(b) prsnts th angl-dopplr tra wth PRF 30 khz. Targt powr wll ompt wth luttr rdgs. SBR usng a sngl mdum PRF gnrats hghly ambguous rang and Dopplr data and suffrs from a numbr of blnd rgons n rang and vloty. Th non-stablty of luttr and th ambguty of rang and Dopplr wll dgrad STAP prforman sgnfantly and should b ompnsatd. (a) spa-tm luttr sptrum (b) angl-dopplr tra Fgur 4. Th spa-tm luttr sptrum wth PRF 30 khz 5. Conluson Ths papr ntrodus th luttr modl of SBR wth th onsdraton of arth's rotaton fft. Bas on th modl, w gt th spa-tm luttr sptrum and luttr angl-dopplr tras of sdlookng SBR. Th rsults gvn n ths papr may srv as a bass for omparson and a startng pont for th dsgn of luttr mtgaton algorthms. Furthrmor, th modl an b usd to hlp dsgnng SBR s paramtrs suh as orbt nlnaton, orbt hght and so on, to ahv bttr luttr mtgaton prforman. 171

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