MUSIC Based on Uniform Circular Array and Its Direction Finding Efficiency

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1 Intrnatonal Journal of Sgnal Procssng Systms Vol. 1, No. 2 Dcmbr 2013 MUSIC Basd on Unform Crcular Array and Its Drcton Fndng Effcncy Baofa Sun Dpartmnt of Computr Scnc and Tchnology, Anhu Sanlan Unvrsty, Hf, Chna Emal: sunbaofa@sohu.com Th wav-lngth of short-wav sgnal usd n th wrlss communcaton s usually n mtr grad or tn-mtr grad. Thrfor, th lngth of ULA for DF of short-wav sgnal approachs tns of mtrs or vn hundrds of mtrs. Somtms, th numbr and th dstanc of antnnas should b ncrasd to fnd th drctons of sgnals mor accuratly. Ths wll ncras th array lngth furthr. For so long array, t s dffcult to rman th array unform lnar n battlfld. Evn n stratgy DF, th unqual lngths of fdback lns of antnnas wll mak channl nconsstnt or unbalancd and thus arous DF rror although t s possbl to choc a nat and spacous plac. On th othr hand, snc th lctromagntc wavs travlng along th ground fad rapdly, rsarchrs hop to lft th transmttng or rcvng antnnas,.. to us arborn or spac born lctronc support systm. Lt th mttng powr of rado wav s 10W, th snstvty of lctronc support systm s 1~5 µv/m, thn rado sgnal travlng along th ground can b dtctd by groundbasd lctronc support systm n 10km. Whras ar to ar ntrcpton rang for ths sgnal s mor than 150km. Furthrmor, arborn lctronc support systm can b clos to or vn dp nto th nmy battlfld. So arborn lctronc support systm can gratly mprov SNR, and thn mprov DF accuracy. Howvr, t s unthnkabl to layout ULA mor than tns of mtrs or vn hundrds of mtrs n an arcraft (spcally small UAV) or n a satllt. MUSIC basd on ULA can not fnd 2-D drctons of sgnals. Rado communcaton sgnals can arrv at rcvr through onosphr rflcton n short-wav band, so th DF must jontly masur th azmuth and lvaton of a sgnal. Thrfor, th array structur can't b straght ln, but should b plan array or thr-dmnsonal array. In vw of th waknss of lnar antnna array, t s ncssary to consdr som othr array structurs, such as crcular array. Compard wth lnar array, th sz of crcular array can b fxd. For a crcumfrnc wth th fxd radus, th numbr of antnnas whch ar arrangd n t s flxbl. Furthrmor, to ncras th numbr of antnnas dos not ncras th sz of th array. Crcular array wth 8 antnnas s commonly appld to DF. Th mathmatcal modl of crcular array wth 8 antnnas s shown n Fg. 1. Eght antnnas ar arrangd Abstract Th mathmatcal modl of unform crcular array was stablshd and som smulaton xprmnt systms wr constructd. Th drcton fndng ffcncy of MUSIC basd on unform crcular array was studd by smulaton xprmnts. Thn MUSIC basd on unform crcular array was compard wth MUSIC basd on unform lnar array. Th conclusons ar as followng. Two knds of MUSIC can fnd th drctons of ndpndnt sgnals and thr DF accuracy s clos. Thy all cannot fnd th drctons of cohrnt sgnals. Th advantag of MUSIC basd on UCA: th array sz s smallr; t s asr to ncras antnna to mprov th DF accuracy; th angl dstngushng ablty of sgnals s hghr; thr s nthr mag vagunss nor aprtur vagunss. Th waknss of MUSIC basd on UCA: t cannot lmnat th cohrnc of cohrnt sgnals; th ablty to fnd th drcton of wak sgnal s poorr. Indx Trms unform crcular array, unform lnar array, MUSIC, smulaton, drcton fndng I. INTRODUCTION TO MUSIC BASED ON UCA Rf. [1] dscussd th MUSIC for drcton fndng (DF) of ndpndnt wavs, Rf. [2] dscussd th Smoothng algorthm for drcton fndng of cohrnt sgnals and Rf. [3] dscussd matrx dcomposng algorthm for pr-stmaton of numbr and cohrnt stat of sgnals. Abov thr algorthms ar all basd on unform lnar array (ULA). Thortcal analyss and smulaton xprmnt rsults ndcatd that ULA was abl to complt th task of multpl mttr drcton fndng and prstmaton of numbr and cohrnt stat of sgnals. Th structur of ULA s smpl and mathmatcally modlng basd on ULA s asy. Bcaus of ths advantags, rsarchrs wll choos ULA at frst whn thy dsgn and layout antnna array. Howvr, ULA s not prfct. Th waknss s manly manfstd n th followng two aspcts. Th array s too long. Suppos a lnar array s composd of N antnnas, th dstanc of two adjacnt antnnas s d, thn th array lngth s (N1)d. Th array for DF s usually consttutd wth mor than 8 antnnas, and th dstanc of two adjacnt antnnas s gnrally half a wav-lngth. Manuscrpt rcvd August 28, 2013; rvsd Novmbr 16, 2013 Anhu Provnc Natural Scnc Fund Projct: J2013B Engnrng and Tchnology Publshng do: /jsps

2 Intrnatonal Journal of Sgnal Procssng Systms Vol. 1, No. 2 Dcmbr 2013 n a horzontal crcl wth th radus of d unformly, th north antnna s numbrd as 0, th ls antnnas ar numbrd as 1~ clockws. At frst, w consdr th nductd voltag of on sgnal at ach antnna. For smpl, w just fnd th azmuth of sgnal,.. suppos th lvaton of sgnal to b 90. Fgur 1. Th unform crcular array wth 8 antnnas Lt th sgnal at th cntr O of th crcl s s (. Connct th cntr O wth th th antnna and gan th ln O ( 0,1, 2,,. Th angl from th wav vctor P to O0 s. Mark as th angl from P to O, thn 45. Th phas dffrnc btwn th sgnal rcvd by th th antnna and s ( s ( 2d / )cos ( 0,1,,, so th sgnal rcvd by th th antnna s thn th array nducton voltag vctor can b xprssd as followng X ( a( ) s ( a( ) s ( N( 1 1 A( ) S( N( Th stps of MUSIC basd on unform crcular array (UCA) s as followng: at frst, rcord th array nducton voltag vctor X(; scondly, calculat th array covaranc matrx; thrdly, dcompos th array covaranc matrx basd on gnvalu; fourthly, construct th spatal spctrum functon; and fnally, sarch azmuth angls along th spatal spctrum and gt th drctons of sgnals. Ths stps ar xactly sam as th MUSIC basd on ULA, so w shall not rlat thm any mor. II. INTRODUCTION TO SIMULATION SYSTEM OF MUSIC BASED ON UCA Th smulaton systm of MUSIC basd on UCA conssts of sx moduls, such as sgnal transmttr, channl, UCA, rcvr, MUSIC and th rsults dsplay. Ths moduls form a complt smulaton systm of MUSIC basd on UCA accordng to th logc squnc, as shown n Fg. 2. 2d j j cos s( ( 0,1,,. x ( s( In gnral, suppos sgnals ar narrowband plan wavs whch ar mutually ndpndnt, and mark : th wavlngth of sgnals,,,, 1 2 : th drctons of sgnals, 45 ( k 1, 2,, ; 0,1,, k k : th angl from O to th wav vctor of th kth sgnal, k (2d / ) cos k : th phas dffrnc of th kth sgnal btwn th sgnal rcvd by th th antnna and s k (, a ( ) jk jk jk T ) (,,, :th drc-ton k vctor of th kth sgnal, A( ) a( 1),, a( ) sgnals, S ( s (,, s ( 1 T : th drcton matrx of : th sgnal vctor of sgnals at th cntr O of th crcl, n antnna, ( ( 0,1,, N n (, n (,, n ( ( rcvd by th array, X x (, x (,, x ( ( : th nos rcvd by th th T T : th nos vctor : th array nducton voltag vctor rcvd by th array, Fgur 2. Th smulaton systm of MUSIC basd on UCA III. SIMULATION ANALYSES OF DF EFFICIENCY OF MUSIC BASED ON UCA In followng xprmnts, th radus of UCA s 1.0λ, th sarch stp of MUSIC s 0.1 and th nos ntnsty s -12dB xcpt for spcal dclar. A. DF Effcncy of Indpndnt Sgnals Th smulaton systm ntrfac of MUSIC for ndpndnt sgnals DF s shown n Fg.2. In th smulaton systm, t s possbl to fnd drctons of 1, 2, 3 or 4 sgnals by sttng th ntnsty of som sgnals to b 0. In four xprmnts, th sgnals ar ndpndnt for thr modulaton mods ar dffrnt. Th sgnal paramtrs and DF rsults of four xprmnts ar shown n Tabl I. Th xprmnt rsults ndcat that MUSIC basd on UCA can fnd th drctons of 1, 2, 3 or 4 ndpndnt sgnals accuratly, so MUSIC basd on UCA has th functon of fndng th drctons of ndpndnt sgnals. Exprmnt 1 shows that MUSIC basd on UCA can fnd th drcton of on sgnal Engnrng and Tchnology Publshng 24

3 Intrnatonal Journal of Sgnal Procssng Systms Vol. 1, No. 2 Dcmbr 2013 TABLE I. THE SIGNAL PARAMETERS AND SIMULATION RESULTS OF INDEPENDENT SIGNALS Sgnal paramtrs DF rsults Sgnal Modulaton mod Ampltud Angl( ) Angl( ) Pak valu DF rrors 1 1 2AS AS BPS AS BPS QPS AS BPS QPS BFS B. Angl Dstngushng Ablty Two smulaton xprmnts ar to nvstgat th angl dstngushng ablty of two ndpndnt sgnals. Th sarch stp of MUSIC s 1.0. Th sgnal paramtrs and DF rsults of two xprmnts ar shown n Tabl II. Tabl II shows that th angl dstngushng ablty of two ndpndnt sgnals of MUSIC basd on UCA rachs to 2 at last and 1 at most whn th sarch stp s 1.0. Whras th smulaton xprmnts showd that th angl dstngushng ablty of two ndpndnt sgnals of MUSIC basd on ULA rachd to 5 at last and 4 at most. So th angl dstngushng ablty of MUSIC basd on UCA s hghr than MUSIC basd on ULA. It must b pontd out that th angl dstngushng ablty s rlatd to th sarch stp. Th angl dstngushng ablty wll b hghr whn th sarch stp s lss. So w can mprov th angl dstngushng ablty of MUSIC basd on UCA by dcrasng th sarch stp whn ncssary. TABLE II. THE ANGLE DISTINGUISHING ABILITY OF MUSIC BASED ON UCA 1 2 Sgnal paramtrs DF rsults Sgnal Modulaton mod Ampltud Angl( ) Angl( ) Pak valu DF rrors 1 2AS BPS AS BPS C. Mrror Imag Vagunss MUSIC basd on ULA has th problm of mrror mag vagunss. In ordr to solv th problm, MUSIC basd on orthotropc ULAs should b usd [2]. For two antnna arrays, MUSIC sarchs th angl n (-90, 90 ) accordng to dfnd stp rspctvly, and dtrmns th drctons of sgnals by skng th sam angls of two sts of angls found. Th spctrum curv of MUSIC basd on ULA n (-90, 90 ) s symmtrcal wth th curv n (90, 20 ), thrfor, t s not ncssary to sarch n (-90, 20 ), t s nough to sarch only n (-90, 90 ). By ths way, th sarch rang of MUSIC basd on sngl ULA s rducd by half. Durng th smulaton xprmnt, MUSIC basd on two ULAs sarch th angl at th sam tm, thn th tm of smulaton xprmnt can b rducd on tm by paralll procssng tchnology. Th smulaton rsults show that MUSIC basd on UCA dos not hav th problm of mrror mag vagunss. Durng th smulaton xprmnt, th sarch rang of MUSIC basd on UCA s not (-90, 90 ), but (- 90, 20 ). Thrfor, th sarch rang s doubl to MUSIC basd on ULA, so th sarch tm s doubld. Undr th sam smulaton nvronmnt and wth th sam lctromagntc paramtrs, th runnng tm of MUSIC basd on UCA s narly doubl to MUSIC basd on orthogonal ULAs. D. Aprtur Vagunss MUSIC basd on ULA has th problm of aprtur vagunss. Aprtur vagunss occurs whn th dstanc of two adjacnt antnnas s larg than 0.5λ. Hr, w study whthr MUSIC basd on UCA has th problm of aprtur vagunss by smulaton xprmnt. Th mthod s to obsrv th spctrum curv changng wth th chang of radus of UCA. Th lctromagntc nvronmnts of sx xprmnts ar sam. On sgnal s 2AS modulaton, drcton angl s ; anothr sgnal s BPS modulaton, drcton angl s 5.0. Th ampltuds of two sgnals ar all 5.0. Th xprmnt rsults ar shown n Tabl III. Tabl III shows that th accuracy of DF mprovs gradually wth th radus of UCA ncrasng, and thr s no vagunss angl. Thrfor, MUSIC basd on UCA dos not hav th problm of aprtur vagunss Engnrng and Tchnology Publshng 25

4 Intrnatonal Journal of Sgnal Procssng Systms Vol. 1, No. 2 Dcmbr 2013 TABLE III. THE EXPERIMENT RESULTS OF MUSIC BASED ON UCA WITH DIFFERENT RADIUSES Radus Angls of DF( ) Errors of DF( ) Avrag rror( ) 1 0.1λ λ λ λ λ λ E. Influnc of SNR on DF Accuracy Abov smulaton xprmnts ar carrd out at -12dB nos ntnsty. Nxt, w do th smulaton xprmnt of MUSIC basd on UCA at dffrnt SNR. Th lctromagntc nvronmnts of sx xprmnts ar sam. On sgnal s 2AS modulaton, drcton angl s ; anothr sgnal s BPS modulaton, drcton angl s 5.0. Th xprmnt rsults ar shown n Tabl IV. Th avrag rrors of MUSIC basd on ULA ar lstd at th last column to compar MUSIC basd on UCA wth MUSIC basd on ULA. It s asy to fnd from Tabl IV that, th DF accuracy of MUSIC basd on UCA dcrass wth th dcras of SNR. Whn SNR s lowr than -3dB, th DF rror s mor than 1 for som sgnals. Compar th last two columns of TAB. IV and t can b found that, at th sam SNR, thr s not much dffrnc btwn th avrag rrors of two knds of MUSIC, thr DF accuracs ar smlar. TABLE IV. THE EXPERIMENT RESULTS OF MUSIC BASED ON UCA AT DIFFERENT SNR SNR(dB) Angls of DF( ) Errors of DF( ) Avrag rror( ) Avrag rror( ) of MUSIC basd on ULA F. Influnc of Sgnal Intnsty on Pak Valu of Spctrum Curv Sgnal ntnsty nfluncs th pak hght of spctrum curv. Whn sgnal nhancs, th pak hght ncrass; othrws, th pak hght dcrass. In th smulaton xprmnts of MUSIC basd on ULA, th sgnal ampltuds wr st as 1.0. Whn SNR (db) 0, th pak hght corrspondng to th sgnal was n 10 4 ordrs, th pak hght of spctrum curv corrspondng to th sgnal was rathr hgh. In abov smulaton xprmnts of MUSIC basd on UCA, th sgnal ampltuds ar nhancd to 5.0. Th rason s that, for MUSIC basd on UCA, th pak hght of spctrum curv corrspondng to th sgnal s usually low. In ordr to ras th pak hght, t s ncssary to nhanc th sgnal ampltuds. Smulaton rsults show that, undr th sam paramtrs, th pak valu of MUSIC basd on UCA s smallr two ordrs than MUSIC basd on ULA. Why s th pak valu of MUSIC basd on UCA smallr than MUSIC basd on ULA? It can b xpland by th array structur. For ULA, lt th nducton potntal at th frst antnna s s (, thn th nducton s( 2 ( 1) d j sn potntal at th th antnna s, namly th nducd potntal at ach antnna s th nducd potntal at th formr antnna multpld by th factor j 2d sn. Ths rgularty strngthns th sgnal n th array. For UCA, th nducton potntal at ach antnna dos not own such rgularty. Th rrgular varaton of phas maks th sgnal of ach antnna not b strngthnd, mayb b offst ach othr. Th total ffct s that th sgnal rducs. Th rsults rflctng to spctrum curv s that th pak hght of spctrum curv s rlatvly low. Th pak valu of MUSIC basd on UCA s small. Ths fact mans that th ablty of MUSIC basd on UCA to fnd th drcton of wak sgnal s poor, bcaus th pak valu corrspondng to th wak sgnal s vry small, t s fltrd out asly. G. DF Ablty of Cohrnt Sgnals Fgur 3. Th smulaton systm of MUSIC and Smoothng algorthm basd on UCL 2013 Engnrng and Tchnology Publshng 26

5 Intrnatonal Journal of Sgnal Procssng Systms Vol. 1, No. 2 Dcmbr 2013 Th smulaton systm of MUSIC and Smoothng algorthm basd on UCA s shown as n Fg.3. Th modulaton mod of two sgnals s BPS, and th ampltud of two sgnals s 5.0. Th drcton of on sgnal s 45 and th drcton of anothr sgnal s 0. Snc th frquncy and modulaton mod of two sgnals ar sam, two sgnals ar cohrnt sgnals. Run smulaton program, th smulaton rsult of MUSIC s as shown n Fg. 4 and th smulaton rsult of Smoothng algorthm s as shown n Fg. 5. Th xprmnt rsults ndcat that MUSIC and Smoothng algorthm basd on UCA arn t abl to fnd th drctons of cohrnt sgnals. Fgur 4. Th smulaton rsult of MUSIC basd on UCA Two knds of MUSIC ar n common: thy all hav th DF functon of sngl sgnal; thy all hav th DF functon of multpl ndpndnt sgnals; th DF accuracy s rlatd to many factors such as SNR, th sarch stp lngth, th dstanc of two adjacnt antnnas, th numbr of antnnas; th DF accuracy of two knds of MUSIC s clos n th sam lctromagntc fld; thy all can not fnd th drctons of cohrnt sgnals. Th advantag of MUSIC basd on UCA: th array sz s smallr; t s asy to ncras antnna to mprov th DF accuracy; th angl dstngushng ablty of sgnals s hghr than MUSIC basd on ULA; thr s no mag vagunss; thr s no aprtur vagunss. Th waknss of MUSIC basd on UCA: ULA can lmnat th cohrnc of cohrnt sgnals by spatal smoothng tchnqu, but UCA can not drctly lmnat th cohrnc of cohrnt sgnals, vn can not lmnat th cohrnc of cohrnt sgnals by spatal smoothng tchnqu. Ths s th most srous dfct of UCA. Th ablty of MUSIC basd on UCA to fnd th drcton of wak sgnal s poor compard wth MUSIC basd on ULA. In summary, w rcommnd MUSIC basd on UCA n arborn DF systm for th followng rasons. At frst, t s asr to arrang th crcular array on an arcraft or a satllt. Scondly, th sgnals wth sam frquncy ar ndpndnt for aral rflctors around th antnna ar fwr, ths avod th dfct of MUSIC basd on UCA. Fnally, th hgh SNR of arborn antnnas can hghtn th spctrum pak, and ncras probablty of sgnal captur. REFERENCES Fgur 5. Th smulaton rsult of Smoothng algorthm basd on UCA Rf. [4] pontd out that w could fnd th drctons of cohrnt sgnals basd on UCA and th mthod was as followng: carry on Smoothng to th mod spac of UCA and gan th rvsd matrx; apply MUSIC to th rvsd matrx and stmat th drctons of cohrnt sgnals. Rf. [5] put forward anothr mthod to fnd th drctons of cohrnt sgnals. For UCA, whn th antnna numbr s larg nough, do dscrt Fourr transform to th mod spac and turn t nto th form of ULA, thn apply Smoothng algorthm basd on ULA to dstngush cohrnt sgnals. Howvr, ths mthods ncrasd DF complcatons, thrfor, UCA s wors than ULA for dstngushng cohrnt sgnals. IV. CONCLUSIONS Th DF smulaton systm of MUSIC basd on UCA s constructd. Th ffcncy of MUSIC basd on UCA and MUSIC basd on ULA ar summarzd as follows accordng to th smulaton xprmnt rsults. [1] B. F. Sun and Z. X. Sh, Smulaton study of spatal stmaton, Radar and ECM, Srs no. 140, no. 3, pp. 9-13, Sp (n Chns) [2] B. F. Sun, MUSIC basd on orthotropc ULAs for dtrmnng undrctonal DOAs, n Proc. ITA2013, Chngdu, (n prss) [3] B. F. Sun, Smulaton study of stmaton of numbr and cohrnt stat of sgnals, Computr and Informaton Tchnology, Srs no. 136, no. 1, pp , Jan (n Chns) [4] Y. L. Wang, H. Chn, Y. N. Png, and Q. Wan, Thory and Algorthm of Spatal Estmaton, 1st d. Pkng, Chna: Tsnghua Unvrsty Prss, 2004, ch. 11, pp (n Chns) [5] X. C. Xao, Array sgnal procssng wth EW applcaton: Ystrday, today and tomorrow, Elctronc Warfar, Srs no. 94, no. 1, pp. 1-, Jan (n Chns) Baofa Sun was born n Hf, Abhu, Chna on Nov Mastr of Scnc was arnd n Anhu Unvrsty n 1996, Ph. D. of sgnal and nformaton procssng was arnd n Elctronc Engnrng Insttut of PLA n H workd n Elctronc Engnrng Insttut as a tachr from 1996 to 2008, n Hf Insttut of Fnanc and Economcs as th Dan of Engnrng Collg from 2008 to 2010; n Anhu Sanlan Unvrsty as a tnurd assocat profssor snc H took charg of and compltd 3 projcts of unvrsty lvl, partcpatd n 4 projcts of provncal lvl as man rsarchr. H publshd mor than 50 paprs. H publshd two books: Applcaton of Thory (Pkng: Educaton and Cultur Prss of Chna, 2006) and A Concs Cours of Computr Applcaton Bass (Dalan, Laonng: Dalan Unvrsty of Tchnology Prss, 2011). Hs currnt rsarch ntrsts ar ncludng computr applcaton, communcaton systm smulaton, mbddd systm and ntrnt of thngs. Dr. Sun s th xcutv drctor of Anhu Provncal Assocaton of Houshold Applancs. Mor than tn paprs of Dr. Sun won outstandng papr awards Engnrng and Tchnology Publshng 2