Comparison of Conventional Subspace-Based DOA Estimation Algorithms With Those Employing Property-Restoral Techniques: Simulation and Measurements

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1 'EEE CUPC' 96, Cambridg, MA, Sptmbr 29 - Octobr 2, 1996 Comparison of Convntional Subspac-Basd DOA Estimation Algorithms With Thos Employing Proprty-Rstoral Tchniqus: Simulation and Masurmnts Rias Muhamd and Thodor S. Rappaport Mobil and Portabl Radio Rsarch Group Bradly Dpartmnt of Elctrical Enginring Virginia Polytchnic nstitut and Stat Univrsity Blacksburg, VA 2461, USA Abstract: n this papr w compar th prformanc of convntional subspac-basd dirction-of-arrival (DOA) stimation tchniqus such as ESPRT and MUSC with th intgratd approachs that combin th constant modulus algorithm with subspac-basd tchniqus. Simulatd and masurd rsults ar prsntd for a varity of signal conditions. Th intgratd approach was found to prform significantly bttr than th convntional ESPRT approach. Also, multipath prsnt in th channl significantly dgrads th prformanc of th DOA stimation algorithms, and this has bn confirmd by masurmnt and ray tracing simulation. This work has application to smart antnnas and position location.. NTRODUCTON Dirction-of-arrival (DOA) stimation has bn an activ ara of rsarch. With th rapidly growing intrst in smart antnnas, DOA stimation has gaind importanc in wirlss communications. DOA stimation tchniqus can b usd for dtrmining th spatial-tmporal multipath structur of radio channls and has application to position location. n this papr w compar th prformanc of two diffrnt approachs to DOA stimation - th subspac-basd approach. and th intgratd approach that combins th trativ Last Squars Projction-basd Constant Modulus Algorithm (LSP-CMA) with subspac-basd tchniqus. A mor dtaild comparison is mad btwn two spcific algorithms - th TLS-ESPRT algorithm and th intgratd LSP-CMA with TLS-ESPRT algorithm. ll. BACKGROUND This sction. provids a brif ovrviw of th algorithms compard in this papr. Subspac-basd algorithms ar high rsolution tchniqus which xploit th ign-structur of th input data or covarianc matrix. Th MUSC algorithm proposd by Schmidt [ 1] was on of th frrst to xploit th structur of th input data matrix for th cas of arrays of arbitrary gomtry. Th ESPRT algorithm dvlopd by Roy t. al., is a computationally fficint subspac-basd tchniqu applicabl to arrays, such as th uniform linar array (ULA), that possss a displacmnt invariant structur [2]. n th intgratd approach, th spatial signaturs of th incidnt signals ar obtaind first, and th DOA's ar stimatd from th spatial signatur. LSP-CMA, proposd by Talwar t. al., is an fficint tchniqu to simultanously stimat th spatial signaturs of multipl constant modulus signals [3]. f a signal has only on componnt, its spatial signatur is idntical to th string vctor corrsponding to its DOA. Hnc, if w hav an stimat of th spatial signatur of a signal with a singl componnt, w can stimat its DOA by sarching through all possibl string vctors, and dtrmin th on closst in th two norm to th stimatd spatial signatur. Mathmatically, th DOA, 9, is givn by = argminla( )-ass12 (2) a whr a(9) is th string vctor corrsponding to 9, and is th stimatd spatial signatur. W rfr to this tchniqu as LSP-CMA with ML. Xu and Liu [4] proposd a novl tchniqu to stimat th DOA's of th dirct and multipath componnts of a signal from its spatial signatur. n subspac-basd algorithms, th DOA is stimatd from th covarianc matrix Rxx = xxh constructd from th input data vctor x, whos signal subspac is th span of th spatial signatur matrix A. f w hav an stimat of A, w can as wll form a spatial signatur covarianc matrix on which th ign dcomposition may quivalntly b prformd to obtain th DOA stimats. n th prsnc of cohrnt signals, it is rquird to prform forward/backward avraging and form a spatially smoothd spatial signatur covarianc matrix bfor ign dcomposition [ 4] for MUSC or ESPRT can b prformd. m. SMULATON RESULTS Extnsiv simulations wr run in MA TLAB, assuming a six lmnt ULA with an intrlmnt spacing of a half wavlngth. All signals incidnt on th array ar assumd to b narrowband plan wavs with th azimuth arrival angl masurd countrclockwis from th array axis. Nois at ach antnna lmnt is assumd to b whit Gaussian and uncorrlatd with th nois at othr lmnts. Simulations wr run for th cas of non-cohrnt (uncorrlatd) as wll as cohrnt (fully corrlatd) narrowband (CW) signals. Cohrnt sourcs wr simulatd using multipl CW ton signals at th sam frquncy, and non-cohrnt signals wr simulatd using tons at slightly diffrnt frquncis. Furthr dtails ar givn in []. Root man squar rror (RMSE) is usd. as th mtric to compar th prformanc of ths algorithms. Th RMSE in DOA stimation is computd as th squar root of th avrag squard angular rrors ovr rpatd DOA stimation trials, and is dfmd as whr, K is th numbr of DOA stimation trials ovr which th rror is avragd, N is th numbr of incidnt plan wavs, n is (2) /96$

2 ,.. th tru DOA of th nth plan wav, and 9n is th DOA of th nth plan wav as stimatd by th DOA stimation algorithm. Figur l shows th RMSE in DOA stimation as a function of SNR for th cas of two uncorrlatd signals, and Figur 2 shows th sam for cohrnt signals. As sn from Figurs 1 and 2, all of th algorithms prform about qually wll whn th SNR is high. Undr low SNR conditions it is sn that th intgratd algorithms prform bttr than th convntional subspac mthods. (This is also tru whn a smallr numbr of array snapshots ar usd to comput th DOA.) For instanc, from Figur 2, it is sn that with snapshots, th intgratd approach can stimat th DOA within an accuracy of about 1 dgr at an SNR of db, whil th normal subspac mthods ar abl to rsolv only whn th SNR is at last 1 db. t is also sn that, though th subspac basd tchniqus ar abl to rsolv cohrnt multipath through spatial smoothing, th prformanc of all of th algorithms ar poorr undr cohrnt signal conditions whn compard to thir prformanc undr uncorrlatd signal conditions. 6 'i a n o MUSC LSP CMA with MUSC LSP CMA with Ml LS ESPRT -- --TLS ESPRT o LSP LSESPAT LSP TLSESPRT numbr of sampls Figur 1: RMSE in DOA stimation as a function of SNR. n ths simulations, two uncorrlatd signals with qual powr wr incidnt on a six lmnt ULA at 9 and 9 dgrs, rspctivly. array snapshots, takn at a 64 khz sampling rat, wr usd to stimat th DOA. Th RMSE is avragd ovr 2 rpatd DOA stimation trials. 7. " 1,, 1 1 ',,,, lq,, 1 o MUSC LSP CMA.with MUSC LS ESPAT TLS ESPRT numbr of sampls 'Q-.. '::. = :_-.:, ':. ----_:... :::. _,_.--=--... =-..::::::::::::: Slgnal lo-nols Ratio (db) Figur 2: Simulation paramtrs sam as in Figur 1 with th two sourcs bing cohrnt. Figurs 3 and 4 show th prfonnanc of ESPRT and LSP CMA with ESPRT algorithms undr various angl sprad conditions. Multipl signals wr simulatd with diffrnt angular sparation and arrival angls. Figur 3 shows th RMSE curv for up to four signals with th signals incidnt at 6, 6+Ll9, 6+2.ll9, and 6+39 dgrs, rspctivly, whr Ll9.is th angl of sparation btwn adjacnt signals. Figur 4 shows th sam for cohrnt signals. t is clarly sn that thr is a rapid dgradation in prformanc as Ll9 dcrass. t is sn that th intgratd LSP-CMA with ESPRT algorithm prforms bttr than th convntional ESPRT algorithm, and th improvmnt in prformanc is most significant whn thr ar multipl uncorrlatd signals. Th prformanc improvmnt ovr th convntional ESPRT algorithm incrass with incrasing numbr of signals, and dcrasing angular sparation. Using th constant modulus proprty, th LSP-CMA algorithm is abl to sparat multipl usrs and hnc achivs an improvmnt in prfonnanc. Evn undr cohrnt signal conditions, th intgratd approach outprforms th convntional ESPRT algorithm whn thr ar a larg numbr of signals arriving at closly spacd angls.,... -! 2 6 : lii 1. 1 b signals + 3 signals o4 signals T LS-ESPRT... LSP-TLSESPRT First signal arrivs at 6 Scond signal arrivs at 6 +A Third signal arrivs nt Fourth signal arrivs at 6+ 3M OL _ Angl of sparation btwn adjacnt signals (as in dg.) Figur 3: RMSE in DOA stimation as a function of angl of sparation btwn adjacnt signals(-19 in dg.). All sourcs ar uncorrlatd, with qual powr at an SNR = 2 db. Th stimations ar mad using snapshots and RMSE is avragd ovr 2 trials. tju 2 signals + 3 signals 2 o4 signals ""':' T LS ESPRT... LSP-TLSESPRT c 2 :::: First signal arrivs at 6 Scond signal arrivs at 6 +A ' Third signal arrivs at 6 +2A Fourth signal arrivs at 6+3Aa. n Angl of sparation btwn adjacnt signals (ds in dg.) Figur 4: Simulation paramtrs ar th sam as usd in Figur 3, xcpt that th signals ar prfctly corrlatd as would b th cas in a cohrnt multipath nvironmnt. Forward/backward avraging is usd to dcorrlat th cohrnt signals. 1

3 V. DOA EXPERMENTS Svral xprimnts wr conductd using an antnna array tstbd to vrify th prfonnanc of th DOA stimation algorithms. Th tstbd consists of a six lmnt ULA oprating at 2 MHz. Th antnna lmnts ar mad of quartiwav monopols mountd ovr a ground plan. Th RF front-nd is a singl convrsion stag which downconvrts th input RF signal at 2 MHz to a 12kHz F. Thr DSP boards, ach fittd with two ND convrtrs and a Motorola 962 procssor ar usd to sampl th six F signals at a rat of 64 khz and stor th collctd data on th host PC. Th collctd data was procssd off-lin for DOA stimation. This systm is dscribd in [6]. Two sts of xprimnts wr conductd in a parking lot adjacnt to th MPRG building to collct data undr uncorrlatd and cohrnt signal conditions. To st up uncorrlatd signals, multipl antnnas positiond at diffrnt locations at known angls with rspct to th rcivr array wr fd from diffrnt sourcs transmitting CW ton signals at slightly (1 khz) diffrnt frquncis around 2 MHz. To st up cohrnt signals, multipl antnnas positiond at diffrnt positions at known angls with rspct to th rcivr array, wr fd from th sam sourc transmitting a CW ton signal at 2 MHz. Undr this st up, multipl signals (rays) that ar prfctly corrlatd ar incidnt on th array at known angls. This is idntical to a cohrnt multipath situation whr th multipath rays ar attnuatd and phas shiftd vrsions of th sam signal []. Figurs and 6 show th DOA masurmnt rsults for th cas of uncorrlatd signals. t is clarly sn that whil th intgratd approach is abl to stimat th DOA' s within a fw dgrs, th convntional TLS-ESPRT algorithm producs much largr rrors, spcially whn thr ar thr signals. - "t:l TLS-ESPRT ' LSP-CMA with TLS-ESPRT ' First signal arrivs at 6 dg. ' Scond signal arrivs at 6+M dg. 1', ',',''',,' l 1 1! ! 4 Angl of Spamtion (L9) btwn th adjacnt signals in dgrs Figur : DOA Masurmnt Rsults - RMSE in DOA stimation as a function of angl of sparation, a, btwn th two uncorrlatd signals. Th first signal arrivs at 6. dgrs and th scond signal arrivs at 6+a dgrs. Figurs 7 and show th DOA masurmnt rsults for th cas of two and thr cohrnt signals, rspctivly. t is sn that whil both of th algorithms ar abl to stimat th DOA's within fw dgrs for th cas of two cohrnt signals, both th algorithms fail whn thr ar thr cohrnt signals. t should b notd that whil th intgratd approach showd prformanc improvmnt ovr TLS-ESPRT in th cas or uncorrlatd signals, thr is no apprciabl improvmnt for th cas of cohrnt signals. Sction V provids insight to th caus of rrors. - 3 "t:l 311'- - - c: 'i s! --- ' ' ' ' ' ' '... ' TLS-ESPRT LSP-CMA with TLS-ESPRT -- First signal arrivs at 6 dg. Scond signal arrivs at 6+t9 dg. Third signal arrivs at 6+2A9 dg. _ ! 2 2! 3 Angl of Spamtion (AS) btwn th adjacnt signals in dgrs Figur 6: DOA Masurmnt Rsults - RMSE in DOA stimation as a function of angl of sparation, a, btwn adjacnt uncorrlatd signals. Th first signal arrivs at 6 dg., th scond signal arrivs at 6+a dg., and th third signal arriv at 6+2.d9 dg PRT-, _._._._ TLS-ES "t:j LSP-CMA with TLS-ESPRT. 7 First stgnal arrivs at 6 dg.... Scond signal arrivs at 6+M dg J.... J. 3 Cll ' 2 L &----sso Angl of Spamtion (6.6) btwn th adjacnt signals in dgrs Figur 7: DOA Masurmnt Rsults - RMSE in DOA stimation as a function of angl of sparation, a, btwn th two corrlatd (cohrnt) signals. Th first signal arrivs at 6 dgrs and th scond signal arrivs at 6+A9 dgrs. 9 - "t:l c: c c 7 6 'll J Cll 2 1 ' TLS-ESPRT LSP-CMA with TLS-ESPRT First signal arrivs at 6 dg. Scond signal arrivs at 6+t9 dg. Third signal arrivs at 6+2A9 dg. 2 2 Angl of Sparation (L9) btwn th adjacnt signals in dgrs Figur : DOA Masurmnt Rsults - RMSE in DOA stimation as a function of angl of sparation, A, btwn adjacnt cohrnt signals. Th first signal arrivs at 6 dg., th scond signal arrivs at 6+A9 dg., and th third signal arriv at 6+2A9 dg. i 16

4 V. ERROR ANALYSS Th xprimntal (masurmnt) rsults showd that both th TLS-ESPRT and th intgratd approach wr abl to stimat th DOA in most cass within an accuracy of ± dgrs. For th cas of cohrnt signals, th algorithms producd larg rrors whn mor than two transmittr antnnas wr usd. As sn from th simulation rsults prsntd in sction ll, undr idal conditions, both th algorithms should prform significantly bttr than thy did in th DOA xprimnts. W hypothsizd that ths rrors could b du to on or mor of th following rasons: (1) prturbations in antnna lmnt location, (2) RF phas calibration rrors, and (3) multipath xisting in th channl To vrify th hypothsis, simulations wr conductd to study th ffct of ths rrors on th prformanc of th algorithms. Prturbation rrors and RF phas calibration rrors wr simulatd as random variations in th string vctors with th variancs slctd basd on th actual prturbations and phas rrors that xistd in th array. This was don so that th simulations would duplicat th actual xprimntal rrors as closly as possibl. Th masurmnt hardwar was carfully calibratd To invstigat if th multipath that xists at th masurmnt sit was th caus for th larg rrors sn in som of th DOA masurmnts, w studid th multipath structur of th masurmnt sit. Th multipath structur at th sit was charactrizd through powr dlay profil masurmnts and ray tracing, using tchniqus dscribd in [7], [], [9]. Powr dlay profil masurmnts showd that for ach of th transmittr locations, thr wr at last on multipath componnt arriving with a dlay of approximatly 2ns, and about 1 to 2 db blow th lin-of-sight componnt. For many locations, thr wr additional multipaths, too. Figur 9: llustration of ray tracing at th masurmnt sit. n ordr to study th ffct of ths multipath rays on DOA stimation algorithms, w also ndd to know th angl-of- arrival, and rlativ powr lvls of ach of ths rays. W usd ray tracing to dtrmin th angl-of-arrival of th multipath rays. To facilitat ray tracing, th masurmnt sit was modld using MPRG's sit spcific propagation prdiction softwar [9]. Th dimnsions of th four buildings around th sit wr masurd, and modld as four rctangular concrt boxs ovr a flat trrain. Through ray tracing, it was found that for ach of th transmittr locations at which masurmnts wr mad, apart from th LOS ray, thr wr at last thr othr significant (about 1 to 2 db blow LOS) multipath rays, arriving at th rcivr. Figur 9 shows an xampl scnario whr th transmittr is locatd at 2 dgrs with rspct to th rcivr. Ray tracing producd powr dlay profils which wr consistntly vry clos to masurd powr dlay profils ,., _ TLS-ESPRT LSP-CMA with TLS-ESPRT First signal arrivs at 6 dcg. Scond signal arrivs at 6+a dcg. With RF chain Phas Errors = - -o-_ = = = :ZO 2 3 Angl of Sparation (d9) btwn th adjacnt signals in dgrs Figur 1: Rsults of simulations that rcratd masurmnt scnario dscribd undr Figur with rrors incorporatd. g (.J ll _ -= -=-=-:-=:=-=-=-=-= = :..,. = = = 1 :zo 21 Angl of Sparation (d9) btwn th adjacnt signals in dgrs Figur 11: Rsults of simulations that rcratd masurmnt scnario dscribd undr Figur 6 with rrors incorporatd. Aftr obtaining th DOA's and powr lvls of th multipath rays through ray tracing, ths multipath rays wr incorporatd into th simulations, and th DOA stimatfon algorithms wr tstd to dtrmin th rror du to th xistnc of multipath rays. Figurs 1 through 13 show th rsults of simulations that rcratd th masurmnt scnarios incorporating th possibl sourcs of rror. Sparat simulations wr run for ach of th thr possibl sourcs of rror, and th rror du to ach is prsntd sparatly. Th rsults show that th dominant sourc of rror is th multipath xisting in th channl. t is sn that th TLS-ESPRT algorithm producs much largr rrors than th 3 17

5 intgratd LSP-CMA with TLS-ESPRT algorithm. Whil th intgratd approach is abl to stimat th DOA within ± dgrs, th TLS-ESPRT algorithm fails compltly for many cass. This is also tru with th actual masurmnt rsults shown in Figurs through. Thrfor, for th. DOA masurmnts using uncorrlatd signals, w can conclud that th rrors obsivd with th TLS-ESPRT algorithm was du to th xistnc of multi path in th channl r , 2P TLS-ESPRT " g LSP-CMA with TLS-ESPRT First signal arrivs at 6 dg. Scond signal arrivs at 6M9 dg.! (/) ::E sl_--o====12========3====o 1 2! 3... Angl of Sparation (d9) btwn th djacnt signals in dgrs Figur 12: Rsults of simulations that rcratd masurmnt scnario dscribd undr Figur 7 with rrors incorporatd. -bo u " g c.g ca. 1ii LJ. LJ (/) ::E 2! 2 TLS-ESPRT LSP-CMA with TLS-ESPRT First signal arrivs at 6 dg. Scond signal arrivs at 6+69 dg. Third signal arrivs at 6+29 dg Angl of Sparation (d9) btwn th adjacnt signals in dgrs Figur 13: Rsults of simulations that rcratd masurmnt scnario dscribd undr Figur with rrors incorporatd. Th suprior prformanc of th intgratd approach undr uncorrlatd signals may b attributd to its ability to sparat th uncorrlatd signals bfor dtrmining thir DOA' s. By oprating in a rstrictd signal subspac, th intgratd approach dos not bcom ovrloadd with multipath rays as much as th convntional ESPRT algorithm dos. Sinc th intgratd approach cannot sparat cohrnt signals, it dos not gain much prfonnanc improvmnt in th cas of cohrnt signals. Vi. CONCLUSON Through simulations and actual masurmnts, w dmonstratd th suprior prformanc of th intgratd approach ovr th convntional subspac-basd approach. W also showd that multipath xisting in th channl can ovrload th array and ca1:1s significant rrors in DOA stimation. Furthr work is ndd to xplor an.d mitigat multipath-inducd ovrloading. V. ACKNOWLEDGMENT This work was sponsord by th Dfns Advancd Rsarch Projct Agncy and th MPRG ndustrial Affiliats Program. vn. REFERENCES [] R.. Schmidt, "Multipl Emittr Location and Signal Paramtr Estimation," Procdings of RADC Spctrum Estimation Workshop, Griffiss AFB, NY, 243-2, [2] R. Roy, T. Kailath, "ESPRT-Estimation of Signal Paramtrs via Rotational nvarianc Tchniqus," EEE Transactions on Acoustics, Spch, and Signal Procssing, vol. 29, no. 4, pp , July 199. [3] S. Talwar, M. Vibrg, "Blind Estimation of Multipl Cochannl Digital Signals Using an Antnna Array," EEE Signal Procssing Lttrs, vol. 1, no. 2, pp , Fbruary [4] G. Xu, H. Liu, "An Effctiv Transmission Bamforming Schm for Frquncy-Division-Duplx Digital Wirlss Communication systms," Procdings of th CASSP, pp , 199. [] R. Muhamd, T. S. Rappaport, "Dirction of Arrival Estimation Using Antnna Arrays," Tchnical Rport, MPRG-TR-96-3, Virginia Tch, January [6] J. Librti, T. S. Rappaport uanalysis of CDMA Cllular Communication Systms Employing Adaptiv Antnnas," Tchnical Rport, MPRG-TR-9-17, Virginia Tch, Sptmbr 199. [7] W. G. Nwhall, K. Saldana, T. S. Rappaport, "Using RF Channl Sounding Masurmnts to Dtrmin Dlay Sprad and Path Loss in a Train Yard," RF Dsign, January 1996, pp. 2-. [] W. G. Nwhall, T. S. Rappaport, D. G. Swny, "A Sprad Spctrum Sliding Corrlator Systm for Propagation Masurmnts," RF Dsign, April1996, pp [9] S. Y. Sidl, T. S. Rappaport, "Sit-Spcific Propagation Prdiction for Wirlss n-building Prsonal Communication Systm Dsign," EEE Transactions on Vhicular Tchnology, Vol. 43, No.4, Novmbr 1994, pp