Doppler frequency offset estimation and diversity reception scheme of high-speed railway with multiple antennas on separated carriage

Transcription

1 Joural of Moder Trasportatio Volume, umber 4, Deember, Page 7-33 Joural homepage: jmtswjtuedu DO: 7/BF33583 Doppler frequey offset estimatio ad diversity reeptio sheme of high-speed railway with multiple ateas o separated arriage Yaoqig YAG, Pigyi FA,* Departmet of Eletroi Egieerig, Tsighua Uiversity, Beijig 84, Chia atioal Mobile Commuiatios esearh Laboratory, Southeast Uiversity, ajig 96, Chia Abstrat: The halleges of severe Doppler effets i high-speed railway are osidered By buildig a ooperative atea system, a algorithm of joit hael estimatio ad Doppler frequey offset (DFO) estimatio is proposed based o iea hael model First, a maximum likelihood estimatio (MLE) algorithm for DFO is desiged, showig that the Doppler estimatio a be obtaied by estimatig movig veloity of the trai ad the path loss with the exploitatio of pilots that are plaed iside the frame The a joit detetio algorithm for the reeiver is proposed to exploit multi-atea diversity gais Last, the theoretial Crammer ao boud (CB) for joit hael estimatio ad DFO estimatio is derived The steady performae of the system is ofirmed by umerial simulatios partiular, whe the iea fadig hael parameter equals 5 ad the veloities of trai are m/s ad 5 m/s, the estimatio variaes of DFO are very lose to the theoretial results obtaied by usig CB Meawhile, the orrespodig sigal to oise ratio loss is less tha 5 db whe the bit error rate is -5 for 6QAM sigals ey words: Doppler frequey offset (DFO); high-speed railway; iea hael; ooperative atea system JMT All rights reserved trodutio O e of the halleges i the fast developmet of high-speed railway (HS) i Chia is that urret systems, suh as GSM- whih oly supports a maximum data rate of kbps [], aot meet the ireasig demads for multi-media aess while travelig May efforts have bee made to desig a advaed ommuiatio system for extreme evirometal oditios, ad to develop the overall workig apabilities of ewly proposed stadards suh as LTE- ad Wi- MAX [-3] The most hallegig problem i HS is the severe Doppler effets aused by high speeds up to 486 km/h [4] Hee evaluatig Doppler spread so as to remove frequey offset beomes ruial [5] Most of urret work o Doppler estimatio emphasizes the diret estimate of Doppler frequey offset (DFO) i OFDM systems [6-7] t was reported reetly that multi-path effets i HS haels are muh great, due eeived Ot, ; revisio aepted ov 4, * Correspodig author fpy@mailtsighuaedu (PY FA) JMT All rights reserved doi: 3969/jiss95-87X46 to the domiat existee of lie-of-sight (LOS) ompoets [4,7] Thus it is importat to first speify the hael models, ad the desig algorithms to estimate Doppler effets This paper, based o the iea hael model, ivestigates the effet of LOS ompoet ad the path loss Also, power issues are highlighted sie the sigals may suffer from severe peetratio loss whe goig through the arriage body made of alumium ad stailess steel [4] May atea-based tehologies have bee proposed to solve this problem ef [3], a promisig solutio was proposed by usig a reeive atea outside the trai body to ommuiate with a group of base statios This tehology greatly redues peetratio loss this paper, the tehology is exteded to multi-atea situatios, i the ase that there is oe reeive atea o eah arriage of the trai This extesio has proved to be effetive i improvig the performae of Doppler frequey offset estimatio The mai otributio of this work is to build a ooperative atea system outside the trai body ad desig joit hael estimatio ad Doppler frequey offset (DFO) estimatio algorithm Furthermore, the theoretial Crammer ao boud (CB) for estimatio is derived based o iea hael model Fially, the performae of the proposed system is ivestigated by simulatio

2 8 Yaoqig YAG et al / Doppler frequey offset estimatio ad diversity reeptio sheme of System model Cooperative atea system for HS Suppose that there is a fast movig trai t will reeive the dowlik sigal from a base statio The trai has a ooperative multi-atea reeivig system with oe reeive atea o eah arriages, as show i Fig The base statio is set lose to the rail with a distae of d The typial value for d is about 3 m [4] Sie base statio has a height, we defie d=5 m i simulatio setio The foot poit is defied as poit O, ad the distae betwee poit O ad the first reeive atea is a Base statio d With movig veloity v Fig A ooperative atea system for HS The trai is movig toward O o the rail with the veloity v ; so the Doppler shift for the first atea aused by high movig veloity a be defied as fv Dt () os (), t () os ( t ) a vt (avt) d Oe reeivig atea was istalled o eah arriage of the trai The legth of the trai arriage is l, so is the separatio distae betwee two eighborig reeive ateas Typial value for l is about m, log eough for the additioal oise resultig from eah atea to be irrelevat The ateas are umbered from = to, ad the Doppler shift for eah atea a be defied as fv D() t os (), t (3) alvt os ( t), ~ (alvt) d Chael modelig Alog the rail trak O a l Atea system () (4) The base statio modulates the trasmitted sigal s() t with a arrier frequey f The reeived sigal x() t suffers from a power loss lt ( ), a frequey shift D ad a added white Gaussia oise wt () with a variae of The radom phase shift aused by trasmissio is evely distributed i [,) The the reeived sigal x() t a be writte as st ()exp j( f Dt ) x() t w() t (5) lt () All the ateas a reeive sigals, ad we sample the basebad reeived sigal with a samplig period T The, the reeived sigal a be expressed as s exp j[ DmT s ] x( m) s( m) w( m),,, ; m,,, M, where a l, D is defied i (3) ad M represets the umber of symbols i a data frame this simulatio, we defie =6, meaig that oe trai has 7 arriages The we slightly modify the hael represetatio i (6) by itroduig iea fadig effet: where (6) h x ( m) s( m) expj D mt w ( m), (7) s l h exp(j ) z rexp(j ) ad z ~ C (,), is the so-alled iea fator, r obeys iea distributio with the eter, ad is evely distributed i [,), similar to the defiitio i (6) The probability desity futio (PDF) of all r a be writte as r k ( k) f () r ( k )exp r k(k )r,(9) k ( k) where () is the zero order Bessel futio 3 Frame ofiguratio ad pilot positio (8) Estimatig the Doppler shift is doe by isertig pilots ito a data frame As is show i (7), Doppler shift brigs a hage i the phase of eah reeived symbol order to get eough iformatio for Doppler frequey offset estimatio, pilots are iserted ito separated plaes of a frame, as show i Fig We put pilots ito M reeive symbols to have (M)/ symbols after eah pilot The ratio (M)/ a represet the effi-

3 Joural of Moder Trasportatio (4): iey of trasmissio There is ertaily a trade-off betwee estimatio auray ad trasmissio effiiey as well as estimatio omplexity Pilots Fig Frame ofiguratio ad pilot positio Whe the trai speed is m/s ad f =8 GHz, the oheret time will be /D=/fv6 ms, ad we a set a frame iterval to ms to miimize the effets of Doppler frequey shift 3Joit DFO ad hael estimatio For eah frame, pilots are used to estimate the Doppler frequey shift t must be stated here that a frame eeds to be desiged properly to make sure that the Doppler frequey shift will ot hage i oe frame The ideal frame legth should be less tha D max, where D max represets the maximum Doppler shift With osiderig atea, the whole reeived sigals x ( k ) for pilots s( k ) are represeted as h M x( k) s( k) exp j Dk Ts w( k),,,,, k,,,, () where all h are defied i (8) Defie r M A, B( k) Dk Ts, l () ad simply take sk ( ) for eah pilot The Eq () a be simplified ito x ( k) A exp j B ( k) w ( k),,,,, k,,, () All D are determied by Eqs (3) ad (4) ad the distae a is estimated with uttig-edge equipmets, suh as a laser ragig equipmet The estimatio of veloity v ad hael fadig oeffiiets h eed to be ivestigated However, the veloity estimatio remais a tough problem for mobile ommuiatio [8-] this paper we propose a maximum likelihood estimatio (MLE) algorithm to estimate the veloity f the two parameters a ad v are determied, we a alulate eah D diretly With the assumptio that w ( k ) is additive white Guassia oise (AWG), the PDF for eah x ( k ) is f ( x( k); v,h) exp ( ) x k ( ) Aos B( k) exp x ( ) k A si ( ), (3) B k where x ( k ) ad x ( k ) are real ad imagiary parts of x ( ) k, respetively, ad f ( x;v, h ) f ( x ( k); v, h ) (4) k 3 MAP estimatio for path loss r We fous o the path loss estimatio for eah r Eq (4) is slightly differet from those dedued i previous works[8-9] i that we use MAP (maximum a posteriori) estimatio istead of the ML (maximum likelihood) estimatio i order for better performae based o the prior PDF of r i (9) Hee, oe must solve the followig equatio: f( x; h, v) f( h) r r r k r [ f( x ( k); h, v)] f( h) f( r ) os ( ) B k x ( k ) A os( B ( k ) ) k si ( ) B k x ( k ) A si( B ( k ) ) l Sie x ( k) is the real part of x ( k ) show i (), it is lear that or x ( k)os B ( k) x ( k)si B ( k) x ( k ) The equatio above a be simplified to r f ( ) r x ( ), k k l l r (5)

4 3 Yaoqig YAG et al / Doppler frequey offset estimatio ad diversity reeptio sheme of r argmax ( ) x k r k r f () r (6) k l 3 ML estimatio for veloity v For a better estimatio of Doppler shift, the estimatio for veloity eeds to be solved To solve f ( x,v,h) / v, we have v x k A B k argmax [ ( ) os( ( ) )] k [ x ( k) A si( B ( k) )] argmax x ( k) A os( B ( k) ) k x ( k) A si( B ( k) ) argmax e Ax( k)expj( B( k) ) k argmax abs A x( k)exp j B( k ) (7) k 33 ML estimatio for radom phase To obtai the phase estimatio, oe eed to solve f( x; h, v) f( h) f ( x ( k); hv, ) f( h) k A [ si( ( ) )] ( ) B k x k k os( B ( k ) ) x ( k ) l whih meas argmax [ A os( B ( k) ) x ( k) k A si( B ( k) ) x ( k)] argmax e x( k)expj( B ( k) ) k argmax e expj x ( )exp j ( ) k B k k agle ( )exp j ( ) x k B k (8) k summary, the whole estimatio steps are listed: () Estimate the path loss r usig (6) () Estimate veloity v usig (7) ad alulate the Doppler shift D (3) Estimate the radom phase usig (8) After alulatig all parameters, we a the deode the reeived sigals i the frame Simulatio results will prove the effiiey of estimatio algorithm 4 Theoretial symbol error rate (SE) performae The reeived sigals a be writte as (7) By defiig rexp j( DmTs ) h ( m), (9) we have l x( m) s( m) h( m) w( m),,,, m,,, M () Therefore, the liear ombiatio of all the sigals is give as follows: ym ( ) ( mx ) ( m) ( mh ) ( msm ) ( ) ( mw ) ( m) () The orrespodig S for eah symbol is S ( mh ) ( msm ) ( ) ( mw ) ( m) i sm ( ) ( H ) sm ( ) ( mw ) ( m) ( m) () f all the parameters are aurately estimated, we a simply let * H (3) H to ahieve the highest diversity gais ad get sm ( ) S max H (4)

5 Joural of Moder Trasportatio (4): From ef [], we kow that u u PA B Q Error A B H ( ), (5) where ua u B is the miimum distae o the ostellatio diagram The A ad B are two eighborig ostellatio poits the simulatio setio, hoosig 6QAM as the modulatio sheme leads to a better spetrum effiiey From ef [] we have sm ( ) Smax E H 5 ua ub H, 8 (6) [ ], (3) i j ad the Crammer ao Bouds a be alulated as CB (3) The diagoal ompoets of matrix CB are the real variae bouds for the estimated parameters From (3), ad, beause A has othig to do r vr with v ad, ad B ( k ) has othig to do with r To measure the auray of Doppler offset estimatio, we eed to alulate the CB for v ; i other words, we oly eed to alulate Fisher Matrix for v ad all, that is, (33) T [ v, v; v, ], E b BE Q Smax Q (7) where is a diagoal matrix, ad v is a row vetor From (3), fially we a get CB for v : 5 Crammer ao bouds for estimatio The exat iformatio of r ad is ukow Whe r, ad v are determied, eah reeived symbol x ( k ) obeys a omplex ormal distributio The PDF of eah x ( k ) ad the joit distributio of all x ( ) k a be writte as Eqs (3) ad (4) CBs a be foud by alulatig the Fisher iformatio matrix first The Fisher iformatio otet for eah parameter is defied as f ( x; ) E, v, r, The we have M e( sa exp j( B( k)) k M m( sa expj( B( k)) k M ( B( k) ) A A, k vr,, (8) (9) Similarly, the Fisher iformatio otet for joit parameters is M B( k) B( k) A A i j A (3) k i j i j Fially, the Fisher matrix is obtaied T CB v (, ) / ( v v v ) (34) To alulate the CB for hael estimatio, we have to alulate CB by (3) ad CB from the iverse of (33) From (8), we have h r r CB CB r CB (35) The losed form for CB i (3) is redudat here, beause is represeted by may summatio forms i j ote that CB v is irrelevat to the veloity Thus it is expeted that the estimatio a have a steady performae i differet situatios However, the CB for veloity will have some radom variables i its expressio Here we hoose the expetatio of CB v to represet its theoretial performae 6 Simulatio Let f 35 GHz, ad the samplig time Ts 5 s The time rage for oe frame is ms Eah frame has M 4 symbols, ad 5 symbols are used as pilots to estimate the Doppler shift Assume that a relatively aurate estimatio of distae a is reahed with laser ragig equipmet istalled o the base statio whe the trai is withi m of the base statio The estimatio error is set to % of the real distae Whe the trai is out of this rage, it a be assumed that a rough estimatio is esured with equipmet like GPS ad otrol estimatio error to be o more tha 5% of the whole distae

6 3 Yaoqig YAG et al / Doppler frequey offset estimatio ad diversity reeptio sheme of 6 Estimatio performae ompared with CB Fig 3 shows the relative Doppler frequey estimatio error for the 9th atea whe v= m/s ad k 5 fat, it was reported the typial value for k raged betwee 5 ad ad its average value for k was about 85 [4] The theoretial results are alulated aordig to the proedure i Setio 5-6 BE performae ompared with AWG hael Fig 5 shows the bit error rate (BE) usig 6QAM The theoretial BE value is derived i Setio 6 This alulatio is based o the AWG hael whe There is still some loss i BE performae due to the iauray of joit hael ad DFO estimatio The BE performae beomes slightly better whe k, sie the hael fadig beomes less obvious - DFO estimatio error - Theoretial results Simulatio performae whe v= m/s, k= a (m) Fig 3 elative DFO estimatio error performae whe v= m/s Fig 4 shows the situatio whe v=5 m/s ad k 5, where the Doppler frequey offset ireases a lot With the speed ireasig from to 5 m/s, the absolute estimatio error has o obvious irease, whih meas that the relative error drops The simulatio results also idiate that the performae of the proposed DFO estimatio algorithm is stable, sie the estimatio error is very lose to that obtaied by usig CB This is beause that CB is the lowest boud of all the ubiased parameter estimates DFO estimatio error - - Theoretial results Simulatio performae whe v=5 m/s, k= a (m) Fig 4 elative DFO estimatio error performae whe v=5 m/s BE Theoretial k= Simulatio, k=5 Simulatio, k= S (db) Fig 5 BE performae ompariso of 6QAM with ad without DFO estimatios for differet iea haels 7 Colusios A ooperative atea system is set up to solve the problems of severe Doppler effets emergig i highspeed railways, ad a algorithm for joit hael estimatio ad Doppler frequey offset (DFO) estimatio is proposed Beause the relative movig speeds of every reeivig ateas outside the arriage are differet, the DFOs for every ateas are also differet order to improve the DFO estimatio performae by exploitig the beefit of multi-atea diversity, a ew sheme to estimate the Doppler frequey offsets is developed The theoretial dedutio shows that the Doppler estimatio a be obtaied by estimatig the movig veloity of the trai ad the path loss with the exploitatio of pilots plaed iside the frame The a joit algorithm for MAP estimatio of path loss ad ML Estimatio for DFOs is desiged based o the movig veloity of the trai We also proposed a joit detetio algorithm i reeiver to exploit multi-atea diversity gais The theoretial CB for the joit hael estimatio ad DFO estimatio is also derived Simulatio results shows low DFO estimatio error ad BE, ad the simulatio performae approahes the theoretial lower bouds, espeially whe the k is large ( k 5)

7 Joural of Moder Trasportatio (4): Akowledgmets This work was partly supported by the Chia Major State Basi esearh Developmet Program (973 Program, o CB36), atioal atural Siee Foudatio of Chia (o 6764), the Chia atioal Siee ad Tehology Major Projet (o ZX33-3), SFC (o 6) ad the Ope esearh Fud of atioal Mobile Commuiatios esearh Laboratory, Southeast Uiversity (o D3) eferees [] JZ Wag, HL Zhu, J Gomes, Distributed atea systems for mobile ommuiatios i high speed Trais, EEE Joural o Seleted Areas i Commuiatios,, 3(4): [] DT Fokum, VS Frost, A survey o methods for broadbad iteret aess o trais, EEE Commuiatios Surveys & Tutorials,, (): 7-85 [3] Gua, ZD Zhog, B Ai, Assessmet of LTE- usig high speed railway hael model, : Pro 3rd teratioal Coferee o Commuiatios ad Mobile Computig, Qigdao, : [4] L Liu, C Tao, JH Qiu, et al, Positio-based modelig for wireless hael o high-speed railway uder a viadut at 35 GHz, EEE Joural o Seleted Areas i Commuiatios,, 3(4): [5] YQ Zhou, F Adahi, XD Wag, et al, Broadbad wireless ommuiatios for high speed vehiles, EEE Joural o Seleted Areas i Commuiatios,, 3(4): [6] LH Yag, GL e, ZL Qiu, A ovel Doppler frequey offset estimatio method for DVB-T system i HST eviromet, EEE Trasatios o Broadastig,, 58(): [7] EP Simo, L os, H Hijazi, et al, Joit arrier frequey offset ad hael estimatio for OFDM systems via the EM algorithm i the presee of very high mobility, EEE Trasatios o Sigal Proessig,, 6(): [8] AG Zaji, Estimatio of mobile veloities ad diretio of movemet i mobile-to-mobile wireless fadig haels, EEE Trasatios o Vehiular Tehology,, 6(): 3-39 [9] YH Zheg, CS Xiao, Mobile speed estimatio for broadbad wireless ommuiatios over iia fadig haels, EEE Trasatios o Wireless Commuiatios, 9, 8(): -5 [] CH Tepedelelioglu, GB Giaakis, O veloity estimatio ad orrelatio properties of arrow-bad mobile ommuiatio haels, EEE Trasatios o Vehiular Tehology,, 5(4): 39-5 [] D Tse, P Viswaath, Fudametals of Wireless Commuiatio, Cambridge: Cambridge Uiversity Press, 5 [] J Proakis, M Salehi, Digital Commuiatios, ew York: The MGraw-Hill Compaies, (Editor: Yao ZHOU)