An Effective Technique for Enhancing Anti-Interference Performance of Adaptive Virtual Antenna Array

Transcription

1 34 ACES JOURNAL VOL. 6 NO. 3 MARC 11 An Effctv Tchnqu for Enhancng Ant-Intrfrnc Prformanc of Adaptv Vrtual Antnna Array 1 Wnxng L 1 Ypng L 1 Ll Guo and Wnhua Yu 1 Collg of Informaton and Communcaton Engnrng arbn Engnrng Unvrsty arbn 151 Chna Elctromagntc Communcaton Lab Th Pnnsylvana Stat Unvrsty Unvrsty Park PA 168 Abstract - In ths papr w proposd an ffctv tchnqu to nhanc th ant-ntrfrnc prformanc of th adaptv antnna arrays. Th null dpth n th drcton of ntrfrrs dtrmns th ant-ntrfrnc prformanc of an adaptv antnna array. owvr th null dpth gnratd by th convntonal vrtual array transformaton (VAT) algorthm s usually not suffcnt. By ntroducng th ntrfrnc drcton nformaton nto th transformaton matrx w can ffctvly mprov th lvl of null dpth; n turn th ant-ntrfrnc prformanc of th adaptv antnna arrays s sgnfcantly nhancd. Th numrcal xprmnts ar mployd to valdat th proposd approach. Indx Trms - Bam formng null dpth SINR transformaton matrx vrtual array. I. INTRODUCTION Gnrally spakng th numbr of ntrfrnc sgnals procssd by an antnna array should b lss than th dgrs of systm frdom [1 ]. In th practcal applcatons th sz and numbr of array lmnts ar fnt; howvr frquntly th numbr of ntrfrrs s much largr than th numbr of array lmnts. Obvously som of th ntrfrrs wll not b ffctvly nhbtd whn th numbr of ntrfrrs xcds th dgrs of systm frdom. Frdlandr [3] has proposd a vrtual array transformaton (VAT) mthod that th numbr of vrtual array lmnts can b ncrasd to b mor than th dgrs of systm frdom so that all th ntrfrrs can b procssd. Whn Frdlandr s mthod s usd n th bam formng of an adaptv antnna array th null dpth s rlatvly shallow compard to th ral antnna array. Consquntly th output sgnal to ntrfrnc and nos rato (SINR) wll b dcrasd; n turn t s not sutabl for th applcatons that rqur th hghr communcaton qualty. Th xstng mprovmnt tchnqus wth rgardng to th VAT prformanc [4-6] ar concntratd on th applcatons n th stmaton of ntrfrnc arrvng drcton. Shubar t al. combnd th last man mxd norm (LMMN) algorthm and ntalzaton usng sampl matrx nvrson (SMI) to control th rror norms and offr th xtra dgrs of frdom [7]. In ordr to achv th bttr vrtual array prformanc th nflunc gnratd by th transformaton ara slcton on th bam formng s analyzd n th ltratur [8]. Th ltratur [9] proposd a mthod to transform an arbtrary shapd array nto a vrtual unform lnar array (ULA) and thn supprss multpl cohrnt ntrfrncs through th spatal smoothng tchnqu. Basd on th convntonal VAT bam formng algorthm an mprovd VAT mthod s prsntd n ths papr whch can b ffctvly appld to ras th nhbton gan by mprovng th null dpth. By projctng th transformaton matrx on th ntrfrnc spac that nhancs th ntrfrnc componnts n th vrtual covaranc matrx a hghr ntrfrnc nhbton gan can b achvd. II. VIRTUAL ARRAY TRANSFORMATION TEORY Consdrng an array wth N lmnts [1] whn M far fld narrow band sgnals ar ncdnt on an antnna array th rcvd data X can b xprssd as follows: X AS( t) N ( t) (1) ACES

2 LI LI GUO YU: TECNIQUE FOR ENANCING ANTI-INTERFERENCE PERFORMANCE OF ADAPTIVE VIRTUAL ANTENNA ARRAY 35 whr S() t [ s1() t s() t s ()] T M t s a vctor contanng th complx sgnal nvlops of M narrow-band sgnal sourcs. T dnots th matrx transposton. N() t [ n1() t n() t n ()] T N t s a vctor of zro-man spatally wht snsor nos of varanc n. A [ a( 1) a( ) a( M )] s an array manfold vctor whr a( k )( k 1 M) rprsnts a strng vctor n th k drcton. If an antnna array wth N lmnts s unform and lnar w hav: d d j sn k j( N1) snk T a( k ) [1 ] () whr d s th spac btwn two adjacnt lmnts. If both th sgnal and nos ar lnarly ndpndnt th data covaranc can b rprsntd as: s n R E X() t X () t AR A I (3) whr E() dnots th mathmatcal xpctaton. R S( )S s E t ( t) rprsnts th autocorrlaton matrx of sgnal complx nvlops. s th nos powr. I s th unt n matrx and dnots th matrx conjugat transposton. Th array covaranc matrx s stmatd usng th fnt snap data X () : K ˆ 1 R X() X () K 1 whr K s th snap numbr. In th array ntrpolaton opraton th ral array manfold s transformd on a prlmnary spcfd vrtual array manfold ovr a gvn angular sctor namly an ntrpolaton matrx B s dsgnd to satsfy: Ba( ) a ( ) (4) whr a ( ) and a ( ) ar N 1 and N 1 strng vctors of th ral and vrtual arrays rspctvly; N s th numbr of vrtual lmnts; vrtual array manfold a ( ) corrsponds to a unform lnar array (ULA). Th computaton of ntrpolaton matrx B s carrd out by choosng k rprsntatv drctons 1 k from th ntrpolaton sctor and mnmzng th sum of quadratc ntrpolaton rrors n ths drctons: k F( B) Ba( ) a( ) BAA (5) 1 whr A and A ar th ral and vrtual array manfold vctor matrxs rspctvly; and dnots th Frobnus mold. Th F optmal mnmum varanc obtand from (5) s: 1 B AA ( AA ). (6) Aftr transformaton th covaranc of vrtual array bcoms: R BRB. (7) Through th nos-prwhtnng procss [3] th optmal wght can b obtand by usng th mnmum varanc dstortonlss rspons mthod: 1 Wopt R a ( ) (8) whr a ( ) rprsnts a vrtual array strng vctor n th dsrd sgnal drcton; and th 1 1 coffcnt a ( ) R a ( ). III. NULL DEEPENING TECNIQUE Compard to th ral array wth th sam paramtrs th null dpth formd by a vrtual array n th Frdlandr s VAT mthod s rlatvly shallow. To mprov th null dpth w projct th transformaton matrx B on th ntrfrnc spac and thus th constrant nformaton of th ntrfrnc drcton can b mportd nto th transformaton matrx to nhanc th ntrfrnc componnts n th samplng covaranc matrx. Th dtald procdur s dscrbd as follows: If th ntrfrnc drctons ar and th numbr of ntrfrrs s 1 M M th vrtual array strng vctor n th ntrfrr drctons a( 1) a( ) a( ) M can b calculatd. Dfn a projcton matrx C as: M C ( ) ( ). a a (9) 1 Projctng th transformaton matrx on th ntrfrnc spac w hav: B CB. (1) Now th covaranc matrx of vrtual array bcoms: R BRB CBRB C CRC. (11) F

3 36 ACES JOURNAL VOL. 6 NO. 3 MARC 11 Aftr th mathmatcal opratons th nformaton of th ntrfrnc drcton has alrady bn nvolvd n th transformd vrtual covaranc matrx R and th ntrfrnc componnts s strngthnd. IV. TEORETICAL ANALYSIS Accordng to Schmdt s orthogonal subspac rsoluton thory usng th gnvalu dcomposton from (7) R can b xprssd as [11]: R UΣU (1) whr U s an gnvctor vctor of covaranc matrx R th dagonal matrx Σ consttutd by th corrspondng gnvalus s: 1 Σ. N (13) If a vrtual array wth N lmnts s ULA th strng drctons can b wrttn as: d d j sn j( N1) sn T a( ) [1 ] (14) whr d s th spac btwn two adjacnt lmnts. W hav: 1 j dsn jdsn ( 1) d j N sn a( ) a ( ) [1 ]. jn ( 1) dsn jdsn ( 1) sn 1 j N d jdsn dsn ( 1 1) d j j N sn j( N 1) dsn ( 1 1) sn ( 1) j N d dsn j N (15) Substtut (15) nto (9) w can obtan th xprsson of projcton matrx C : M M 1 1 C a( ) a ( ) jdsn ( 1) d j N sn 1 jdsn dsn ( 1 1) d j j N sn Substtut (1) and (13) nto (11) thn w hav: jn ( 1) dsn ( 1 1) sn ( 1) jn d d j N sn 1. N R CRC C UΣU C C U U C Substtut C nto (17) R can b xprssd as:.. (16) (17)

4 LI LI GUO YU: TECNIQUE FOR ENANCING ANTI-INTERFERENCE PERFORMANCE OF ADAPTIVE VIRTUAL ANTENNA ARRAY 37 jdsn ( 1) sn 1 j N d 1 M jdsn dsn ( 1 1) d j sn j N U U 1 jn ( 1) dsn ( 1 1) dsn ( 1) d jn sn j N N R M 1 jdsn ( 1) d j N sn 1 jdsn dsn ( 1 1) d j j N sn jn ( 1) dsn jn ( 1 1) dsn ( 1) d j N sn (18) can b furthr smplfd as: M 1 jdsn jd sn 1 1 M j( N 1) dsn j( N 1) d sn 1 M 1 N R U U UΣ U 1 U N U whr U s th gnvctor matrx 1 corrspondng to R Σ s N th dagonal matrx consttutd by th gnvalus of R. From (19) t s obvously obsrvd: 1 N. () Th gnvalus of th covaranc matrx obtand by usng th mprovd VAT algorthm ar bggr than thos obtand from th convntonal VAT algorthm. Nxt w brfly ntroduc th mnmum varanc dstortonlss rspons (MVDR) bam formng mthod [1]. In th drcton of (18) (19) th dsrd sgnal th gan s constrand to b 1 and th array output powr s nsurd to b mnmum namly th ntrfrnc and nos wll gnrat th mnmum output powr. Appld to th vrtual array th wght vctor of th MVDR bam formng s th soluton to th followng problm: WMVDR arg mn EW X( k) W a( ) 1 arg mn W RW (1) whr th W a( ) 1 arg W a( ) 1 mn rprsnts th optmal soluton whch can mnmz th functon valu n and satsfy th qualty W a ( ) 1. Th arg rprsnts an nvrs functon. It can b solvd usng Lagrangan multplr mthod:

5 38 ACES JOURNAL VOL. 6 NO. 3 MARC 11 1 R a( ) WMVDR 1 a ( ) R a( ) whch s quvalnt to (8). Th charactrstc of th MVDR mthod n th dsrd sgnal drcton s that th gan s rstrand to b 1 and th smultanously array output powr s nsurd to b mnmum. Th hghr th ntrfrnc powr n array s th strongr t s nhbtd n ths drctons. By ntroducng th constrant nformaton of th ntrfrnc drcton nto th transformaton matrx B n th mprovd VAT algorthm th nw gnvalus of th covaranc matrx bcom bggr and th sgnal componnts corrspondng to thm ar strngthnd. Thrfor n ths drctons th nhbton gans wll ncras by th th MVDR mthod namly th null dpths wll b dpr as showd n th bam pattrn. V. SIMULATION VERIFICATION Th orgnal array wth 5 lmnts s unform and lnar and th lmnt spac s. Th xpctd sgnal llumns from th drcton. Th sgnal to nos rato s SNR=dB. Thr ndpndnt ntrfrrs com from -6-4 and 5 drctons rspctvly. Th sgnal to ntrfrnc rato s SIR 4dB. Th vrtual array wth 8 lmnts s unform and lnar and th lmnt spac s /. Th vrtual transformaton ara s [ ]. Th stpsz s.1. Th numbr of snapshots s. Fgur 1 shows th gan comparson obtand by usng th MVDR bam formng through th ral array mthod th convntonal and mprovd VAT algorthms. Fgur shows th gnvalu comparson of covaranc matrx obtand usng thr mthods. Fgur 3 shows th comparson of output SINR obtand by thr mthods. Gan (db) Ral array mthod Convntonal VAT algorthm Improvd VAT algorthm Azmuth Angl(dgr) Fg. 1. Bam pattrns usng th dffrnt mthods. It s obsrvd from Fgurs 1 to 3 that whn th numbr of ndpndnt ntrfrrs s not largr than th numbr of th array lmnts th nulls of th bam formng usng th ral array convntonal VAT and th mprovd VAT algorthm ar gnratd prcsly n th ntrfrr drctons and th man lob s pontd to th dsrd sgnal drcton. Th nhbton gan usng th ral array and convntonal VAT algorthms s about -35 db and -45 db rspctvly. owvr th nhbton gan usng th proposd algorthm can rach up to -15 db. Th gnvalu of th covaranc matrx has bn sgnfcantly mprovd n th proposd mthod. Smlarly th output SINR has bn sgnfcantly mprovd as wll n th proposd mthod. Egnvalu(dB) Ral array mthod Convntonal VAT algorthm Improvd VAT algorthm Indx Fg.. Egnvalus of th covaranc matrx n th dffrnt mthods.

6 LI LI GUO YU: TECNIQUE FOR ENANCING ANTI-INTERFERENCE PERFORMANCE OF ADAPTIVE VIRTUAL ANTENNA ARRAY Gan (db) Ral array mthod Convntonal VAT algorthm Improvd VAT algorthm Azmuth Angl(dgr) Fg. 3. Output SINR usng th dffrnt mthods. Nxt w us an xampl to valdat th proposd mthod n whch th orgnal array wth 5 lmnts and spac btwn th adjacnt lmnts s unform and lnar. Th dsrd sgnal ncdnc coms n th drcton. Th sgnal to nos rato s SNR db and fv ndpndnt ntrfrrs com n and 7 drctons rspctvly. Th sgnal to ntrfrnc rato s SIR 4dB. Th vrtual array wth 8 lmnts and spac /btwn th adjacnt lmnts s unform and lnar. Th vrtual transformaton ara s [ ] and th stp sz s.1. Th numbr of snapshots s. Fgur 4 shows th comparson of th MVDR bam formng usng th dffrnt mthods. Fgur 5 shows th gnvalu comparson of th covaranc matrx usng th thr mthods. Fgur 6 shows th comparson of output SINR usng thr mthods. Gan (db) -5-1 Ral array mthod Convntonal VAT algorthm Improvd VAT algorthm Azmuth Angl(dgr) Fg. 4. Bam formng of fv ndpndnt ntrfrrs usng th dffrnt mthods. Egnvalu(dB) Ral array mthod Convntonal VAT algorthm Improvd VAT algorthm Indx Fg. 5. Egnvalus of fv ndpndnt ntrfrrs usng th dffrnt mthods. Gan (db) 5 Ral array mthod Convntonal VAT algorthm Improvd VAT algorthm Azmuth Angl(dgr) Fg. 6. Output SINR of fv ndpndnt ntrfrrs usng th dffrnt mthods. It s obsrvd from Fgs. 4 to 6 that whn th numbr of ntrfrrs xcds th frdom of orgnal array th nulls n th ral array mthod cannot b gnratd n ths ntrfrnc drctons. Th vrtual array wth 8 lmnts cannot procss all th ntrfrrs but th nulls prcsly pont to ths ntrfrrs. Th nhbton gan usng th convntonal and proposd VAT algorthms s about -3 db -1 db rspctvly. Th gnvalu of th mprovd algorthm has sgnfcantly mprovd as wll as th SINR. VI. CONCLUSIONS An mprovd VAT mthod has bn prsntd n ths papr compard wth th convntonal approach; th null prformanc of bam formng s sgnfcantly mprovd. Th nulls pontng to ntrfrnc drctons can b mor stadly gnratd and ntrfrnc nhbton gans ar much bttr and nsur a hghr output SINR. Compard to

7 4 ACES JOURNAL VOL. 6 NO. 3 MARC 11 th convntonal algorthm th proposd mthod only nds on mor matrx multplcaton opraton. REFERENCES [1] M. Zatman Dgr of Frdom Archtcturs for Larg Adaptv Arrays Confrnc Rcord of th Aslomar Confrnc on Sgnals Systms and Computrs vol. 1 pp [] R. Gams and R. Wllams Prformanc Analyss of a Concurrnt Adaptv Last- Squars Sdlob Cancllaton Systm wth Excss Dgrs of Frdom IEEE APS Int Symp Dg. vol. 1 pp [3] B. Frdlandr Th Root-Musc Algorthm for Drcton Fndng wth Intrpolatd Arrays Sgnal Procssng vol. 3 no. 1 pp [4] P. ybrg M. Jansson and B. Ottrstn Array Intrpolaton and Bas Rducton Sgnal Procssng vol. 5 no. 1 pp [5] M. Gavsh and A. Wss Drcton Fndng Usng Esprt wth Intrpolatd Arrays IEEE transactons on Sgnal Procssng vol. 39 no. 6 pp [6] M. Psavnto A. Grshman and Z. Luo. Robust Array Intrpolaton Usng Scond Ordr Con Programmng IEEE Sgnal Procssng Ltt vol. 9 no. 1 pp [7] R. Shubar S. Jmaa and A. Omar Robust Adaptv Bamformng Usng Last Man Mxd Norm Algorthm Appld Computatonal Elctromagntc Socty (ACES) Journal vol. 3 no. 3 pp [8] S. Baow Robust Adaptv Bam Formng Va Array Transformaton IEEE AP-S Intrnatonal Symposum on Antnnas and Propagaton DC USA vol. 1B pp [9] T. L and T. Ln Adaptv Bam Formng wth Intrpolatd Arrays for Multpl Cohrnt Intrfrrs Sgnal Procssng vol. 57 no. pp [1] K. Rddy and V. Rddy Analyss of Intrpolatd Arrays wth Spatal Smoothng Sgnal Procssng vol. 54 no. 3 pp [11] R. Schmdt Multpl Emttr Locaton and Sgnal Paramtr Estmaton IEEE Trans on Antnnas and propagaton vol. 34 no. 3 pp [1] M. Soudn and J. Bnsty A Study of th LCMV and MVDR Nos Rducton Fltrs IEEE Transactons on Sgnal Procssng vol. 58 no. 3 pp