Linear-Combined-Code-Based Unambiguous Code Discriminator Design for Multipath Mitigation in GNSS Receivers

Transcription

1 4 J.W. RE, H.H. CHE, W.. JIA,.L. YAO, UABIGUOUS CODE DISCRIIAOR FOR ULIPAH IIGAIO I GSS Lnear-Combned-Code-Based Unambguous Code Dscrmnator Desgn for ultpath tgaton n GSS Recevers Jawe RE, Huhua CHE, Wemn JIA, nl YAO X an Research Insttute of Hgh echnology, X an, Chna wdrjw@yahoo.com.cn, chenhuhuachna@hotmal.com, jwm62@63.com, yaomnl@sohu.com Abstract. Unambguous tracng and multpath mtgaton for Bnary Offset Carrer (BOC sgnals are two mportant requrements of modern Global avgaton Satellte Systems (GSS recevers. A GSS dscrmnator desgn method based on optmzaton technque s proposed n ths paper to meet these requrements. Frstly, the dscrmnator structure based on a lnear-combned code s gven. hen the requrements of deal dscrmnator functon are converted nto the mathematcal constrants and the objectve functon to form a non-lnear optmzaton problem. Fnally, the problem s solved and the local code s generated accordng to the results. he theoretcal analyss and smulaton results ndcate that the proposed method can completely remove the false loc ponts for BOC sgnals and provde superor multpath mtgaton performance compared wth tradtonal dscrmnator and hgh revoluton correlator (HRC technque. oreover, the proposed dscrmnator s easy to mplement for not ncreasng the number of correlators. Keywords GSS, multpath, BOC, HRC.. Introducton In the Global avgaton Satellte System (GSS recevers, the code dscrmnator, whch s the core unt of the delay loc loop, s responsble for the synchronzaton of the local and receved codes n the presence of multpath []. Code dscrmnator desgn determnes the tracng accuracy of the GSS, whch s affected by numerous factors. Among these factors, the multpath s a domnant source of tracng error [2]. ultpath errors are generated by the corrupton the lne-of-sght sgnal that s attrbuted to the delayed reflected sgnal. In modern GSS recevers, multpath errors result n approxmately a m tracng error. umerous multpath mtgaton technques have been proposed to enhance multpath mtgaton performance through the mprovement of code dscrmnator structure. hese technques can be classfed as the parameter estmaton, the correlaton processng, the correlaton combnaton and shapng technques. he parameter estmaton technques use the statstcal method to estmate the multpath parameters ncludng the number of multpath paths, multpath ampltude and delay. he most representatve technque of ths class s the multpath estmatng delay loc loop (EDLL [3]. he technques that belong to ths class are the most effectve for multpath mtgaton compared wth other classes. However, such technques are too complcated to mplement n the GSS recever [4]. he correlaton processng technques process correlaton values to determne the lneof-sght sgnal delay. he early-late-slope (ELS [2] and the dfferental correlaton (DC methods [3] are two representatve technques n ths class. hese methods do not ncrease hardware complexty but they are senstve to the nose n the sgnal. he correlaton combnaton and shapng technques use addtonal correlators or local lnearcombned-codes to shape the correlaton or the dscrmnator functon. he hgh resoluton correlator (HRC [5] and the code correlaton waveform (CCRW [6] are the representatve technques of ths class. hese methods exhbt effectve multpath mtgaton performance wth a mnmal ncrease n complexty. oreover, [7] has proven that the lnear-combnaton of several correlators equally correlates the receved sgnal by usng a local lnear-combned-code, thus, the complexty can be reduced n further. In ths paper, we wll focus on correlaton shapng technques. he ey of these technques s to generate a dscrmnator functon (S-curve wth enhanced multpath mtgaton performance by usng optmum lnear-combned-codes (or equally by usng lnear-combned-correlators. Several S-curve desgn methods have been proposed, such as by [8], whch s a desgn method amed at mnmzng the multpath error, but t doesn t consder the ambguty problem. he ambguty problem can be attrbuted to multple sde peas n the autocorrelaton functon of Bnary Offset Carrer (BOC modulated sgnals whch are wdely used n modern GSS to acheve spectral separablty [9]. he ambguty problem nduces a false loc whch may result n a large and rreparable tracng error. herefore, the ambguty problem must frst be solved n modern

2 RADIOEGIEERIG, VOL. 2, O. 4, DECEBER 22 4 GSS recevers. he desgn objectves of the unambguous dscrmnator as well as the calculaton of the combnaton weghts of the correlators are presented n []. However, ths approach only lmts the multpath-nduced error nto a certan bound nstead of enablng such error to reach the mnmum value. Furthermore, ths approach uses a multcorrelator structure, thus the optmzaton s lmted by hardware complexty. he goal of ths artcle s to propose a code dscrmnator desgn method that s based on the lnear-combnedcode structure. In ths artcle, we present the constrants of the unambguous S-curve and the objectve functon to obtan the mnmzed multpath error. hese constrants and functon form a non-lnear optmzaton problem. he lnear-combned weghts can be calculated after solvng ths problem. hese weghts are used to generate a local code, whch s mplemented n the code dscrmnator to obtan the optmum S-curve. he remander of ths paper s organzed as follows: In Secton 2, the code dscrmnator model s analyzed and a dscrmnator structure that s based on lnear-combned code s dscussed. Secton 3 presents the requrements of the deal S-curve and bulds a non-lnear optmzaton problem. Secton 4 dscusses a number of ey ponts n solvng the optmzaton problem. he desgn results for BOC(, and BOC(,5 are presented n Secton 5. Fnally, the concluson s drawn n Secton Code Dscrmnator odel he S-curve comes from the correlaton between the receved sgnal and the local sgnal. he receved BPSK or BOC modulated sgnal can be modeled as: rt ( Pdtmt ( (cos( t Pd( t d m( t d cos( t nt ( where P s the power of the receved sgnal. d(t represents the data code, m(t s the spreadng code after subcarrer modulaton or not for BOC and BPSK respectvely. denotes the sgnal frequency. he frst term s the drect lne-of-sght sgnal wth the phase. he second term represents sgnals of multpath, and each has the attenuaton a, the relatve delay d and the phase. he thrd term s the nose whch can be gnored at the desgn stage. In the code tracng process, the receved sgnal r(t s multpled by local I-phase and Q-phase carrer replcas and t becomes. I ( (cos ( cos ( r t Pc t Pc t d, (2 r ( t Pc(sn t Pc( td sn, (3 Q where c(t denotes the modulated data code d(tm(t, s the carrer phase error. After the carrer strppng, the sgnals of I and Q arms wll correlate wth the local replca code c(t-j R where j R s the correlator poston and R s a constant whch represents the tme resoluton of the delay, then the jth I-phase and Q-phase correlators output are I P( j cos a P( j d cos, (4 j R R Q P( j sn a P( j d sn (5 j R R where s the autocorrelaton of the modulated date code c(t. he ( can be expressed as ( Ect [ ( ct ( ] (6 where E[ ] represents the expectaton operator, s the convoluton operator. here are two nds of dscrmnator namely coherent and noncoherent dscrmnator can be mplemented to trac the GSS sgnals. When the carrer phase nformaton s avalable, whch means =, the coherent dscrmnator can be used to acqure a better antnose performance []. he output of coherent dscrmnator s D ( wj I j (7 j where w j s the lnear combnaton weght of correlator whch should be determned. Substtutng (4 and (6 nto (7, we can derve j R j R j R j D ( w{ PEct [ ( ct ( j] apect [( d ct ( j]cos } PEct { [ ( wct ( j] aect [( d wct ( j]cos } j R j where represents the multpath delay phase. From (8, we can dscover that lettng a new lnear combned code (8 lt ( wct j ( jr. (9 j It means that the lnear-combned correlators can be changed nto a lnear-combned code. In other words, nstead of usng multple correlators, the same dscrmnator output can be obtaned by correlatng the receved sgnal wth a local generated lnear combned code l(t [7]. he dscrmnator structure based on lnear-combned code s llustrated n Fg.. We should also remar that l(t s a mult-level code nstead of a bnary one, ths wll mae recever a lttle more

3 42 J.W. RE, H.H. CHE, W.. JIA,.L. YAO, UABIGUOUS CODE DISCRIIAOR FOR ULIPAH IIGAIO I GSS Fg.. Dscrmnator structure based on lnear-combned code. complex, however, mult-level code generaton s not very dffcult n modern GSS recever [7]. he most mportant advantage of ths structure s that s unlmted because the large wll not ncrease the hardware complexty of the recever. he output of ths coherent dscrmnator can be obtaned as D ( E[ r ( t l( t]. ( In the absence of multpath, D ( D( as I can be smplfed to D( P wj( jr. ( j Smlar formulatons can also be derved for the noncoherent scheme whch s mplemented when the phase cannot be accurately loced. he output of noncoherent dscrmnator s defned as 2 2 nc ( j ( j D w I Q. (2 Substtutng (4, (5 and (6 nto (2, the output can be rewrtten as D nc ( ( jr a ( jr d (3 2 wp j 2 ( jr a( jr dcos j 2 aa m( jr d ( jr dmcos m m where represents the multpath delay phase. However, snce the dscrmnator functon s nonlnear, there s no way to use a lnear-combned code to generate ths output. he noncoherent dscrmnator can only be mult-correlators structure. Under ths structure, the correlators number s lmted for the hardware complexty and some optmum desgn s done n []. Hereafter n ths paper, we wll only dscuss coherent dscrmnator based on lnear-combned code structure. 3. Code Dscrmnator Desgn Requrements ypcally, the desgn requrements of the dscrmnator are as follows. In the absence of nose and multpath, the estmaton of the tme delay s unbased. 2 he dscrmnator senstvty s greater than a prescrbed value. 3 he S-curve s non-ambguous for BOC modulated sgnals n pull-n range. 4 he code tracng error n the presence of multpath s as small as possble. hese requrements can be fulflled by desgnng the weghts w j. In the followng, these requrements wll be converted nto the constrants and the objectve functon to buld a non-lnear optmzaton problem. In the absence of nose and multpath, the requrement mples that when the tme error s zero, the dscrmnator output s zero too. hs can be expressed as: Substtutng ( nto (4, we have D(. (4 wj( jr w g (5 j where the vector w s defned as w=[w - w -+ w ] and g s the (2+ vector whose (j++th entry s Λ(-j R. he senstvty of the dscrmnator s defned as the dervatve of E(D( wth respect to, evaluated at = []. he senstvty represents the gan of the dscrmnator. he hgh senstvty means a small resdual error. he requrement 2 ndcates that the senstvty should be hgher than a prescrbed value s, whch means de( D( s. (6 d he value s can be selected accordng to the tracng loop desgn needs. (6 can be rewrtten as ( jr P wj s j d ( jr s wj j d P w h s (7 where s denotes as s / P named normalzed senstvty, h s the (2+ vector whose (j++th entry s ( j R. d

4 RADIOEGIEERIG, VOL. 2, O. 4, DECEBER he non-ambguty constrant (requrement 3 can be stated as that there s no zero-crossover nsde the pull-n range except the zero pont, whch means D(, (8 D(, where s a postve number and s a negatve number and the pull-n range s from to. Let m be the (2+ vector whose (j++th entry s Λ(τ-j R, (8 can be rewrtten to (9, w m,. (9 w m, ypcally, the crteron to evaluate the multpath mtgaton performance of a dscrmnator s the multpath error envelope (EE. It commonly uses two paths, both nphase and out-of-phase to calculate EE [2]. he EE curve has no analytcal expresson and the ponts of ths curve s related to the solutons of the followng equatons D (, d ( d [,.5] chps. (2 For smplfy, we wll use the functon name EEcurve( to denote the curves of EE hereafter. An example of the EE of tradtonal early mnus late (EL dscrmnator for BOC(, sgnal s llustrated n Fg.2, the ampltude of the second-path s 6 db lower than the one of the lne-nsght path. he early-late spacng s set to. chps. Averaged Code racng Error(eters ultpath Delay(Chps Fg. 2. he EE of EL dscrmnator for BOC(, sgnal. he multpath ampltude a =.5,. chps. From Fg. 2 we can dscover that there s an enclosed area between the absolute value of the upper EE and the absolute value wth mnus sgn of the lower EE [8]. Here we use the unt m chp to ndcate ths area and the area s defned as area EEcurve( d. (2 It can be seen as a nonlnear functon of w. he enclosed area of tradtonal EL dscrmnator for BOC(, s.35 m chp. he mnmzed multpath error crteron (requrement 4 s equvalent to mnmze the enclosed area of EE. On the whole, a non-lnear optmzaton problem can be bult from above objectve functon and constrants. For coherent dscrmnator, the problem can be expressed as mn area w w g w h s. (22 w m, w m, 4. Optmzaton Problem Soluton he problem (22 s establshed by a nonlnear objectve functon and some lnear constrants of w. hs nonlnear problem can be solved by the sequental quadratc programmng (SQP method. hs method s sutable for the problems nvolvng lnear and nonlnear wth equalty and nequalty constrants. SQP method can fnd an optmum soluton from arbtrary startng pont and t wll have fewer evaluatons and gradents compared. he detal of ths method can be found n [3]. he requrements (6-(9 are all related to the contnuous varable. In order to use computer to get the soluton, we must sample ths one to a dscrete varable. Set [, ] as the chp delay feld of nterest of dscrmnator functon and the number of sampled ponts s K. hen the sampled delay pont for dscrmnator functon s 2,,, K. (23 K oreover, the EE should also be dscretzed to mae objectve functon dscretzaton. Set [, ] as the chp delay feld of nterest of EE and the number of sampled ponts s L. hen the sampled delay pont for EE curve s,,, L. (24 L he area (2 can be rewrtten as area L L EEcurve(. (25 he start pont of w whch s denoted as w should also be chosen before soluton. Although n theory t can be set arbtrarly, a sutable start pont wll reduce the calculaton steps and acqure better result. here s an S- curve shapng method proposed n [7] for coherent dscrmnator. We can use ths method to set w correspondng to EL dscrmnator functon. A system of lnear equatons s obtaned as

5 44 J.W. RE, H.H. CHE, W.. JIA,.L. YAO, UABIGUOUS CODE DISCRIIAOR FOR ULIPAH IIGAIO I GSS w D target (26 where s the K (2+ vector whose (+, (j++th entry s ( jr, D target = (D EL ( K and D EL s the S-curve of EL dscrmnator. he least squares soluton wth the smallest norm of ths system can be used as the start pont w. hs soluton can generate a dscrmnator curve nearly the same as D target. After the dscretzaton processng, the optmzaton problem can be solved and the lnear-combned codes can be generated accordng to (9 by the computer. Although the soluton processng of nonlnear optmzaton problem s very complcated, we should remar that the lnear-combned codes can be generated only once n a computer and stored at the recever sde. So the proposed method wll not ncrease the complexty of the recever. 5. Code Dscrmnator Desgn Results In ths secton, we wll use the proposed desgn method to calculate the weght vector to form dscrmnator functons wth mnmzed multpath error for modern GSS sgnals. As a Galleo recever s to be realzed, the BOC(, modulaton s mplemented. BOC(, s also wdely used n other modern GSS [4]. So n ths paper, we wll frstly desgn a dscrmnator for BOC(,. Specfc parameters that are used n the optmzaton process are as follows: = 4, R = /2 chps, = chps, =- chps, α =.5 chps and =.5 chps. he normalzed senstvty s requred can be set to greater than 2 [], whch means s = 2. Weghts w w Code Delay(Chps Fg. 3. he start pont w and the optmum result w (for BOC(, sgnal. Fg. 3 and Fg. 4 show the optmum results of weghts and S-curve comparng wth the orgnal ones. It can be seen that the orgnal S-curve whch s generated accordng to w s ndeed the same as the theoretc EL S-curve. Startng wth w, he optmum weght w s obtaned and the result S-curve s generated accordng to (9 and (. We can dscover that the result S-curve s asymmetrc around the orgn and there s only one zero-crossover pont. oreover, the functon values from delay - chps to -. chps are not but very small negatve values because of the constrant (8. Dscrmnator Output EL Orgnal S-curve Optmum S-curve Code Delay(Chps Fg. 4. he EL, orgnal and the optmum S-curve (for BOC(, sgnal. Fg. 5 shows the EE for BOC(, sgnal tracng, as well as for hgh-resoluton correlator (HRC technque for comparng. he HRC technque proposed n [5] s a typcal multpath mtgaton technque for modern GSS sgnals. From Fg. 5, t can be seen that the optmum EE came from proposed method s much more mproved than the orgnal EE. Comparng wth HRC, the dfference between the proposed method and HRC s mnmal at short multpath delays wthn to. chps whle the proposed method can nearly completely remove the multpath error around the medum and long multpath delay. Averaged Code racng Error(eters Orgnal EE HRC Optmum EE ultpath Delay(Chps Fg. 5. EE for orgnal and optmum desgn and HRC (for BOC(, sgnal. BOC(,5 s also a popular modulaton n modern GSS [4]. he hgher modulaton order mae t more dffcult to do unambguous tracng and multpath mtgaton than BOC(,. ext, we wll desgn an optmum dscrmnator for BOC(,5. he same parameters as above are used n ths desgn.

6 RADIOEGIEERIG, VOL. 2, O. 4, DECEBER Weghts Dscrmnator Output Code Delay(Chps Fg. 6. he start pont w and the optmum result w (for BOC(,5 sgnal EL Orgnal S-curve Optmum S-curve w w more peas. But the performance of the proposed method doesn t decrease much comparng wth BOC(,. In long delay range, the multpath restrant performance of proposed method s stll much better than HRC. Even n short delay range wthn [,.] chps, the proposed method s slghtly better than HRC. 6. Conclusons In ths paper, an optmum dscrmnator desgn method for GSS recevers s presented. he am of ths optmum dscrmnator s to trac BOC unambguously and have mnmzed multpath error. he proposed method use a dscrmnator structure based on lnear-combned code whch s easly mplemented n GSS receves. An optmzaton problem s formed and solved to acheve the desgn am. he desgn examples wth respect to BOC(, and BOC(,5 sgnals demonstrate that the proposed method can completely remove the false loc ponts and provde much better performance for multpath mtgaton than HRC technque. Besdes, the proposed method gves a new way based on optmzaton to desgn dscrmnator. hs approach may mae the desgn reach the theoretcal optmal f the objectve functon and constrants are perfect. Future wors wll focus on extendng ths method to noncoherent dscrmnator and mprove the optmzaton objectve functon and constrants to acqure better results. Averaged Code racng Error(eters Code Delay(Chps Fg. 7. he EL, orgnal and the optmum S-curve (for BOC(,5 sgnal Orgnal EE HRC Optmum EE ultpath Delay(Chps Fg. 8. EE for orgnal and optmum desgn and HRC (for BOC(,5 sgnal. Fg. 6 to Fg. 8 demonstrate the desgn result of BOC(,5 dscrmnator. From Fg. 7, t s obvously that the optmum S-curve s unambguous whle the orgnal S- curve has sx false loc ponts. From Fg. 8, t can be seen that the performance of HRC for BOC(,5 s much worse than for BOC(, because the S-curve of BOC(,5 has Acnowledgements hs wor was supported by atonal ature Scence Foundaton of Chna under grants 6794 and References [] JUAG, J., CHE, Y., KAO,., SAI, Y. Desgn and mplementaton of an adaptve code dscrmnator n a DSP/FPGAbased Galleo recever. GPS Solutons, 2, vol. 4, no. 3, p. 255 to 266. [2] WU, J., DEPSER, A. G. BOC-Gated-PR, A multpath mtgaton technque for BOC(n,n waveforms. IEEE ransactons on Aerospace and Electronc Systems, 2, vol. 47, no. 2, p [3] BHUIYA,. Z. H., LOHA, E. S., REFORS,. Code tracng algorthms for mtgatng multpath effects n fadng channels for satellte-based postonng. EURASIP Journal on Advances n Sgnal Processng, 28, p. -8. [4] YOO, S., LEE, Y., YOO, S., KI, S. Y. Generalzed advanced regon correlaton (G-ARC scheme for BOC(m, n modulated code tracng n future GSS. In Proceedngs of the Internatonal echncal Conference on Crcuts/Systems, Computers and Communcatons. Shmonose (Japan, 28. [5] ROUABAH, K., CHIKOUCHE, D., BOUOU, F., HARBA, R., RAVIER, P. GPS/Galleo multpath mtgaton usng the frst sde pea of double delta correlator. Wreless Personal Communcatons, 2, p

7 46 J.W. RE, H.H. CHE, W.. JIA,.L. YAO, UABIGUOUS CODE DISCRIIAOR FOR ULIPAH IIGAIO I GSS [6] UES, F. D., SOUSA, F.. G., LEIAO, J. E.. Gatng functons for multpath mtgaton n GSS BOC sgnals. IEEE ransactons on Aerospace and Electronc Systems, 27, vol. 43, no. 3, p [7] PAY,., IRSIGLER,., EISSFELLER, B. S-curve shapng: A new method for optmum dscrmnator based code multpath mtgaton. In Proceedngs of IO-GSS 25, Long Beach (USA, 25, p [8] HURSKAIE, H., LOHA, E. S., HU, X., RAASAKKA, J., URI, J. ultple gate delay tracng structures for GSS sgnals and ther evaluaton wth Smuln, SystemC, and VHDL. Internatonal Journal of avgaton and Observaton, 28, p. 2 to 37. [9] YAO, Z., LU,. Sde-peas cancellaton analytc desgn framewor wth applcatons n BOC sgnals unambguous processng. In Proceedngs of IO-I 2. San Dego (USA, 2, p [] JUAG, J. ult-objectve approach n GSS code dscrmnator desgn. IEEE ransactons on Aerospace and Electronc Systems, 28, vol. 44, no. 2, p [] HOLES, J. K. oncoherent late mnus early power code tracng performance wth front end flterng. In Proceedngs of IO-GPS 997. Kansas (USA, 997, p [2] HARRIS, R. B., LIGHSEY, E. G. A general model of multpath error for coherently traced BOC modulated sgnals. IEEE Journal of Selected opcs n Sgnal Processng, 29, vol. 3, no. 4, p [3] OCEDAL, J., WRIGH, S. J. umercal optmzaton. Sprnger Verlag, 26. [4] UIED, AIOS. Current and planned global and regonal navgaton satellte systems and satellte-based augmentatons systems. In Proceedngs of Internatonal Commttee on Global avgaton Satellte Systems Provder Forum, 2, p [5] CGRAW, G. A., BRAASCH,. S. GSS multpath mtgaton usng gated and hgh resoluton correlator concepts. In Proc. of IO San Dego (USA, 999, p About Authors Jawe RE was born n Luoyang, Chna, n 985. He obtaned hs aster degrees from the X an Research Insttute of Hgh echnology, X an, Chna, n 2. Currently he s pursung the doctor degree n Electrcal Engneerng n the X an Research Insttute of Hgh echnology, and hs man research nterests s the satellte navgaton sgnal structure desgn and sgnal processng. Huhua CHE was born n Fujan, Chna n 983. He receved hs.sc. from X an Research Insttute of Hgh echnology, X an, Chna n 29. He s currently worng toward the Ph.D. degree at X an Research Insttute of Hgh echnology. Hs research nterests nclude satellte navgaton sgnal structure desgn and sgnal processng. Wemn JIA was born n Hebe, Chna n 97. She receved her Ph.D degree from X an Research Insttute of Hgh echnology, X an, Chna n 27. She s an assocate professor n the Department of Communcaton Engneerng, X an Research Insttute of Hgh echnology, X an, Chna. Her current research nterests nclude Sat- CO, Spreadng Communcaton. nl YAO was born n Shanx, Chna n 966. He obtaned hs.sc. from X an Research Insttute of Hgh echnology, X an, Chna, n 992, and Ph.D. degree from X an Jao ong Unversty, X an Chna n 999, respectvely. He s currently a professor at the Department of Communcaton Engneerng, X an Research Insttute of Hgh echnology, X an, Chna. Hs research nterests nclude satellte navgaton sgnal structure desgn and sgnal processng, Sat-CO, and Spreadng Communcaton.