Open Access An Improved Algorithm of Spatial Difference MUSIC for Direction of Arrival Estimation in a Smart Antenna

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1 Sen Orers for Reprnts to he Open Cybernetcs & Systemcs Journal, 205, 9, Open Access An Improve Algorthm of Spatal Dfference MUSIC for Drecton of Arrval Estmaton n a Smart Antenna L Bo,2, ngtng L, L L 2, Yang u 2 an Chuanla Yuan 3,* School of Informaton Engneerng, East Chna Jaotong Unversty, Nanchang, 33003, Chna; 2 Key Laboratory Avance Control & Optmzaton of Jangx Provnce, Nanchang, 33003, Chna; 3 College of Electrcal an Informaton Engneerng, unan Unversty of echnology, Zhuzhou, 42007, PR Chna Abstract: he estmaton of recton of arrval (DOA) of a smart antenna s not able to perform hgh resoluton n a mxe nose fel wth hgh correlaton. In ths paper, a mofe multple sgnal classfcaton (MUSIC) algorthm base on spatal fference s propose for mprovng the resoluton of DoA estmaton. he algorthm can elmnate the effect of mxe nose through computng the fference of the output sgnal covarance matrx an resolvng the uncorrelate an coherent sgnal respectvely. In orer to obtan the orthogonal subspaces of the sgnal an nose, the oepltz ecomposton an sngular value ecomposton (SVD) algorthm are apple to reconstruct the matrx. Accorngly, the MU- SIC algorthm s aopte to estmate the DOA effcently. In our research, several contrastve smulatons corresponng to DOA estmaton between the tratonal MUSIC algorthm an the propose metho are mplemente an analyze. he results emonstrate the feasblty an hgh effcency of our propose algorthm. Keywors: DOA estmaton, MUSIC, smart antenna, spatal fference.. INRODUCION Wth wely applcaton of personal communcatons servces, how to logcally allocate the lmte spectrum resource has become an mportant ssue. By ntroucng the fourth menson multple access, smart antenna can fferentate sgnals wth space propagaton recton uner the crcumstances wth the same tme, the same frequency an the same aress coe, an consequently mprove the utlze of spectrum resource []. As an aaptve array sgnal processng technque, the recton of arrval (DOA) n a smart antenna becomes one of the vtal problems to be resolve [2-3]. Generally speakng, a majorty of researches on DOA estmaton are carre out uner the assumpton of whte nose [4-8] For example, Capon, lnear precton approach, MU- SIC, ESPRI. Unfortunately, the sgnals of target sources n smart antenna are suffere from the effects of multple paths, ffracton n wave propagaton, color nose an mxe nose nterference. Accorngly, the DOA estmaton n mxe noses fels of coherent array sources becomes ntensve topcs n recent years. [9-0] Conserng the problem of narrowban DOA estmaton uner spatally colore noses, a new metho for maxmum lkehoo DOA estmaton of stochastc an mxe sgnals was propose [-2] presente a spatal smoothng wth mprove aperture metho to mprove the effectve array aperture ; [3] presente an algorthm that ve the array covarance matrx nto oepltz structure an non-oepltz structure matrx, then cancelle color noses by utlzng matrx fference translaton metho; [4-7] presente multple sgnal classfcaton (MUSIC) metho base on egen-ecomposton of receve sgnal correlaton matrx, on the assumng of enough precse of moel, the DOA estmaton coul acheve arbtrary hgh resoluton theoretcally. As mentone above, currently a majorty of DOA estmatng algorthms only take nto account of Gaussan whte noses or some customzng nose fels, an o not gve conseraton of both coherent an uncorrelate sources for sgnals recognton n mxe noses fels. o analyze the mxe nose of DOA estmaton, a novel DOA estmaton algorthm whch combne wth oepltz an Sv methos s propose an satsfes the hgh resoluton DOA estmatng uner hgh correlate, low SNR an near stance sources n mxe noses fels. Base on the MUSIC algorthm, a matrx fference metho whch can nvually recognze uncorrelate an correlate (coherent) sources s also presente. Beses, a phenomenon of fact that conventonal MUSIC metho woul mstakenly estmate DOA n mxe noses fels s etecte by a number of smulaton an numerc analyss. 2. DOA ESIMAION MODEL OF SMAR ANEN- NA he confguraton of smart antenna [,2] s shown n the followng Fg. (). As shown n Fg. () that the nput sgnals can be treate as planar waves, so the phase fferences are unquely etermne by carrer wavelength, angle of arrve an the space strbuton of antenna. As for the elements n a smart antenna, carrer wavelength an the space strbuton are almost 874-0X/5 205 Bentham Open

2 52 he Open Cybernetcs & Systemcs Journal, 205, Volume 9 Bo et al. the same, whereas the sgnal ntensty of array s stnctly fferent snce the fferent angles of arrval of nput sgnal nuce phase fference. ence, the problem of DOA estmaton plays an mportant role n smart antenna processng. k x( t) x2 () t xm () t w w 2 w M yt () Fg. (). A functonal block agram of a smart antenna system. he DOA estmaton Moel of target sources n mxe noses fels s gven as the followng Fg. (2). N j () t D j M Fg. (2). he DOA estmaton moel of strbute target sources. In Fg. (2), s steerng vector of the th target sgnal source, an D s the quantty of target sgnal sources. he unform lnear array s consste of equally space M( M > D) elements, whch have the equal behavor to sotropy n recton an equal stance, whose value s less than half of sgnal wavelength wth the max frequency. When the target sgnals arrval at the array, the jth element output vector can be represente as the followng form: D j j () t = ( ) s (, t) + () t = Where s (, t) x N () s the recton sgnal ensty functon of th target sgnal source at tme t an N j () t s the mxe nose vector. In the applcaton envronment of smart antenna the raatng sgnals of fferent strbute source commonly are coherent. Base on the theory of Schwartz Inequaton, the fference between the two sgnals s a constant complex value when they are nterfere, an the parameter s(, t) n formula () can be revse as followng formula (2): s (, t) s ( t) g ( ) where g ( ) = (2) s the sgnal angle strbuton functon of the th target source, an t s a etermnstc functon centere wth g satsfes wth:, an parameter ( ) g( ) = (3) An the receve sgnals moel can be expresse as: () t = () t + () t X BS N (4) 3. E SPAIAL DIFFERENCE MUSIC ALGO- RIM FOR DOA ESIMAION 3.. Spatal Dfference Algorthm Spatal fference algorthm s apple to elmnate the effects of mxe noses n the covarance matrx [8]. Base on formula (4) the covarance matrx of recevng ata can be wrtten as: R= E{ X() t X() t }= R + RN + Q (5) Where R s the correlaton matrx of uncorrelate sources, whch s a ermte-oepltz matrx; R s the correlaton matrx of the correlate or coherent sources, whch N s a ermte matrx but not a oepltz matrx; Q s the covarance matrx of mxe noses, an t s ermte-oepltz matrx on the supposng n the presence of statonary an correlaton nose fels. Defnton : Suppose the matrx E s n oepltz form an J represents the exchange matrx, the followng formulaton s satsfe: JE J = E (6) Defnton 2: he spatal fference matrx s formulate as: R = R JR J (7) heorem If there exsts several correlate, coherent an uncorrelate sources n the group of unform lnear strbute target sources envronment, space fference matrx of sgnals oes not contan nformaton of the uncorrelate sources an t can cancel mxe noses n oepltz forms. Proof of theorem : Combnng formula (5) an the efnton (), (2), we can get the followng concluson: R R JR J = ( ) = R + R + Q J R + R + Q J N N N ( N ) = R J R J From the formula (8) we can see that the fference matrx o not contan oepltz terms, whch contans nether uncorrelate sources nformaton, nor the mxe noses nformaton. So the sources can be classfe by types an (8)

3 An Improve Algorthm of Spatal Dfference MUSIC he Open Cybernetcs & Systemcs Journal, 205, Volume 9 53 entfe respectvely. Furthermore, t ecreases the effect from mxe noses sources n DOA estmaton. Consequently, the estmaton matrx R woul come close to the actual covarance matrx R by eopltzng operaton, namely mn RS R R (9) Where S s the oepltz matrx set oepltz Approxmaton Algorthm he essence of oepltz approxmaton algorthm s computng the average of oblque agonal elements n covarance matrx, whch can be escrbe as the followng formulas: m p r( p) = r( ), 0 p< M (0) + n M p * ( ) ( ) = r p = r p () Where r j s the element of the covarance matrx, an M s the quantty of array elements. In the last the elements the matrx R s revse wth rj = r(, so the reconstructe j) covarance matrx RX have oepltz character that be utlze to realze uncorrelatng an unnterference Sv Algorthm he goal of Sv metho s to ecompose covarance matrx RX, an then acheve two orthogonal sgnal subspaces an mxe noses subspace whch prove possblty for effcent utlzaton of MUSIC algorthm. Step : On the assumng of above array moel, the frst proceure s ecomposng the reconstructe covarance matrx RX as: [,, ] = sv( ) USV RX (2) Where U an V are two orthogonal matrces, whch respectvely represent sgnal subspace an nose subspace, an the matrx S s a agonal matrx. So the egenvector of the max nose egenvalue can be get by Vn = U (:, D+ : M). Step 2: As to two correlate sgnal sources, the nose subspace vectors also contan some other egenvectors beses vector V n. On the precton of ensurng the Sv ecomposng precson, aopt matrx low-rank approxmaton metho to reconstruct a low-rank matrx RXX rather than ecompose matrx RX wth Sv metho. Matrx RXX reconstructng as the followng: RXX = U SS V (3) Set SS = S an SS SS ( M M ), = 0 ( M M ) 2, 2 = 0 SS ( M, M ) = 0 he matrx RXX can be ecompose as followng [,, ] = Sv (, ) UU SSS VV RXX X (4) In the noses subspace, assumng V to be the egenvector set of egenvalues except the max egenvalue of V, that uu s Vuu = UU (:, D+ : M). Step 3: A mean-value scheme s aopte for the noses subspaces V n an V to acheve a hgh resoluton of spatal uu spectrum estmaton wth the formula (5). VU = V + V (5) ( ) 2 uu u In the left of formula (5) matrx VU s the expecte nose subspace DOA Estmaton Base on MUSIC Algorthm After processng of the prevous three proceures, two orthogonal spaces of sgnal subspace an mxe noses subspace can be acheve by the strbute sgnal sources n mxe noses fels, then aopt MUSIC algorthm to realze hgh resoluton DOA recognzng. In MUSIC, subspace ecomposng metho utlzes orthogonalty between sgnal subspace an mxe noses subspace, to reconstruct spatal spectrum functon that gves an ncaton of the angles of arrval base upon maxma vs. angle. he proceures of DOA estmaton are lste as the followng: Step : collectng the nput sample X (), =,, N, an estmatng the covarance matrx of nput sgnal as the followng: N RX = X() X () (6) N = Step 2: Makng use of the oepltz approxmatng algorthm, get the reconstructe covarance matrx RX whch have the oepltz character. Step 3: akng utlzaton of Sv algorthm to ecompose RX n two tmes, constructng hgh resoluton spatal spectrum estmaton of nose subspace VU. Step 4: On the bass of acheve noses subspace VU, aopt MUSIC algorthm to reconstruct spatal spectrum functon, then estmate DOA values. Combnng wth formula (), formula (2) an formula (4), we can see that the steerng vectors relate to sgnal vectors are orthogonal wth egenvectors of noses subspace, namely on the precton that when the DOA estmatng values of multple path assume to be t exst: ( ) ( ) ( ) = 0 VU VU (7) In the practcal realzaton for the covarance matrces are acheve by the estmatng ata wth fnte observaton, the estmatng egenvector of nose subspace wll brng some errors urng the covarance matrces beng ecompose. So when errors s exst n VU the rght of the formula (7) s not zero vector. hereby, the DOA of multple nput sgnals can be recognze by estmatng spectral peaks of MUSIC spatal spectrum, an the spectral peaks values can be compute as:

4 54 he Open Cybernetcs & Systemcs Journal, 205, Volume 9 Bo et al. P ( ) = ( ) VU( VU) ( ) = 2 VU MUSIC ( ) (8) In the above formula (8) the DOA value s evaluate wth the customzng spectrum peak value n the pattern. 4. SIMULAIONS AND ANALYSIS 4.. DOA Estmaton Smulatons an Analyss n Atve Gaussan Whte Nose Fels In ths secton, the non-eal envronment exst atve Gaussan whte nose wth varance of.0. We have performe three experments to test the performance of our algorthm by contrast wth the tratonal MUSIC algorthm. Frstly, t s suppose that the presence of three movng target sources at azmuth angles [ 60, 40, 45 ] mpngng on the array. In the experment, the sources are non-correlate an the SNR s 0B. he result pattern of ths experment s shown n the followng Fg. (3a). In the secon experment, three movng target sources at azmuth angles [ 60, 30, 45 ] mpngng on the array, n whch the movng targets wth azmuth angles [ 60, 30 ] are hghly correlate, an the SNR s also 0B. Fg. (3b) s the result pattern of ths experment. hrly, we suppose that low SNR noncorrelate movng targets wth SNR 5B at azmuth angles [ 3, 0, 45 ] mpngng on the array, an the result s shown n Fg. (3c). From Fg. (3) we can observe that n the presence of atve Gaussan whte nose fels MUSIC as well as our algorthm success to recognze DOA wth non-correlate sources as shown n Fg. (3a), whereas MUSIC fal to recognze DOA for hghly correlate sources an contrarly our algorthm success to estmate n the same case as shown n Fg. (3b). Lastly n the Fg. (3c), n the presence of near stance an wth low SNR, n whch the fferences of the sources are nconspcuous an the SNR are 5B, tratonal MUSIC algorthm fal to estmate the mult-doa wth near angle stance, but our algorthm can effectvely estmate the case DOA Estmaton Smulatons an Analyss n Mxe Color Noses Fels Another scenaro has also been teste for the propose algorthm apple n the mxe color noses fels, where two nterference sources of color noses are presente at backgroun. he varances of the hypothess noses are 2.25 an 3.24, an the mean values of them are.0 an.2 respectvely. hree experments have also been performe to test the performance of our algorthm by contrast wth the tratonal MUSIC algorthm. In the frst experment, we suppose the presence of three movng targets whch SNR s 0B an non-correlate at azmuth angles [ 60, 40, 45 ] mpngng on the array. he result of ths experment s shown n Fg. (4a). Seconly hghly correlate movng targets at azmuth angles [ 60, 30, 45 ] mpngng on the array, an the SNR of them are 0B. he result spectral pattern s shown n Fg. (4b). In the last experment we suppose the azmuth fferences of the sources are nconspcuous an the SNR are 5B, an the result spectral pattern s shown n the followng Fg. (4c). tratonal musc algorthm ths paper algorthm (a) DOA estmaton spectrum pattern of non-correlaton sources tratonal musc algorthm ths paper algorthm (b)doa estmaton spectrum pattern of hgh correlaton sources tratonal musc algorthm ths paper algorthm (c) DOA estmaton spectrum pattern of near stance noncorrelaton sources wth low SNR noses Fg. (3). Smulaton results n atve Gaussan whte noses fels.

5 An Improve Algorthm of Spatal Dfference MUSIC he Open Cybernetcs & Systemcs Journal, 205, Volume 9 55 (a) DOA estmaton spectrum pattern of non-correlaton sources (b)doa estmaton spectrum pattern of hgh correlaton sources tratonal musc algorthm ths paper algorthm tratonal musc algorthm ths paper algorthm tratonal musc algorthm ths paper algorthm (c) DOA estmaton spectrum pattern of near stance noncorrelaton sources wth low SNR noses Fg. (4). Smulaton results n mxe color noses fels. In Fg. 4(a)-(c), we show the result patterns of angle an spectral power relaton as functon of the number of snapshots for the tratonal algorthm an our algorthm for mxe color noses fels. From 4(a) we can see that n the backgroun of mxe color noses the tratonal MUSIC algorthm an our algorthm both can estmate the DOA values, an comparatvely our algorthm can generate more sharp spectral peaks an lower selobes n the same SNR. As for hghly correlate sources smulaton shown n Fg. 4(b). he last smulaton for the scenaro of unrelate near stance sources n space wth low SNR envronment, both the tratonal MUSIC algorthm an the propose algorthm can estmate the DOA of 45, whch s far away from the other sources an our algorthm have more sharp spectral peaks an lower selobes. CONCLUSION hs paper propose a novel spatal fference MUSIC (SDMUSIC) algorthm whch aopts the metho of fference reconstructon base on MUSIC metho to resolve hgh-resoluton DOA estmate n mxe noses fels. Smulaton results confrm that our metho can not only effectvely resolve hgh resoluton DOA estmaton for uncorrelate sources wth atve whte noses envronment n smart antenna, but also exactly estmate DOA values for near stance, low SNR an hgh correlate sources n mxe noses fels. CONFLIC OF INERES he authors confrm that ths artcle content has no conflct of nterest. ACKNOWLEDGEMENS hs work was supporte by the MOE (Mnstry of Eucaton n Chna) Project of umantes an Socal Scences (2YJCZ099), the unan Provncal Natural Scence Founaton of Chna (Grant No. 205JJ5025), the Natural Scence Founaton of Jangx Provnce of Chna (204BAB207) an the scence an technology plan project of Jangx Provnce (2022BBE500048). REFERENCES [] R.M.Shubar, M.A.A.Qutayr, an J.M.Samhan, A setup for the evaluaton of MUSIC an LMS algorthms for a smart antenna system, Journal of Communcatons, vol.2, no.4, pp.7-77, [2] M.Bakhar, an Dr.V.R.M.P.V.unagun, Egen str- ucture base recton of arrval estmaton algorthms for smart antenna systems, Internatonal Journal of Computer Scence an Network Securty, vol.9, no., pp.96-00, [3] S.Katarya, A survey on smart antenna system, Internat- onal Journal of Electroncs&Communcaton echnology, vol.2, no.3, pp.23-26, 20. [4] S. C. Km, I. Song, S. Yoon an S. R. Park, DOA estm- aton of angle-perurbe sources for wreless moble com- muncatons, IE- ICE rans. Communcaton, vol. E83-B, no., pp , [5] J.X.Wu,.Wang, Z.Y.Suo, an Z. Bao, DOA estmaton for ULA by spectral Capon rootng metho, Electroncs Letters, vol.45, no., pp.84-85, [6] J.M.Xn an A. Sane, Lnear precton approach to recton estmaton of cyclostatonary sgnals n multpath envron- ment, IEEE ransactons on Sgnal Processng, vol.49, no.4, pp , 200. [7] E.Grosck, K. Abe-Meram, an K.Y.ua, A weghte lnear precton metho for near-fel source localzaton, IEEE ransactons on Sgnal Processng, vol.53, no.0, pp , [8].B.Lavate, V.K.Kokate, an A.M.Sapkal, Performance analyss of MUSIC an ESPRI DOA estmaton algorth- ms for aaptve array smart antenna n moble communc- aton, Internatonal Journal of Computer Networks, vol.2, no.3, pp.52-58, 200. [9] D.F.Zha, an.s.qu, Drecton fnng n non-gaussan mpulsve nose envronments, Dgtal Sgnal Processng, vol.7, no.2, pp , 2007.

6 56 he Open Cybernetcs & Systemcs Journal, 205, Volume 9 Bo et al. [0] K.Wang, Y.S.Zhang, an D. Sh, Novel algorthm on DOA estmaton for correlate sources uner complex sy- mmetrc toepltz nose, Journal of Systems Engneerng an Electroncs, vol.9, no.5, pp , [] A.Kslansky, R.Shavt, an J.abrkan, Drecton of arrval estmaton n the presence of nose couplng n antenna arrays, IEEE ransactons On Antennas An Propagaton, vol.55, no.7, pp , [2] A.hakre, M.aart, an K.Grhar, Sngal snapshot spatal smoothng wth mprove effectve array aperture, IEEE Sgnal Processng Letters, vol.6, no.6, pp , [3] Y.Zhang, Q.Wang, an A.M.uang, Localzaton of narr- ow ban sources n the presence of mutual couplng va sparse soluton fnng, Progress n Electromagnetcs Re- search, vol.86, pp , [4] C.R.Dongarsane, an A.N.Jahav, Smulaton stuy on DOA estmaton usng MUSIC algorthm, Internatonal Journal of echnology an Engneerng System, vol.2, no., pp.54-57, 20. [5] K.K.Kumar, B.Suheer, an K.V.Suryakran, Algorthm for recton of arrval estmaton n a smart antenna, Internatonal Journal of Communcaton Engneerng Applcatons, vol.2, no.4, pp.44-49, 20. [6] A.rata,.Mormoto, an Z.Kawasak, DOA estmaton of ultaweban EM waves wth MUSIC an nterferom- etry, IEEE Antennas an Wreless Propagaton Letters, vol.2, no., pp.90-93, [7] F.aga, Smart Musc algorthm for DOA estmaton, Electroncs Letters, vol.33, no.3, pp.90-9, 997. Receve: May 26, 205 Revse: July 4, 205 Accepte: August 0, 205 Bo et al.; Lcensee Bentham Open. hs s an open access artcle lcense uner the terms of the ( whch permts unrestrcte, noncommercal use, strbuton an reproucton n any meum, prove the work s properly cte.