Joint Doppler frequency shift compensation and data detection method using 2-D unitary ESPRIT algorithm for SIMO-OFDM railway communication systems

Transcription

1 Jont Dopper frequeny shft ompensaton and data deteton method usng 2-D untary ESPRIT agorthm for SIMO-OFDM raway ommunaton systems Huyue Y, Member, IEEE Abstrat In ths paper, we present a jont Dopper frequeny shft ompensaton and data deteton method usng 2-D untary ESPRIT agorthm for SIMO-OFDM raway ommunaton systems over fast tme-varyng sparse mutpath hannes. By reatng the spato-tempora array data matrx utzng the ISI-free part of the CP (y prefx), we frst propose a nove agorthm for obtanng auto-pared jont DOA and Dopper frequeny shft estmates of a paths va 2-D untary ESPRIT agorthm. Thereafter, based on the obtaned estmates, a jont Dopper frequeny shft ompensaton and data deteton method s deveoped. Ths method onssts of three parts: (a) the reeved sgna s spatay ftered to get the sgna orrespondng to eah path, and the sgna orrespondng to eah path s ompensated for the Dopper frequeny shft n tme doman, (b) the Dopper frequeny shft-ompensated sgnas of a paths are summed together, and () the desred nformaton s deteted by performng FFT on the summed sgna after exudng the CP. Moreover, we prove that the hanne matrx beomes tme-nvarant after Dopper frequeny shft ompensaton and the ICI s effetvey avoded. Fnay, smuaton resuts are presented to Ths work was supported n part by the Natona key projet under Grant 20ZX and 202ZX , n part by the Sene and Tehnoogy Breakthrough Pan of Shangha Sene and Tehnoogy Commttee under Grant 0DJ Huyue Y s wth the Shangha Researh Center for Wreess Communatons (WCO) and Key Laboratory of Wreess Sensor Networks & Communaton, Shangha Insttute of Mrosystem and nformaton tehnoogy, Chnese Aademy of Sene, 6th foor, Lane. 280-, Lnhong Road, Changnng Dstrt, Shangha , P. R. Chna (e-ma: y_huyue@yahoo.om.n; huyue.y@ma.sm.a.n).

2 2 demonstrate the performane of the proposed method and ompare t wth the onventona method. Index Terms Untary ESPRIT; dreton of arrva; array sgna proessng; beamformng; Dopper frequeny shft; spata fterng I. INTRODUCTION Aong wth the deveopments of the hgh-speed raway n many ountres, the onventona Goba System for Mobe Communatons Raways (GSM-R) []-[2] an t meet the requrement for aessng hgh bandwdth for broadband mutmeda serves wth suffent eve of QoS from nreasng number of passengers on hgh-speed trans. In order to meet ths requrement, a W-F based ommunaton system was ntrodued for the ground-tran onneton [3]. Though W-F based system s attratve n terms of the ost effeny, t s not easy to mantan the ommunaton quaty beause the overage of eah wreess aess pont (AP) s sma and the mobe trans experene frequent Layer 2 and Layer 3 handovers. Wth the nreasng of tran speed and demandng of data rate, t s gettng more and more mportant to provde a better nk quaty n hgh-mobty ommunaton systems. Broadband aess on the tran s provded through the tran aess termna (TAT) [4]-[5], where data from a passengers n the tran are frst oeted by the TAT, and then though the antenna on the top of the tran devered to the ground base staton (BS). Reenty, the Long Term Evouton for Raway (LTE-R) beomes a promsng souton to provde hgh data rate n hgh-speed raway ommunaton [6]. The OFDM and MIMO are two ore tehnques of the LTE systems. In fadng hannes wth very hgh mobty, the tme-varyng wreess hannes wth arge Dopper spread may hange at eah OFDM symbo tme [7]-[2]. Ths tme varaton of the hanne over an OFDM symbo perod resuts n a oss of subarrer orthogonaty and thus w ead to nter-arrer nterferene (ICI) due to power eakage among OFDM subarrers [3]-[4].

3 3 As shown n [8], the tme-varyng mutpath hanne produes a tme-varyng ompex mutper at eah subarrer. Consequenty, trakng tme-varyng hannes wth arge Dopper spreads s a rta task to mtgate the ICI. There urrenty exst agorthms for hanne estmaton n mobe MIMO-OFDM systems wth arge Dopper shfts [0]-[2]. However, these agorthms a requre the use of extensve preambes or tranng sequenes n the tme frequeny doman, whh w derease the spetrum effeny. As s we known, array sgna proessng tehnques are wdey empoyed to aqure spata dreton-of-arrvas (DOA) of movng targets [5]-[6] and apped n wreess ommunatons [7]-[8]. In [9], a jont DOA-frequeny offset estmaton and data deteton method was ntrodued for the upnk MIMO-OFDM networks wth SDMA tehnques. In [20], the authors ntrodued an agorthm for jont estmaton of the parameters nudng the frequeny offsets, deays, and the ange seetvty n the upnk of mutuser MIMO-OFDM nterferene network. However, the method n [9] does not onsder the tme deay of dfferent paths, whe the agorthm n [20] onsders that the effet of the Dopper frequeny spreadng on the frequeny offsets of dfferent paths of the same user are neggbe. Therefore, the methods n [9]-[20] an not appy to the hgh-speed raway hanne wth arge deay spread and rapd Dopper transton whh an t be negeted. Reenty, ots of researh works [2]-[25] have shown the hannes n broadband wreess ommunaton systems an often be modeed as a sparse hanne, where the deay spread oud be very arge, but the number of domnant paths s normay very sma. In a vadut for the hgh-speed raway envronment where the traksde base staton (BS) s about 0-30 meters away from the raway trak [26], the satters are mted n ths envronment, and thus the speuar LOS omponents are muh stronger and other mutpath ehoes are enountered ess frequenty between the mobe tran and the traksde BS, whh provdes a bengn envronment for the broadband mobe rado provson. In [27], the raway ommunaton hanne mode s modeed as a sparse tme-varant mutpath hanne. In ths paper, we mode the raway ommunaton hanne as a

4 4 sparse fast tme-varyng mutpath hannes [7], and fous on nvestgatng Dopper frequeny shft ompensaton and data deteton method for SIMO-OFDM raway ommunaton systems. For SIMO-OFDM systems, some soutons to ombat ICI have been proposed [28]-[29], whh suppress Dopper-ndued ICI va reeve beamformng or adequate ombnng of the antenna sgnas. However, these approahes expot ony the statsta propertes of the ICI and therefore an ony partay mtgate the ICI effets. In [30], the authors ntrodued an ICI ompensaton tehnque for SIMO systems to ombat the nstantaneous Dopper-ndued ICI dstortons n the frequeny doman. Sne the FFT ntrodues the ICI beause of Dopper frequeny shft, there w be an rredube error foor for data deteton va frequeny-doman Dopper frequeny shft suppresson method n [30] when the normazed Dopper frequeny shft s reatvey hgh. Consequenty, the Dopper frequeny shft shoud be ompensated n the tme doman before the FFT. As a resut, n ths paper we w fous on nvestgatng Dopper frequeny shft ompensaton methods n tme doman before the FFT. Utzng array sgna proessng tehnques, n ths paper we propose an effent jont Dopper frequeny shft ompensaton and data deteton method usng 2-D untary ESPRIT agorthm [3]-[32] for SIMO-OFDM raway ommunaton systems over fast tme-varyng sparse mutpath hannes. We frst propose a nove effent agorthm for obtanng jont DOA and Dopper frequeny shft estmates of eah path for sparse mutpath hannes by utzng 2-D untary ESPRIT agorthm [3]-[32]. In the proposed agorthm, we begn wth reatng spato-tempora array data matrx n a way as n [33] by utzng the ISI-free part of the CP (y prefx), and then obtan the auto-pared jont DOA and Dopper frequeny shft estmates of eah path for sparse mutpath hannes va 2-D untary ESPRIT agorthm. Thereafter, based on the auto-pared jont DOA and Dopper frequeny shft estmates of eah path, a jont Dopper frequeny ompensaton and data deteton method s deveoped. Ths method many onssts of the foowng two parts: (a) the reeved sgna s spatay ftered to get the sgna orrespondng

5 5 to eah path, and the sgna orrespondng to eah path s ompensated for the Dopper frequeny shft, and (b) the Dopper frequeny shft-ompensated sgnas of a paths are summed together n tme doman, and then the desred nformaton s deteted by performng FFT on the summed sgna after exudng the CP. Moreover, we prove that the hanne matrx beomes tme-nvarant after performng Dopper frequeny shft ompensaton and the ICI s effetvey avoded. Sne the Dopper frequeny shft s ompensated n the tme doman before the FFT, the Dopper frequeny shft w not affet the performane of the proposed jont Dopper frequeny shft ompensaton and data deteton method, and therefore the proposed method outperforms the data deteton method [30] va frequeny-doman Dopper frequeny shft suppresson n frequeny doman and the onventona methods [8], []-[2]. Fnay, smuaton resuts are presented to demonstrate the performane of the proposed jont Dopper frequeny shft ompensaton and data deteton method and ompare t wth the onventona method. The organzaton of ths paper s as foows. In Seton Ⅱ, we frst ntrodue the system mode of the SIMO-OFDM raway ommunaton system n fast tme-varyng sparse mutpath hannes. Then, we ntrodue the onventona method, and desrbe ts shortomngs. Fnay, we present a nove jont Dopper frequeny shft ompensaton and data deteton method usng 2-D untary ESPRIT agorthm for SIMO-OFDM raway ommunaton systems. Smuaton resuts and onusons are gven n Setons Ⅲ and Ⅳ, respetvey. II. JOINT DOPPLER FREQUENCY SHIFT COMPENSATION AND DATA DETECTION METHOD USING 2-D UNITARY ESPRIT ALGORITHM FOR SIMO-OFDM RAILWAY COMMUNICATION SYSTEMS In ths seton, we frst ntrodue the system mode for SIMO-OFDM raway ommunaton systems. Then, we brefy ntrodue the onventona data deteton method for SIMO-OFDM ommunaton systems, and desrbe ts dsadvantages. Fnay, we propose a nove jont Dopper

6 6 frequeny shft ompensaton and data deteton method usng 2-D untary ESPRIT agorthm for SIMO-OFDM raway ommunaton systems, and desrbe ts advantages over the onventona methods. A. System mode for SIMO-OFDM raway ommunaton systems Fg. shows the system mode for the SIMO-OFDM raway ommunaton systems, whh onssts of an antenna array of M reeve antennas at the traksde BS and one transmt antenna mounted on the top of a movng tran. In Fg., D s the dstane between the traksde BS and the raway, and orresponds to the DOA of the LoS path wth tg( ) Dr. satter - 2 M 2 antenna array on traksde BS satter D antenna on the tran r raway Fg.. System mode for SIMO-OFDM raway ommunaton systems In OFDM mutarrer systems, the nformaton symbos to be transmtted are frst grouped nto boks of N data symbos at the transmtter on the tran, and the th bok s represented by the vetor d [ d (0), d (),, d ( N )] T. The data symbos d ( k ) from a ertan moduaton onsteaton n a fnte symbo set an be assumed to be equ-probabe and statstay ndependent of dfferent subarrers and boks. Thus, d ( k ) an be approxmated as random varabes wth zero mean and orreaton E d j d j j j, where 2 d s the 2 [ ( ) ( )] d ( ) ( ) power of data symbos and * s the onjugate operator. Eah bok s aed a frequeny-doman

7 7 OFDM symbo. In order to emnate nterferene between parae data streams, an N pont nverse fast Fourer transform (IFFT) s apped to ths bok. Then, a y prefx (CP) of ength N g as a opy of the ast part of the IFFT output s nserted at the begnnng of eah symbo as the guard nterva (GI) to avod nter-symbo nterferene (ISI), and ts ength N g s assumed to be not shorter than the hanne ength. Thus, n dsrete tme, the baseband mutarrer sgna transmtted by the antenna on the tran an be wrtten as foows: N j2 nk / N, Ng k N k 0 s ( n) d ( k) e () When the tran s movng at a speed of v, the Dopper frequeny shft of the reeved sgna w be gven by f d fv v os( ) os( ) (2) where f s the arrer frequeny, s the arrer waveength of the reeved sgna, and denotes the ange between the dreton of the movng tran and the dreton of the traksde BS. Then, the Dopper frequeny shfted OFDM symbo s gven by [9] N [ j2 ( nk / N) j2 ( ) ( ) nfdts] (3) k 0 s n d k e where T s s the duraton of the orgna data symbo. The OFDM s senstve to Dopper frequeny shft and the system performane deterorates wth an nrease n the Dopper frequeny shft. As ustrated n [26]-[27], the raway ommunaton hanne an be modeed as a fast tme-varyng sparse mutpath hanne between the traksde BS and the hgh-speed tran. We assume the hanne vares durng the duraton of an OFDM symbo due to the Dopper frequeny shft. Let Q be the number of resovabe paths n ths mutpath envronment. Eah path s parameterzed by DOA, tme deay (measured n unt of the symbo perods T s ), the Dopper

8 8 frequeny shft f d,, and ompex path attenuaton fator (), whh s assumed statonary wthn an OFDM symbo perod but varyng between OFDM symbos. In addton, the maxmum hanne deay s denoted as max max. We assume orresponds to the DOA of the LoS path Q wth tg( ) Dr, as an be seen from Fg.. Under the above assumptons, the hanne an be modeed as [7] Q ( j2 fd, t) t e t H () a ( ) () ( ) (4) where a ( ) s the M array response to a path from the dreton, whh for the unform near array (ULA) has the form d d j2 sn( ) j2 ( M) sn( ) T a( ) [, e,, e ] (5) where d s the nter-eement spang of the antenna array. Durng the transmsson, the transmtted sgna s ( n ) passes through the mutpath hanne wth the mpuse response H ( t), and gets orrupted by a spatay unorreated addtve whte Gaussan nose. In the th OFDM bok, the dsrete-tme reeved sgna vetor at the antenna array of the traksde BS an be expressed as the onvouton of the transmtted sgna s ( n ) wth the hanne matrx H () t : Q y ( n) ( ) a( ) s( n ) v( n) Q N 2 ( ) j n k j2 ( n) fd, Ts N { ( ) a( ) e [ d( k) e ]} v( n) k0 N 2 d, 2 j nk f Q j k j2 ( n ) N Nf N a k0 d ( k) e [ ( ) ( ) e e ] v( n) (6) where y ( n) s the n th sampe of the antenna array output vetor, and v ( n) s a M AWGN 2 vetor wth ovarane matrx I M ( I M s the M M dentty matrx). Let us defne

9 9 f Q d, j2 ( n ) Nf j2 k/ N k, n e e H ( ) [ ( ) a ( ) ] (7) At the reever, n the range 0 n N of the th OFDM symbo, the reeved sgna s not orrupted by the prevous OFDM symbos due to the presene of the CP. Then, y ( n) an be rewrtten as N j2 nk/ N ( n) d( k), k( n) e ( n) k 0 y H v, 0 n N (8) Our am s to effenty detet the desred nformaton symbo d [ d (0), d (),, d ( N )] T form the reeved sgna y ( n). B. Conventona data deteton approah In the onventona reever [8], the demoduaton s performed usng the FFT after exudng the guard nterva CP. Then, the output for the m th subarrer of the th bok an be expressed as Y m, N N N N n0 y ( ne ) j2 nm/ N N 2 2 N j nk j nm N N [ d( k) H, k( n) e ] e Vm n0 k0 N N j2 ( km) n/ N [ d( k) H, k( n) e ] Vm k0 n0 (9) where N j2 nk / N ( ne ) n 0 Vm v. From (9), we obtan the k th subarrer of the th bok as foows: Yk, Hk, d( k) ηkv k (0) where N k, N n 0 k, H ( / ) H ( n), and N N j2 ( k mnn ) / k N d m 0, m k m, k n e n0 η ( / ) [ ( ) H ( ) ]. The η k represents the ICI aused by the effet of the Dopper frequeny shft. When the maxma normazed Dopper frequeny s reatvey sma, the power of the ICI η k an be negeted

10 0 ompared to the bakground nose power. In ths ase, the desred sgna an be reovered as foows: dˆ ( k ) H Y /( H H ) d ( k ) H ( η V )/( H H ) () H H H H k, k, k, k, k, k k k, k, Beause the hanne matrx H k, s tme-varyng, so t requres ntensve pot subarrers to estmate H k,, whh w derease the spetrum effeny. Moreover, sne the Dopper frequeny shft destroys the orthogonaty between subarrers, the FFT ntrodues ICI η k. Consequenty, there w be an rredube error foor for the onventona method when the normazed Dopper frequeny shft beomes reatvey hgh. C. Jont Dopper frequeny shft ompensaton and data deteton method usng 2-D untary ESPRIT agorthm In ths subseton, we present a nove jont Dopper frequeny shft ompensaton and data deteton method usng array sgna proessng tehnques for the SIMO-OFDM raway ommunaton systems. The proposed method onssts of two stages: () jont DOA and Dopper frequeny shft estmaton usng 2-D untary ESPRIT agorthm; (2) Dopper frequeny shft ompensaton and data deteton. ) Jont DOA and Dopper frequeny shft estmaton agorthm usng 2-D untary ESPRIT In ths subseton, we propose a jont DOA and Dopper frequeny shft agorthm by utzng 2-D untary ESPRIT agorthm [3]-[32]. In vetor form, y ( n) n (6) an be rewrtten as f Q d, j2 ( n ) Nf y ( n) { ( ) a( ) e s ( n )} v ( n) ABd ( n) v ( n) 0 0 (2) M Q where A [ a( ), a( 2),, a( Q )] C, B dag{ () (2) ( Q)} s the Q Q fadng matrx, d ( n) g ( n) s ( n) s the Q tempora sgnature matrx, where denotes the

11 Hadamard produt, f, f d, Q j2 ( n 2 ( ) ) d j n Q N N f f T g ( n) [, e,, e ], and s ( n) [ s ( n ) s ( n ) s ( n )] T. From (2), we an get 2 Q y ( n N ) fd, f Q d, j2 j2 ( n ) f Nf a e e s n N v0 n N { ( ) ( ) ( )} ( ) AΦBg ( n) s ( nn ) v ( nn ) 0 (3) where j 2 f d, f j2 f d,2 f j2 f d, Q f Φ dag{ e, e,, e }. We partton the CP of ength N g nto two parts: ISI-ontamnated part of ength max, and ISI-free part of ength P,.e., Ng max P. Sne s( n) s( N n) ( nn g,, ), then n the ISI-free part we have s ( n) s ( nn ), n P,,. (4) As a resut, we obtan y ( n N ) AΦBd ( n) v ( nn ) 0, n P,, (5) In order to jonty estmate the DOA and Dopper frequeny shft of eah path va 2-D untary ESPRIT [3]-[32], we reate the foowng spato-tempora array data matrx n a smar way as n [33]: y( P) y( P) y( ) Y ( N P) ( N P) ( N ) y y y A BD V AΦ ΩBD V C 2M P (6) where 2M Q Ω s referred to as the spato-tempora array manfod matrx, 2 C M P V s the nose matrx, and D [ d ( P) d ( P),, d ( )]. The ondtons on the parameters M, P n (6) for guaranteeng the resovabty of sgnas of Q paths are anayzed thoroughy n [33], and thus

12 2 s omtted here. Based on the data matrx Y n (6), the auto-pared ( ˆ, ˆ fd, ) estmates (, 2,, Q) an be effenty obtaned usng the 2-D untary ESPRIT agorthm n [3]-[32]. 2) Dopper frequeny shft ompensaton and data deteton method Based on auto-pared ( ˆ, ˆ fd, ) estmates, we propose a nove Dopper frequeny shft ompensaton and data deteton method n ths subseton. For smpfyng the exposton of the proposed method, we assume that ( ˆ, ˆ fd, ) of a paths are perfety estmated,.e., ˆ, and f f (, 2,, Q). The effet of estmaton errors of (, fd, ) on the performane of the ˆd, d, proposed method w be evauated through smuatons. In order to fter out the sgna orrespondng to the th path, we onstrut Q spatay-fterng matres as foows [9]: F ITT,, 2,, Q (7) where T ˆ ˆ ˆ ˆ [ a( ),, a( ), a( ),, a( Q)], and () s the Moore-Penrose pseudo nverse. Then, the spatay-ftered sgnas for the th path s gven by z( n) Fy ( n),, 2,, Q (8) () ( ) e s ( n ) Fv ( n) fd, j2 ( n ) Nf a 0 The spatay ftered sgna z ( n) ony onssts of the desred sgna form the DOA ˆ of the th path. After the spatay ftered sgna z ( n) s mutped wth exp[ j2 nfˆ d, / N f ] to ompensate for the Dopper frequeny shft f d,, we obtan j2 nfˆ d, / Nf x ( n) e z ( n) fd, j2 N j2 nfˆ d, / N f f a () ( ) e s ( n ) e Fv ( n) fd, j2 Nf a v () ( ) e s ( n ) ( n) 0 (9) Then, we ompute the sum of the Dopper-frequeny ompensated sgna x ( n) of a paths n the tme doman as foows:

13 3 f Q d, j2 N Q Nf j2 ( n) k/ N a v k0 N d, f Q k j2 ( ) Nf N j2 nk/ N a v k0 N k 0 Q x ( n) x ( n) () ( ) e [ d ( k) e ] ( n) d ( k){ ( ) ( ) e } e ( n) d k e n j2 nk/ N ( ) H, k v( ) (20) where fd, k Q j2 ( ) Nf N k, () ( ) e H a. Compared wth tme-varyng H, ( n) n (9) n the k onventona method, H k, n (20) beomes tme-nvarant n the duraton of an OFDM symbo. Thus, the requred number of pot subarrers for estmatng H k, w be ess than that for estmatng H k, n (0). The demoduaton s performed on x ( n ) n (20) usng the FFT after exudng the CP. Then, the output for the m th subarrer of the th bok an be expressed as z H v (2) NN j2 n( km)/ N ( m) d( k), ke ( m) N n0 k0 From (2), we obtan the output for k th subarrer of the th bok as foows: z ( k) H d ( k) v ( k) (22), k Comparng wth the onventona data detet method n () where there are ICI term η k aused by the effet of the Dopper frequeny shft, there s no ICI term n (22) beause the Dopper frequeny shfts have been effetvey ompensated n the tme doman before the FFT. As a resut, the Dopper frequeny shft w not affet the performane of the proposed method, whh w be demonstrated va smuatons n Seton Ⅲ. Utzng maxmum rato ombnng (MRC), the frequeny-doman symbo estmates d ˆ ( k ) an be obtaned as: dˆ ( k ) H z ( k )/[ H H ] d ( k ) H v ( k )/( H H ) (23) H H H H k, k, k, k, k, k, Fnay, we an retreve the nformaton bts from d ˆ ( k ).

14 4 III. SIMULATIONS AND DISCUSSIONS In ths seton, we demonstrate through omputer smuatons the performane of the proposed jont Dopper frequeny shft ompensaton and data deteton method usng 2-D untary ESPRIT for the SIMO-OFDM raway ommunaton systems and ompare t wth the onventona method. In smuatons, the number of reeve antennas at the traksde BS s set to M 5, and the reeve antennas take the form of a ULA wth an nter-eement spang of /2. The number of subarrers N s 52, the nterarrer spang s 5kHz, and the maxmum hanne tme deay s. Informaton symbos d ( n ) (,2,,52) are ndependent and dentay dstrbuted max 28 (..d.) QPSK symbos. For the mutpath hanne, we assume the number of path s Q 3. The DOAs of three paths are (, 2, 3) (,35,60 ), and the tme deays are (, 2, 3) (0, 2,6) T s. j The path attenuaton fator for the three path are, respetvey, () e 2, (2) 0.6 j e, and 3 (3) 0.36 j e, where (,2,3) are random nta phases. The veoty of the tran s v 360km/h (.e., 00m/s). In order to ustrate the effet of Dopper frequeny shfts on the performane of the proposed method, the arrer frequeny f s set as 3GHz, 6GHz and 9GHz to produe varous maxmum Dopper frequeny shfts. The maxmum Dopper frequeny shfts orrespondng to 3GHz, 6GHz and 9GHz are, respetvey, 000Hz, 2000Hz, and 3000Hz. As the performane of the proposed Dopper frequeny shft ompensaton and data deteton method depends on the auray of the auto-pared DOA and Dopper frequeny shft estmates, n the foowng we frsty examne the performane of the proposed jont DOA and Dopper frequeny shft estmaton agorthm va 2-D untary ESPRIT. Then, we provde smuaton resuts to ustrate the performane of the proposed Dopper frequeny shft ompensaton and data deteton method.

15 5 A. Performane of the proposed jont DOA and Dopper frequeny shft estmaton agorthm va 2-D untary ESPRIT In ths subseton, we provde smuaton resuts to ustrate the performane of the proposed jont DOA and Dopper frequeny shft estmaton agorthm va 2-D untary ESPRIT. In smuatons, we set the arrer frequeny f 9GHz, and the Dopper frequeny shfts ( f, f, f ) (3000,2500,500)Hz. Fg. 2 shows the mean vaues of the estmates for the DOA d, d,2 d,3 and Dopper frequeny shfts d, f versus E b /N 0 for varous ength P when f 9GHz, and the dashed ne wth a mark * denotes the true vaues of and f d,. Fg. 3 shows the root mean square error (RMSE) of the estmates for the DOA and Dopper frequeny shfts f d, versus E b /N 0 for varous ength P when f 9GHz. The orrespondng resuts for ( 2, f d,2 ) and ( 3, f d,3) are smar and therefore not potted n Fg. 2 and Fg. 3 for arty. At eah E b /N 0, 2000 Monte Caro ndependent tras were performed to obtan the statsta resuts. As an be seen for Fg. 2, the mean vaues for the estmates of and f d, tend to approah the true vaues as the SNR nreases, and onverge to the true vaues for P 25 when E b /N 0 >26dB. It an be seen from the Fg. 3 that the RMSEs for the estmates of and f d, tends to derease as the SNR nreases, and onverge to zero for P 25 when E b /N 0 >26dB. Moreover, the performane of the proposed jont DOA and Dopper frequeny shft estmaton agorthm mproves as the ength P nreases, and ts performane mproves about 4dB when P nreases from 25 to 00.

16 6 (a) 0 DOA (deg) -5 P=25-0 P=50-5 P=00 true E b /N 0 (db) (b) f d, dopper frequeny (Hz) P=25 P=50 P=00 true E b /N 0 (db) Fg. 2 Mean vaues of the estmates for the DOA and Dopper frequeny shfts f d, versus E b /N 0 for varous ength P when f 9GHz

17 7 (a) RMSE (deg) 0 5 P=25 P=50 P= E b /N 0 (db) (b) f d, RMSE (Hz) P=25 P=50 P= E b /N 0 (db) Fg. 3 Root mean square error (RMSE) of the estmates for the DOA and Dopper frequeny shfts f d, versus E b /N 0 for varous ength P when f 9GHz B. Performane of the proposed Dopper frequeny shft ompensaton and data deteton method In ths subseton, smuaton resuts are presented to ustrate the performane of the proposed Dopper frequeny shft ompensaton and data deteton method and ompare t wth the onventona method. In order to fous on the effet of the jont DOA and Dopper frequeny shft estmaton agorthm on the performane of the proposed method, we assume that the hanne matrx H k, n the onventona method () and H k, n the proposed method (23) are perfety known. In addton, we set the Dopper frequeny shft ( fd,, fd,2, fd,3) (3000,2500,500)Hz

18 8 when f 9GHz, ( fd,, fd,2, fd,3) (2000,667,000)Hz when f 6GHz, and ( f, f, f ) (000,833,500)Hz when f 3GHz. d, d,2 d,3 Fg. 4 shows the BER performane of the proposed Dopper frequeny shft ompensaton and data deteton method versus E b /N 0 for varous arrer frequeny f when P 00. The orrespondng resuts for the proposed method wth perfet (, fd, ) and the onventona method are aso shown for omparson. Note that as the arrer frequeny f nreases from 3GHz to 9GHz, the normazed maxmum Dopper frequeny shft nreases from 000/5000 (0.067) to 3000/5000 (0.2). As an be seen from Fg. 4, when the arrer frequeny f nreases from 3GHz to 9GHz, the BER performane of the onventona method deterorates sgnfanty, whe the BER performane of the proposed method wth estmated (or perfet) (, fd, ) remans unhanged. As expeted, the proposed method wth perfet (, fd, ) outperforms the onventona method rrespetve of Dopper frequeny shfts. Ths s beause the Dopper frequeny shft of eah path s effetvey ompensated n the tme doman before FFT n the proposed method, and thus the Dopper frequeny shft w not destroys the orthogonaty between the subarrers. Moreover, due to the estmaton errors of (, fd, ) estmates, the performane of proposed method wth estmated (, fd, ) ( P 00) degrades about 2dB ompared to that wth perfet (, fd, ) when E b /N 0 <24dB and s very ose to that wth perfet (, fd, ) when E b /N 0 24dB. Ths s beause the estmaton errors of (, fd, ) s reatvey arge when E b /N 0 <24dB and s very sght when E b /N 0 24dB n the ase of P 00, as shown n Fg. 2 and Fg. 3. In order to further demonstrate the performane of the proposed Dopper frequeny shft ompensaton and data deteton method, we examne the effet of varous ength P of ISI-free part of the CP on the performane of the proposed method. Fg. 5 shows the BER performane of the proposed Dopper frequeny shft ompensaton and data deteton method versus E b /N 0 for

19 9 varous ength P when the arrer frequeny f 9GHz. The orrespondng resuts for the proposed method wth perfet (, fd, ) are aso shown for omparson. As an be seen from Fg. 5, the performane of the proposed method mproves as the ength P nreases. Ths s beause the estmaton auray of (, fd, ) estmates mproves as the ength P nreases, as shown n Fg. 2 and Fg BER onventoan method:9ghz onventoan method:6ghz onventoan method:3ghz proposed wth perfet (, f d, ):9GHz proposed wth perfet (, f d, ):6GHz proposed wth perfet (, f d, ):3GHz proposed wth estmated (, f d, ):9GHz proposed wth estmated (, f d, ):6GHz proposed wth estmated (, f d, ):3GHz E b /N 0 (db) Fg. 4 BER performane of the proposed Dopper frequeny shft ompensaton and data deteton method versus E b /N 0 for varous arrer frequeny f when P 00

20 BER proposed method wth perfet (, f d, ) proposed method wth estmated (, f d, ): P=00 proposed method wth estmated (, f d, ): P=50 proposed method wth estmated (, f d, ): P= E b /N 0 (db) Fg. 5. BER performane of the proposed Dopper frequeny shft ompensaton and data deteton method versus E b /N 0 for varous ength P when the arrer frequeny f 9GHz IV. CONCLUSION In ths paper, we have presented a nove jont Dopper frequeny shft ompensaton and data deteton method usng 2-D untary ESPRIT agorthm for SIMO-OFDM raway ommunaton systems over fast tme-varyng sparse mutpath hannes. We frst proposed a nove agorthm for obtanng jont DOA and Dopper frequeny shft estmates of a paths by usng 2-D untary ESPRIT agorthm. The proposed agorthm begns wth reatng spato-tempora array data matrx by utzng the ISI-free part of the CP (y prefx), and then obtans the auto-pared jont DOA and Dopper frequeny shft estmates of eah path va 2-D untary ESPRIT agorthm. Thereafter, based on the auto-pared jont DOA and Dopper frequeny shft estmates, a jont Dopper

21 2 frequeny ompensaton and data deteton method has been deveoped. Ths method many onssts of two steps. Frsty, the reeved sgna s spatay ftered to get the sgna orrespondng to eah path, and the sgna orrespondng to eah path s ompensated for the Dopper frequeny shft. Seondy, the Dopper frequeny shft-ompensated sgnas of a paths are summed together n the tme doman, and the desred nformaton s deteted by performng FFT on the summed sgna after exudng the CP. Moreover, we prove that the hanne matrx beomes tme-nvarant after performng Dopper frequeny shft ompensaton and the ICI s effetvey avoded. Fnay, t has been shown va smuatons the effetveness of the proposed jont DOA and Dopper frequeny shft ompensaton agorthm as we as the proposed jont Dopper frequeny shft ompensaton and data deteton method. As expeted, smuaton resuts have shown that the performane of the proposed method s not affeted by the Dopper frequeny shft, and the proposed method exhbts muh better BER performane than the onventona method when the normazed maxmum Dopper frequeny shft s reatvey hgh. REFERENCES [] H. Hofestadt, GSM-R: goba system for mobe rado ommunatons for raways, IEEE Internatona Conferene on Eetr Raways n a Unted Europe, Amsterdam, Netherands, Mar 995, pp. -5 [2] C. Brso-Rodríguez, C. Cortes, F. J. Arques, I. Aonso, Requrements of GSM tehnoogy for the ontro of hgh speed trans, n Pro. Pers., Indoor, Mobe Rado Commun. Conf., Feb. 2002, pp [3] K. Yamada, Y. Saka, T. Suzuk, Y. Kawahara, T. Asam, H. Ada, A ommunaton system wth a fast handover under a hgh speed mobe envronment, IEEE Conferenes on Vehuar Tehnoogy, 200, pp.-5

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