Journal of Applied Research and Technology ISSN: Centro de Ciencias Aplicadas y Desarrollo Tecnológico.

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1 Journal of Appled Reearch and Technology ISSN: Centro de Cenca Aplcada y Dearrollo Tecnológco Méxco Mar, J.; Wu, S. R.; Wang, Y. T.; Ta, K. C. A Three-Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna Journal of Appled Reearch and Technology, vol., núm., abrl, 3, pp Centro de Cenca Aplcada y Dearrollo Tecnológco Dtrto Federal, Méxco Avalable n: How to cte Complete ue More nformaton about th artcle Journal' homepage n redalyc.org Scentfc Informaton Sytem Network of Scentfc Journal from Latn Amerca, the Carbbean, Span and Portugal Non-proft academc project, developed under the open acce ntatve

2 A Three-Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna J. Mar*, S. R. Wu, Y. T. Wang 3, K. C. Ta 4, 3, 4 Department of Communcaton Engneerng Yuan-Ze Unverty Yuan-Ze Unverty 35 Yuan-Tung Road, Jungl, Taoyuan 3, Tawan, R.O.C. *eejmar@aturn.yzu.edu.tw Communcaton Reearch Center Yuan-Ze Unverty Yuan-Ze Unverty 35 Yuan-Tung Road, Jungl, Taoyuan 3, Tawan, R.O.C. ABSTRACT The robut three-dmenonal poton archtecture propoed n the paper, where the hybrd tme dfference of arrval (TDOA and drecton of arrval (DOA poton ytem wa degned to backup the four-taton TDOA poton ytem. The dgtal tme delay etmaton (TDE recever ued for TDOA meaurement and the cylndrcal array antenna ued for DOA meaurement. The general formula of lnear phae compenaton for cylndrcal array antenna n horzontal plane derved. The detecton probablty of the TDE recever and the crcular error probablty (CEP of the poton ytem over Raylegh fadng channel were numercally computed n three-dmenonal pace. Smulaton ndcate that the poton accuracy of the four-taton TDOA poton ytem degraded but the locaton functon can be retaned by the hybrd TDOA and DOA poton ytem when any one of four-taton out of work. Keyword: tme delay etmaton, crcular error probablty, tme dfference of arrval, drecton of arrval.. Introducton Snce the Unted State Federal Communcaton Common (FCC n 996 publhed the E-9 potonng tandard, wrele locaton technology extenvely tuded for t commercal value. The reearch of potonng method, ncludng tme dfference of arrval (TDOA, drecton of arrval (DOA or hybrd TDOA/DOA algorthm, motly bae on Gau-Newton Interpolaton (GNI algorthm to etmate the locaton coordnate of moble taton (MS n two-dmenonal pace []. The GNI algorthm can be appled to dfferent type of meaurement n the poton ytem. For ome applcaton, ncludng land-to-ar communcaton and pave radar; they need to provde the target locaton n the three-dmenonal pace []. The mult-taton TDOA poton ytem, whch employ optcal communcaton to end the receved gnal of each taton to a reference taton to calculate the TDOA between the reference taton and each taton, ha the advantage of hgh accuracy and low ytem complexty. Becaue the ynchronzaton problem become mple and the common channel error can be elmnated among dfferent taton. In th paper, we focu attenton on the tudy of three-dmenonal poton ytem. The data fuon of four-taton TDOA baed on GNI algorthm ndepth nvetgated. The hybrd three-taton TDOA and DOA poton ytem [3] wa ued to extend the locaton functon a oon a one of four fourtaton mng. The cylndrcal array antenna degned to meaure the target DOA for the hybrd poton ytem. A general formula of lnear phae compenaton for cylndrcal array antenna n horzontal plane derved. In addton, the detecton performance of the dgtal tme delay etmaton (TDE recever numercally evaluated. The tructure of the paper decrbed a follow. Secton II preent the prncple of dgtal TDE recever and the GNI algorthm of four-taton TDOA poton ytem. In Secton III, the algorthm of hybrd TDOA and DOA poton ytem and the multmode dgtal beam-former (DBF for cylndrcal array antenna are decrbed. In Secton IV, the detecton probablty for TDE meaurement and the poton accuracy of the four-taton TDOA and hybrd TDOA and DOA poton ytem are mulated. The detecton performance of the Journal of Appled Reearch and Technology 75

3 A Three Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna, J. Mar et al. / 75 8 propoed dgtal TDE recever ung lnear optmum flter compared wth typcal TDE method [4] wthout ung lnear optmum flter to demontrate t uperorty. Secton V conclude the paper. The formula of lnear phae compenaton for cylndrcal array antenna n horzontal plane derved n Appendx A.. Four-taton TDOA locaton cheme. Prncple of dgtal TDE recever j D * M * W ( k S ( k e W ( k S ( k (6 c The typcal TDE ung cro correlaton of wdeband gnal ha been analyzed n [4], where the lnear optmum flter wa not ncluded n the degn.to reduce the occurrence of fale peak due to the channel effect, a lnear optmum flter degned to maxmze the expected gnal peak relatve to the output noe. The tranfer functon of the optmum flter gven by [5] ( k Hk ( [ ( k ( k] [ ( k( ( k ( k] W W W W (7 Where Fgure. Block dagram of dgtal TDE recever. The TDE recever, a hown n Fgure, mplemented by a dgtal cro correlator n frequency doman to detect the poton of the domnant peak energy n tme doman. Here we aume that recever the reference taton. When the movng target ource emt the gnal [n] n three-dmenonal pace, the receved gnal of the frt recever gven by x [ n] [ n] w [ n], n[, M ] ( The receved gnal of other three recever are gven by x [ n] [ nd ] w [ n], n[, M],,3,4 ( Then, the output of the cro correlaton n frequency doman between taton and taton for =,3,4 j D * M w w c R ( k X ( k X ( k ( k e ( k ( k (3 where D the dcrete tme delay between recever and recever, and ( k S ( k (4 ww * ( k W ( k W ( k (5 ( k E[ ( k] E[ S( k ] ( k E[ ( k] E[ W ( k ] W w ( k E[ ( k] E[ W ( k ] W w (8 The correlaton output between recever and recever n tme doman determned by y[ l ] IFFT{ R ( k H( k } (9 Then the dcrete tme delay between recever and recever etmated at a peak energy dcrete tme poton l D,,3,4. The ntal target locaton olved by three hyperbolc equaton. r ( x X ( y Y ( zz, ( x X ( y Y ( zz for,3,4 ( where ( X, Y, Z and ( X, Y, Z are the coordnaton of the th and the th recever; ( x, yz, the target locaton. r can be obtaned from the meaured, tme delay between recever and recever. cd r c,, c( r r Nf ( 76 Vol., Aprl 3

4 A Three Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna, J. Mar et al. / 75 8 where N the ze of the fat Fourer tranform (FFT and f the amplng frequency of the analog-to-dgtal converter. The target locaton n the three dmenonal pace calculated by olvng three hyperbolc of Eq.. Therefore, the meaured TDOA value are expreed a r c,3,4 (,,. GNI algorthm [][] The GNI an teraton algorthm, whch ue the leat quare error (LSE method to correct the ntal etmated target locaton n the teraton untl the error approache zero. If guee of the true ntal target locaton ( x, y, z etmated ung v v v four-taton TDOA method, by mean of the frt order Taylor expanon, the poton equaton expreed n matrx form. A z e (3 where x X x X y Y y Y z Z z Z v v v v v v cr cr cr cr cr cr x X x X y Y y Y z Z z Z v 3 v v 3 v v 3 v A cr cr cr cr cr cr x X x X y Y y Y z Z z Z v 4 v v 4 v v 4 v cr cr cr cr cr cr r ( x, y, z, v v v, c x r ( x, y, z 3, v v v z 3,,, e y 3 c z 4 r ( x, y, z 4, v v v 4, c where (4 (5 r ( x X ( y Y ( z Z v v v (6 for,,3,4 e a meaurement error vector and an etmated poton error vector n the teraton.,,3,4 are dentcal ndependent dtrbuted (IID random varable wth zero mean and covarance matrx R of meaurement error. R 3 (7 4 where,,3,4 are the varance of TDOA meaurement error. Then, the correcton error at each tep T T [ A R A] A R z (8 Thu, the next etmated target locaton replaced wt x v x, yv y, zv z.a oon v x v y v z a approache to zero, the error covarance matrx become x xy xz Q (9 xy y yz xz yz z For etmatng three-dmenonal target poton, the accuracy of the poton etmaton evaluated by the crcular error probablty (CEP [][6] n xyax and xz-ax, whch a functon of Q. When the calculated error are no more than %, the CEP n xy-ax and xz-ax are approxmated by CEP (3 / 4 where a b xy ( z xy ( z xy ( z a b ( { } x y( z xy( z { [( 4 ] } x y( z x y( z xy( z { } x y( z xy( z { [( 4 ] } xy ( z / xy ( z / x y( z x y( z xy( z ( Therefore, the fnal poton etmate are dtrbuted n an error ellpod. Journal of Appled Reearch and Technology 77

5 A Three Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna, J. Mar et al. / Hybrd three-taton TDOA and DOA poton ytem 3. Algorthm For hybrd three-taton TDOA and DOA poton ytem, the target locaton can be etmated by the ame procedure a the four-taton TDOA poton ytem except changngeq.4 and 5 a follow. x X x X y Y y Y z Z z Z v v v v v v cr cr cr cr cr cr x X x X y Y y Y z Z z Z v 3 v v 3 v v 3 v cr cr cr cr cr cr A ( y Y x X v v r r xy xy ( x X ( z Z ( y Y ( z Z r v v v v xy r r r r r xyz xy xyz xy xyz ( By mean of the frt order Taylor expanon, the true DOA angle n horzon and elevaton are gven by [] y Y y Y y Y x X v v v tan ( tan ( x y x X x X r r v xy xy z Z tan ( ( x X ( y Y z Z ( x X ( z Z v v v tan ( x r r r xy xyz xy ( y Y ( z Z r v v y r r r xy xyz xy xyz z (9 (3 and are the varance of meaured DOA error and, repectvely. 3. Cylndrcal Array Antenna r ( x, y, z, v v v, c r ( x, y, z 3, v v v 3, x c 3 z,, e y y Y v tan ( e x X z v z Z v tan ( e rxy where r ( x X ( y Y ( z Z v v v for,,3 (3 (4 A M L cylndrcal array antenna propoed to generate three-dmenonal beam pattern wth equal horzontal beamwdth for hybrd three-taton TDOA and DOA poton ytem.a general formula of lnear phae compenaton for N-element ubarray of M-element cylndrcal array antenna n horzontal plane derved n Appendx A. When N even, the tme delay compenaton for the ubarray antenna ummarzed by d N N n n,,,..., n c M N d N N N t n n,,,..., N d _ even n c M,, N (3 r ( x X ( y Y ( z Z (5 xyz v v v The eparaton dtance among the neghbourng element of the non-unform lnear ub-array are r ( x X ( y Y (6 xy v v The DOA meaurement value n horzon and elevaton are defned a e (7 N N dco,,,..., M N N N d _ even dco,,,..., N M, (3 e (8 To meet the requrement of the.5 (deal beam wdth and -db de lobe level n horzontal plane, 78 Vol., Aprl 3

6 A Three Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna, J. Mar et al. / 75 8 a ub-array wth x omn-drectonal element and Chebyhev weghtng I n = [.36,.6,,,.6,.36] choen to mulate the beam pattern[7]. The multmode DBF cont of a multple beam (MB and DOA mode. For MB mode, the output of each antenna element ubdvded nto N ndependent gnal by a (N--way power dvder. After the lnear phae compenaton, N ndependent gnal are obtaned from N adjacent element and combned wth aocated weghtng to generate a beam pattern of the N- element ub-array wth the -db de lobe level n horzontal plane. The M-element array yeld M beam to cover the 36 n azmuth. Each of the M beam ponted n a fxed drecton. The ampltude comparon DOA mode [7] ue two neghbourng beam of the mult-beam antenna array wth equal beam wdth to receve the target gnal multaneouly. The gnal ampltude multaneouly receved from two neghbourng beam are compared to obtan a dfference gnal. The meaured dfference gnal power correpondng to the DOA of the gnal from an ar target pre-tored n a look-up table of memory. The accuracy of ampltude comparon DOA mode determned by the angular lope, whch defned a the rate of change n the power of the dfference gnal generated from the two neghbourng beam to the patal angle. The more angular the lope, the greater the accuracy of the DOA mode wll be. The mult-beam antenna array degned wth the equal beam wdth o the ampltude comparon DOA mode can acheve the ame accuracy a the DOA etmaton n dfferent drecton. antenna beamwdth 9.4.The DOA meaurement error n horzon and elevaton angle are unformly dtrbuted n (-.7,.7 and (-9.7, 9.7,repectvely. The coordnate of four taton and a three dmenonal target trajectory are hown n Fgure, where the coordnate of four taton expreed n unt of meter are taton (,,, taton (5,6,, taton 3 (5,-6,, and taton 4 (3,,, repectvely, the ntal target locaton (-7,7,376,the nter-dtance of four taton 3Km, the dtance between the taton and the ntal target locaton Km. It aumed that the target peed.6 Km/hr, the taton receve the gnal emtted from target once per 3 Km, and the target trajectory equaton gven by 5 y x.94476x z 376 (33 Fgure 3 how that when the SNR of recever wth lnear optmum flter are -.7dB, -5.45dB, and -8.3dB n Raylegh, Rcan, and AWGN channel, repectvely, the tme delay can be uccefully meaured wth detecton probablty P d =.9 and fale alarm probablty P FA = -4. The propoed method compared wth the typcal method [4] n whch the lnear optmum flter not appled to TDE recever. A hown n Fgure 3, the SNR of recever wthout lnear optmum flter - 7dB n Raylegh channel for P d =.9 and P FA = Smulaton Smulaton are performed to demontrate the accuracy of the four-taton TDOA and hybrd TDOA and DOA poton ytem. The 48-pont ampled orthogonal frequency dvon multplexng waveform (OFDM [8] ued to mulate target emtted gnal over a two-ray Raylegh fadng channel [9]. The ze of FFT 496 pont. The TDOA meaurement error aumed to be Gauan dtrbuted wth N (, nec. For a 6 6 cylndrcal array antenna, the horzontal antenna beamwdth 3.4 and the elevaton Fgure. Tet cenaro. Journal of Appled Reearch and Technology 79

7 A Three Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna, J. Mar et al. / 75 8 Probablty of detecton AWGN Rcan. Raylegh Raylegh (wthout flter SNR (db Fgure 3. Detecton probablty for TDE meaurement. The CEP xy and CEP xz of the four-taton TDOA poton ytem and the hybrd TDOA and DOA poton ytem operated n Raylegh fadng channel are hown n Fgure 4 and 5 for SNR=-.7dB, repectvely. The mnmum and maxmum CEP value are lted n Table, whch demontrate that the accuracy of the four-taton TDOA poton ytem better than the hybrd TDOA and DOA poton ytem. CEP xz (m teraton 4-taton TDOA Hybrd TDOA and DOA 5. Concluon Hybrd TDOA+DOA 4-taton TDOA Fgure 5. CEP xz comparon. CEP xy (meter CEP xz (meter max mn max mn Table. CEP comparon table. CEP xy (m Hybrd TDOA+DOA 4-taton TDOA teraton Fgure 4. CEP xy comparon. In th paper, the dgtal TDE recever degned for TDOA meaurement and a cylndrcal array antenna degned for DOA meaurement. The OFDM gnal ued to tet the poton accuracy over Raylegh fadng channel. When the SNR of the dgtal TDE recever -.7dB, the TDOA can be uccefully meaured wth detecton probablty of.9 and fale alarm probablty of -4. The propoed TDE recever get 5.7dB gan compared wth typcal TDE recever [4] wthout ung lnear optmum flter. The accuracy of the four-taton TDOA poton ytem uperor to the hybrd TDOA and DOA poton ytem. But the locaton functon of the poton ytem tll avalable when the receved gnal of any one of four taton cannot be ent to the reference taton. Smulaton fnd out that the propoed three-dmenonal poton archtecture can provde accurate and relable target locaton functon. 8 Vol., Aprl 3

8 A Three Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna, J. Mar et al. / 75 8 Appendx A. Dervaton of Eq (3 and (3 of lnear phae compenaton for cylndrcal array antenna n horzontal plane Therefore, the angle of the (N/+ th array element π/m. The eparaton dtance among the neghborng element for the rght part ub-array are expreed a N d _ even dco M N N,,,..., N (A3 The tme delay compenaton for the rght part ubarray gven by Fgure A. Sub-array antenna wth even array element number. The M element of the cylndrcal array antenna n horzontal plane are placed at the vertexe of a polygon of M de. The eparaton dtance between the element d and each nternal angle (M-π/M. Power dvder are ued to generate N branche of the output gnal from each ub-array element. Each gnal can be ndvdually combned wth N- other gnal of adjacent element to generate a beam. When N even, for the rght half part of ub-array antenna, a hown n Fgure A, the angle of the (N/ th array element wth reference to horzontal ax derved a ( M M M (A The angle of the (N/+ th array element wth reference to horzontal ax derved a t d _ even N d N n n n c M N N,,,..., N (A4 For the left part ub-array, the angle of the (N/- th array element wth reference to horzontal ax (π/m, and the (N/- th array element wth reference to horzontal ax (π/m. The eparaton dtance among the neghborng element of the non-unform lnear array are N d _ even dco M N,,,..., (A5 The tme delay compenaton for the left part ubarray gven by t d _ even d N n n n c M N,,,..., (A6 ( M M M M M 4 M (A Eq. 3 n term of Eq. A4 and A6 and Eq. 3 n term of Eq. A3 and A5. Journal of Appled Reearch and Technology 8

9 A Three Dmenonal Poton Archtecture Ung Dgtal TDE Recever and Cylndrcal Array Antenna, J. Mar et al. / 75 8 Acknowledgement The reearch work wa upported by the reearch grant from Natonal Scence Councl, Tawan, R. O. C. (NSC 99--E-55-3 and CSIST. Reference [] J. C. Lbert Jr. and T. S. Rappaport, Smart Antenna for Wrele Communcaton: IS-95 and Thrd Generaton CDMA Applcaton, Prentce Hall, 999. [] W. H. Foy, Poton-Locaton Soluton by Taylor- Sere Etmaton, IEEE Tran. on Aeropace and Electronc Sytem, 976. [3] Al Broumandan et al., Practcal Reult of Hybrd AOA/TDOA Geolocaton Etmaton n CDMA Wrele Network, Proceedng of IEEE VTC 8 Fall,Calgary,Alberta,Canada, 8. [4] Y. Bar-Shalom et al., Analy of Wde-Band Cro Correlaton for Tme-Delay Etmaton, IEEE Tran. on Sgnal Proceng, vol. 4. no. I, 993. [5] Joeph C. Haab and Ronald E. Boucher, Optmum Etmaton of Tme Delay by a Generalzed Correlator, IEEE Tran. on Acoutc, Speech, and Sgnal Proceng, vol. ASSF-7, no. 4, 979. [6] J. T. Gll, Computaton of the Crcular Error Probablty Integral, IEEE Tran. on Aeropace and Electronc Sytem, vol. 7, no. 6, 99. [7] R. C. Johnon and H. Jak, Antenna engneerng handbook, nd Ed., McGraw-Hll, Book Co., New York, 984. [8] T. D. Chueh and P. Y. Ta, OFDM Baeband Recever Degn for Wrele Communcaton, John Wley& Son, 7. [9] J. Mar et al., Degn of Software Defned Rado Channel Smulator for Wrele Communcaton: Cae Study wth DSRC and UWB Channel, IEEE Tran. on Intrum. Mea., vol. 58, no. 8, pp , 9. 8 Vol., Aprl 3