Directional Beamforming for High-Speed Railway Communications with. Frequency offset precorrection.

Transcription

1 Chnese Journal of Electroncs Vol.23, No.1, Jan Drectonal Beamformng for Hgh-Speed Ralway Communcatons wth Frequency Offset Precorrecton CAO Yuan 1,2, WEN Ynghong 1,XUWe 3,2 and XIE Xn 3 (1.School of Electroncs and Informaton Engneerng, Natonal Engneerng Research Center of Ral Transportaton Operaton and Control System, Bejng Jaotong Unversty, Bejng 10044, Chna) (2.State Key Laboratory of Ral Traffc Control and Safety, Bejng Jaotong Unversty, Bejng 10044, Chna) (3.Natonal Moble Communcatons Research Lab., Southeast Unversty, Nanjng , Chna) Abstract Ths paper consders a mult-antenna transmsson strategy for hgh speed ralway communcatons. In order to acheve better performance than conventonal space-frequency block codng schemes, we propose a drectonal beamformng strategy for the Hgh-speed ralway (HSR) communcaton by explotng some characterstc of the ralway system ncludng predetermned movng tracks and real-tme postonng nformaton. Moreover, for allevatng the effect of Doppler shft due to the movng tran, a frequency offset precorrecton method s also ncorporated wth drecton beamformng. Theoretcal Sgnalto-nose rato (SNR) gan of the proposed beamformng scheme over tradtonal HSR communcaton schemes s also derved for llustratng the performance enhancement. Numercal results verfy the effectveness of our proposed scheme even wth some knd of mperfect poston nformaton avalable at the transmtter. Key words Multple-nput multple-output (MIMO), Drectonal beamformng, Hgh-speed ralway communcatons, Frequency offset precorrecton. I. Introducton Wth the rapd development of wreless communcaton technologes, people are gettng used to access wreless data servces anywhere and anytme. It s reported that the wreless data servce demand has been coupled annually durng the past few years, and over 70% of the data servces are provded under ndoor scenaros lke at offce, home, and transportatons ncludng Hgh-speed ralway (HSR) [1]. Durng recently years, there has been a sgnfcant development of the HSR transportaton system. The maxmum operaton speed of a HSR can acheve over 350 km/h whch hghly facltates travellng all across the country. However, communcaton qualty wll decrease sgnfcantly and even paralyze due to the great ncrement of the termnal movng speed. It has been revealed that the outage grows from 0% to over 25% of voce servces as the movng speed ncreases to 200 km/h [2]. Asfortheevenhghspeed over 300 km/h, the wreless communcaton qualty and relablty degrades exponentally and becomes a major challenge for the wreless system desgn under hgh speed ralway scenaros. Recently, wth the wdely deployment of hgh-speed ralways, dfferent wreless access demands for both voce and data transmssons are ncreasng dramatcally. Especally for a tran wth about passengers on board, the requred transmsson rate at the entre tran s even larger. There have been multple ways, ncludng WMax [2] and LTE/LTE-R [3,4] etc., for mprovng both the transmsson rate and the relablty under the HSR scenaros. In the most advanced moble communcaton protocol called LTE, there has been a specfed applcaton scenaroguaranteed for hghspeed ralways wth moblty as hgh as 300 km/h. [5] Meanwhle, the Multple-nput multple-output (MIMO) technque has been well acknowledged as a promsng technque for sgnfcantly enhancng the wreless communcaton system by explotng multple antennas at both the transmtter and the recever [6]. As suggested by the Internatonal Unon of Ralways (UIC), the next generaton evoluton of ralway moble communcatons system wll follow the LTE protocol wth usng mult-antenna technques for provdng relable broadband servces and applcatons. Accordng to Ref.[5], the space-tme codng technque s currently exploted under the HSR scenaros for achevng multantenna dversty gans. The Space-frequency blockcodng (SFBC) technque was frstly proposed by Alamout n Ref.[7] for a smple two-by-two MIMO system, and t was then extended for MIMO systems equpped wth more antennas [8,9]. Note that the spacetme codng technque s desgned for a MIMO system wthout any channel nformaton at the transmtters. If the channel nformaton s avalable at the transmtter, t s known that the MIMO performance can be further mproved by explotng beamformng/precodng technques [10]. However, for applcatons lke HSR, t s dffcult to acqure the Channel state nformaton (CSI) especally at the transmtter. Wth conventonal CSI feedback, there can be an obvous CSI msmatch due to severe channel varances under feedback delay and hgh moblty. Therefore, wth an ncreasng tran speed, t s hard to mplement beamformng over the ralway communcatons, hence wthout achevng the addtonal performance gan. On the other hand, n order to reduce the cell swtchng brought about by hgh-speed movement, the coverng method of Manuscrpt Receved Feb. 2013; Accepted Mar Ths work s supported by the Fundamental Research Funds for the Central Unverstes (No.2012JBM023), the State Key Laboratory of Ral Traffc Control and Safety Bejng Jaotong Unversty (No.RCS2011K003), the 973 program (No.2013CB329204), the Natonal Natural Scence Foundaton of Chna (No ), and the Specalzed Research Fund for the Doctoral Program of Hgher Educaton (No , No ).

2 164 Chnese Journal of Electroncs 2014 Base band unt (BBU) and Remote rado unt (RRU) s adopted [11]. When a hgh-speed tran goes through two RRUs common coverage area, t wll receve two peces of RRU sgnal, wth opposte Doppler shft and smlar sze of the sgnal power. Therefore, when the tran s located n the RRUs common coverage area, frequency devaton correcton at the recevng end s dffcult. In order to crcumvent ths dffculty, we propose a drectonal beamformng strategy for the HSR communcaton by explotng some characterstc of the ralway system ncludng predetermnedmovng tracks and real-tme postonng nformaton. Wth the proposed scheme, the beamformng vector at the Base staton (BS) s desgned accordng to the track and postonng nformaton as well as the ray-tracng approaches. Moreover, for allevatng the effect of Doppler shft due to the movng tran, a frequency offset precorrecton method s also ncorporated wth drecton beamformng. Theoretcal Sgnal-to-nose rato (SNR) gan of the proposed beamformng scheme over tradtonal HSR communcaton schemes s also derved for llustratng the performance enhancement. Numercal results show that our proposed drectonal beamformng scheme wth frequency offset precorrecton outperforms conventonal transmsson schemes under dfferent HSR communcaton scenaros. Our proposed method acheves hgh throughput and hence mprovng the relablty of hgh-speed tran to ground communcatons. II. HSR Communcatons Usng SFBC We consder a HSR communcaton system under the framework of LTE whch explots both Orthogonal frequency dvson multplexng (OFDM) and MIMO technques. In an OFDM system, frequency selectve channels can be transformed nto a bunch of subcarrers under flat fadng coeffcents. Therefore, wthout loss of generalty, the transmsson model s characterzed for a sngle subcarrer and the mplementaton across all other subcarrers can be made n the same way. For the HSR system wth n t transmt antennas and n r receve ones, denote H as the wreless MIMO channel between the BS and the antennas at the ralway tran. Then, the system model at the -th subcarrer can be expressed by LoS lnk. Generally, for a HSR channel, typcal values of K can be at least larger than 1 up to over 20. In current LTE for HSR communcatons, the well-known Alamout code based SFBC s utlzed for explotng the mult-antenna gans. For a 2 2 channel, the receved symbols follows ( ) y 0 y 1 = ( x 0 x 1 x 1 x 0 )( h1 h 2 ) + ( n 0 n 1 where x 0 and y0 are the transmt and receve symbol at the -th subcarrer on the frst antenna, respectvely, h 1 denotes the channel fadng at the frst antenna component n channel matrx H, n 1 s the correspondng nose component, and notaton represents the conjugate of the complex number. Then, by utlzng coherent combng at the recever, the symbol can be detected wth an enhanced sgnal-to-nose rato gven by ( h h 2 2 )/N 0 where N 0 s the nose energy of n. III. Drectonal Beamformng The dversty gan of the SFBC n Eq.(4) s proven to be two for the 2 2 channel [7]. However, for a system wth more antennas than four, no such orthogonal SFBC scheme can be found to provde full dversty gans characterzed by multple antennas. Moreover, due to the absence of the CSI at the transmtter, the performance of SFBC s always beaten by the beamformng technques. Therefore, t s natural to desgn a beamformng scheme for the multantenna HSR communcaton system. However, under the scenaro wth very hgh-moblty, t s dffcult to acqure accurate CSI at the transmtter especally for the channel matrx of mult-antenna systems. In the study, we wll present a beamformng desgn strategy ncorporated wth frequency offset precorrecton for the HSR communcaton system by explotng predcted CSI va tran poston nformaton at the transmtter. ) (4) y = Hwx + n (1) where x and y are the transmt and receved symbol at the -th subcarrer, respectvely, w s the pre-processng vector for the MIMO channel, and n represents the addtve whte Gaussan nose. Note that for the HSR system, n order to deal wth the severe penetraton loss due to the tran body, a common way s to deploy a relay staton outsde the tran body for recevng/transmttng mcrowave sgnals from/to the nearest BS. Ths helps the BS save t s transmt power and assst the passengers on board n recevng better qualty sgnals. As the relayng antennas beng utlzed, the channels between the HSR tran and the BS mostly follow the Lne-of-sght (LoS) nstead of a wdely assumed Raylegh fadng channel. Therefore, n ths study, we follow the standard channel model defned n LTE release 9 [5]. The channel H s assumed to be Rcean dstrbuted wth a sgnfcant LoS component and a mnor part of dspersve Raylegh fadng components. The probablty densty functon of a Rcean dstrbuted channel s gven by [6] f Z (Z) = z ( σ 2 exp z2 + A 2 ) ( ) Az 2σ 2 I 0 σ 2, z 0 (2) where z s the Rcean channel fadng, A 2 s the average energy of the LoS channel, and σ 2 s the average power of the Raylegh fadng component. Functon I 0 ( ) s the 0-th Bessel functon of the frst knd. Generally, the rato K = A 2 /2σ 2 (3) s utlzed to characterze the Rcean dstrbuton. For a specal case wth K = 0, the Rcean channel becomes a tradtonal Raylegh fadng channel, whle for K the Rcean channel reduces to a pure Fg. 1. Model of MIMO HSR communcatons 1. Drectonal beamformng desgn In order to desgn beamformng at the BS for the HSR communcaton, t s a prerequste that the channel nformaton should be avalable at the transmtter. However, the channel coeffcent H vares qute fast due to the hgh-speed moblty, hence conventonal methods lke CSI feedback may fal to work. Here, we present to frst predct the major LoS part of the channel accordng to the tran postonng system, and then the estmated LoS channel nformaton s utlzed for beamformng desgn. As for the HSR communcaton lnk usng relays, a major part of the H should be a LoS channel. Ths motvates us to desgn the beamformng drectng to the major LoS part whle gnorng the dspersve Raylegh fadng components. In a HSR system, the poston of the tran s much easer for the BS to have or estmate snce both the real-tme tran postons and movng tracks are avalable for the tran control system. As shown n Fg.1, the BS antennas are mounted at a heght of D and d away from the comng tran. Accordng to the wave propagaton equaton, the drect lnk between the two antennas can be evaluated by h k = a e j2πd k /λ c (5) where d k s the dstance between the -th transmt antenna at the BS and the j-th recevng antenna at the ralway, h k (that s the correspondng entry of the channel matrx H) representsthen- stantaneous channel gan between the two antennas, and a s the propagaton path-loss. As the antenna spacng dstance s much

3 Drectonal Beamformng for Hgh-Speed Ralway Communcatons wth Frequency Offset Precorrecton 165 smaller than the dstance d, the path-loss value a s treated as the same for all dfferent antenna pars. Denote that the transmt antennas at the BS are spaced Δ tλ c n a lne and the space of two adjacent recevng antennas at the ralway s Δ rλ c,whereλ c s the wavelength of the carrer wave. From Fg.1, we can calculate the dstance d k by d k = d +( 1)Δ rλ c cos φ r (k 1)Δ tλ c cos φ t (6) Then, by substtutng Eq.(6) to Eq.(5) and defnng Ω t =cosφ t and Ω r =cosφ r,tgves h k = a e j2πd/λc e j2π(k 1)ΔtΩt e j2π( 1)Δr Ωr (7) Further by stackng the Eq.(7) nto the channel matrx H, thelos part of the MIMO channel s now ready to be expressed by H LoS = a n tn r e j2πd/λc e r(ω r) e t(ω t) (8) where e r (Ω r)=[1, e j2πδrωr, e j4πδrωr,, e j2(nr 1)πΔrΩr ] T (9) and e t(ω t)=[1, e j2πδtωt, e j4πδtωt,, e j2(nt 1)πΔtΩt ] T (10) Generally as llustrated n Eq.(2), for a HSR lnk, the channel s Rcean dstrbuted wth a parameter K. Hence, from Eq.(8), the entre MIMO channel can be modeled by H = K K +1 H LoS(Ω r, Ω t)+ 1 K +1 H Ray (11) where H Ray represents the random component of the MIMO channel,.e., the Raylegh dstrbuted part. As we me stressed above, n a HSR channel, the CSI cannot be acqured by the transmtter properly because the channel vares very fast and CSI feedback strategy does not work. Therefore, from Eq.(8) and Eq.(11), we fnd that the component of H Ray s random and vares very quckly whle the LoS component H LoS only depends on the Arrval of angle (AoA) and the Departure of angle (DoA) of the transmttng waves. That s the LoS channel part H LoS s solely determned by the tran poston gven the BS poston s fxed. By explotng the tran poston nformaton and accordng to Eq.(8), we then are able to desgn the beamformng based on a sgnfcant LoS part of the MIMO channel H. By applyng Sngular value decomposton (SVD) to the LoS channel component, we have H LoS (Ω r, Ω t)=u 1 Σ 1 V H 1 (12) where U 1 and V 1 are untary matrces and Σ 1 s a dagonal matrx wth ts dagonal elements as sngular values of H LoS. To desgn the beamformer for the HSR communcaton, we set w = v 1 (13) where v 1 s the frst column of matrx V 1 whch corresponds to the maxmum sngular value of H LoS. By substtutng the channel Eq.(11) and the beamformer Eq.(13) to Eq.(1) and droppng the subscrpt wthout loss of generalty, the receved sgnal becomes K 1 y = K +1 H LoSv 1 x + K +1 H Rayv 1 x + n (14) Then, the BS detect the receved sgnal by usng a recevng matrx U H 1, t yelds the fnally detected sgnal as r = u H 1 y = 1 h Ray x +ñ (15) K +1 K K +1 σ 1x + where σ 1 s the maxmum sngular value of H LoS, hray = u H 1 H Rayv 1 s the equvalent Raylegh channel component and ñ = u H 1 n s the equvalent Gaussan nose. It s mportant to note that snce u H 1 and v 1 are a unt-norm vector, the equvalent channel h Ray s also a Raylegh dstrbuted component wth zero-mean and varance a 2 and also ñ due to ths reason shares the same Gaussandstrbuton but wth a dfferent varance of N 0. From Eq.(15), we can calculate the nstantaneous receved sgnal-to-nose rato by K 1 2 K +1 σ 1 + h Ray K +1 SNR I = (16) N 0 To further evaluate the system performance, the expected recevng SNR at the recever can then be derved by takng expectatons over the random channel components h Ray.Itgves SNR =E h[snr I ]= K σ a 2 K +1N 0 K +1N 0 = Kσ2 1 + a2 (K +1)N 0 (17) Notced that for a conventonal Sngle-nput sngle-output (SISO) system, the receved average SNR can be easly obtanedby SNR SISO = a 2 /N 0. By comparng the proposed beamformng performance n Eq.(17) wth theconventonal SISO case, the acheved beamformng gan can be characterzed by Gan = SNR SNR SISO = Kσ2 1 /a2 +1 K +1 (18) From the matrx, generally the maxmum sngular value σ1 2 s much larger than ts average squared norm, that s a 2 n Eq.(18). Therefore, the average SNR gan characterzed n Eq.(18) verfes that our proposed beamformng scheme s able to acheve a notceable performance enhancement for the HSR communcaton system. The performance gan over conventonal SFBC scheme wll also be shown by the numercal results. It wll be found that, even under some cases when the poston nformaton s assumed to be naccurate, our proposed drecton beamformng scheme stll outperforms exstng transmsson schemes. The followng descrpton concludes our proposed algorthm n detals. Poston Informaton Aded Drectonal Beamformng 1. Obtan the poston nformaton of the tran and get Ω t and Ω r; 2. Calculate d k and H LoS accordng to Eq.(6) and Eq.(8), respectvely; 3. Apply SVD to H LoS and get w accordng to Eq.(13); 4. Transmt usng the beamformer w over the HSR channel; 5. Do detecton usng U H 1 at the tran sde. 2. Frequency offset precorrecton In the above subsecton, we presented a poston nformaton based drectonal beamformng desgn n the HSR communcaton system. Although a notceable performance gan s evdenced n Eq.(18), the effect of Doppler shft under the HSR scenaro has so far not been consdered. But fortunately n Appendx A, we fnd that by ncorporatng our proposed beamformng wth a proper frequency offset precorrectonapproach, the Doppler shft wll not degrade our beamformng performance gan over exstng schemes. In order to keep the performance gan, a frequency offset precorrecton s requred. It s known that the Doppler shft due to the hgh moblty s gven by f d = f max cos α(t) (19) where f max = v c fc s the maxmal Doppler frequency shft wth fc beng the carrer frequency, v s the velocty of the tran, and c s the constant of speed of lght. Notaton α(t) reprents the angle between the tran movng drecton and the wave propagaton drecton. In a HSR communcaton system, as depcted n Fg.2, the value of

4 166 Chnese Journal of Electroncs 2014 cos α(t) s derved as follows D s/2 vt, 0 t D s/v Dmn 2 +(Ds/2 vt)2 cos α(t) = 1.5D s + vt D 2 mn +( 1.5Ds + vt)2, D s/v t 2D s/v cos α(t mod(2d s/v)), t > 2D s/v (20) Now gven the frequency offset calculated from Eq.(19) and Eq.(20), some standard frequency offset precorrecton methods lke n Refs.[13 15] can be exploted before mplementng the drectonal beamformng. Generally n LTE/LTE-A, the frequency offset s calculated wth the help of usng the plots wthn the OFDM symbols. For the HSR channel, the frequency offset can be done at the uplnk and then precorrecton s carred out for performance enhancement. It s mportant to note that althoughthe moble relay sde can estmate the Doppler shft through the downlnk frequency devaton estmaton, the BS obtans the tran locaton and speed nformaton through the GPS, tran control systems, tran schedules etc., hence gettng more precse nformaton of the Doppler shft. The performance of Doppler shft pre-correcton s proven better than that of frequency devaton correcton at the recever sde. Fg. 2. Doppler shft calculaton n HSR communcatons IV. Numercal Results In ths secton, we present some numercal results by computer smulatons. The performance of dfferent schemes are tested under a standard LTE Release 9 baesd physcal layer smulator. The system parameters are summared n Table 1. We compared our proposed Drectonal beamformng (DBF) strategy wth the conventonal SFBC scheme for HSR communcaton scenaros. The proposed scheme s tested under two dfferent cases wth and wthout accurate LoS channel drectonal nformaton. Note that snce the LoS channel component s estmated based on the postonng nformaton, we represent the LoS channel estmaton mperfecton equvalently by the naccurate postonng nformaton. Several dfferent levels of postonng error wth 5m, 10m, and 20m are tested for verfyng the effectveness over SFBC. Fg.3 frst presents the system throughput performance by usng conventonal SFBC scheme. The SFBC scheme s evaluated under the Rcean channel wth three dfferent parameters K = 0,1,20, and nfnty. Note that K = 0 ndcates that the channel s purely a Raylegh channel wthout any LoS components. Ths s a rare case n ralway communcatons but serves as a benchmark reference for comparsons. Factor K wth nfnty shows the case of a pure LoS channel. Ths s a very typcal HSR communcaton channel model evaluated n LTE R9 test cases. From Fg.3, we can fnd that the SFBC performance hgh depends on the channel types wth dfferent LoS components. For Low SNRs, the Raylegh channel acheves better performance than the pure LoS channel case, whle as the SNR grows, the performance of SFBC grows much faster under the LoS channel case than other channel types. In a HSR communcaton applcaton, the LoS component usually domnates the wreless channel and hence a hgher SNR s preferred by HSR communcatons wth SFBC. Fgs.4 7 compare the proposed drectonal beamformng wth conventonal SFBC schemes. Fg.4 frst demonstrates the performance comparson under the channel wth K beng nfnty, whch means the HSR channel only contans a pure LoS channel component. From Fg.4, t shows that our proposed DBF strategy always outperforms the conventonal SFBC scheme. As the SNR ncreases, the SFBC scheme can acheve the best throughput wth a fxed codng and modulaton rate. Moreover, n Fg.4, we also tested the case wth poston nformaton errors. The postonng error here s set to 10m. Even wth an obvous postonng error of 10ms, Fg.4 shows that the proposed DBF scheme stll outperforms the conventonal SFBC at the low to moderate SNR regme. Note that snce Fg.4 test the channel wth only LoS channel components, our proposed DBF acheves the best throughput performance due to the desgned beamformng perfectly algnng wth the LoS channel drecton. The followng fgures wll show the effectveness of our proposed beamformng scheme for other HSR channel cases wth both LoS and Raylegh (non LOS) channel components. Table 1. System parameters Parameters Values Bandwdth 20 MHz Carrer Frequency 5GHz Number BS Antennas 2 BS Antenna Spacng 10λ BS Coverage 500 m Number Ralway Antennas 2 Ralway Antenna Spacng 0.5λ Dstance between BS and the Trace 50 m Antenna Correlaton Low Channel Model Rcean channel wth factor K Channel Estmaton LTE plot-based channel estmaton SFBC n LTE R9 Precodng Method Proposed drectonal beamformng Codng Turbo codng wth rate 1/3 Modulatons QPSK Layer 1 Detecton MRC Maxmum Doppler for the LoS path 750 Hz Fg. 3. Perforamnce comparson wth SFBC n LTE R9 Fg.5 and Fg.6 provde the result under channels wth K =20 and 1, respectvely. From Fg.5, we fnd smlar obsrvatons from Fg.4. As the Rcean factor K ncreases, t shows that the advantages of our proposed DBF become more obvous. Ths phenomenon can be verfed by comparng the results n Fg.4 and Fg.5 wth Fg.6 whch depcts the performance comparson under a much smaller K = 1. In Fg.6, t can be found that our proposed DBF strategy always outperforms the conventonal SFBC under dfferent SNRs

5 Drectonal Beamformng for Hgh-Speed Ralway Communcatons wth Frequency Offset Precorrecton 167 Fg. 4. Performance comparsons wth SFBC and our proposed DBF (Pure LoS channel case) Fg. 5. Performance comparsons wth SFBC and our proposed DBF (K =20) Fg. 6. Performance comparsons wth SFBC and our proposed DBF (K =1) even wth a mperfect postonng nformaton for channel estmaton. For low SNRs, the performance gan of our proposed DBF over SFBC s approxmately 1dB, whle as the SNR ncreases, the acheved performance gan becomes less sgnfcant. It can also be found n Fgs.5 and 6 that our proposed DBF acheves a part of the maxmum throughput for the Rcean channel models snce the beamformng s only desgned by algnng wth the LoS channel component nstead of the entre channel matrx. As evdenced by the fgures, postonng errors surely degrades the proposed beamformng performance. However, even wth some level of the mperfecton, the proposed DBF stll shows ts superorty to the exstng SFBC scheme. Fnally n Fg.7, we compare the proposed DBF wth SFBC consderng LOS channel component estmaton error due to mperfect postonng. Dfferent levels of postonng error ncludng 5m, 10m and 20m are tested for comparson. From ths fgure, we can fnd that under dfferent cases the proposed DBF outperforms the SFBC schemes. For the channel case wth K = 20, the SFBC acheves better performance at relatvely hgh SNRs. Ths s because for ths almost LoS channel type, the proposed DBF s much more senstve to the channel nformaton mperfecton,.e., the postonng error. From Fg.4, t verfes that when the postonng error reduces to zero, the proposed DBF stll outperforms the SFBC. However, for the case wth K = 1, the results convnced the effectveness of our proposed DBF under dfferent cases even when there s some postonng errors. for HSR communcatons by explotng the postonng nformaton and the characterstcs of the HSR wreless channels. Ths technque asssts the system to acheve the full dversty gan of a multantenna system. Moreover, the performance gan over tradtonal HSR transmsson systems s also analyzed. The effectveness of our proposed scheme s evaluated by computer smulatons over a standard LTE physcal layer smulator. Dfferent cases are tested for verfy our proposed drectonal beamformng strategy. The proposed strategy shows notceable performance gans over exstng SFBC schemes even when there s some postonng errors caused channel nformaton mperfecton for beamforng desgn. Appendx A Wthout loss of generalty, we assume that the Doppler shft ntroduced by the hgh tran moblty s gven by a receved frequency phase rotaton denoted by e jϕ. Then, from Eq.(11), the equvalent channel wth Doppler shft s represented by H K = K +1 e jϕ H LoS (Ω r, Ω t) 1 + K +1 e jϕ H Ray (21) Notced that snce H Ray s a matrx wth ts entres ndependently and dentcally Gaussan dstrbuted, by multplyng by a constant phase rotaton e jϕ the new channel e jϕ H Ray s statstcally equvalent to the orgnal channel matrx H Ray. Therefore, we can focus on the affected LoS channel e jϕ H LoS (Ω r, Ω t). By applyng SVD to H LoS as gven n Eq.(12), we have e jϕ H LoS (Ω r, Ω t)=e jϕ U 1 Σ 1 V H 1 Δ =U 1 Σ 1V H 1 (22) where we defne a new matrx U 1 = e jϕ U 1. It can be easly verfed that U 1 U H 1 = e jϕ U 1 U H 1 ejϕ = I (23) whch ndcates that U 1 s also an untary matrx, hence Eq.(22) mplementng an SVD to the new LoS channel matrx e jϕ H LoS (Ω r, Ω t) affected by the Doppler shft. From the SVD n Eq.(22), we observe that both the sngular values ncludng σ1 2 and the rght beamfomrng vector v 1 are keepng the same as the orgnal channel wthout any Doppler shft. Fg. 7. Performance comparsons wth SFBC and DBFundermperfect postonng V. Concluson In ths paper, an drectonal beamformng strategy s presented References [1] D. Ba, C. Park, J. Lee, et al., LTE-advanced modem desgn: Challenges and perspectve, IEEE Communcatons Magazne, Vol.50, No.2, pp , [2] M. Aguado, O. Onand, P.S. Agustn, M. Hguero and E.J. Taquet, WMaxon rals, IEEE Vehcular Technology Magazne, Vol.3, No.3, pp.47 56, 2008.

6 168 Chnese Journal of Electroncs 2014 [3] T.T. Gao and B. Sun, A hgh-speed ralway moble communcaton system based on LTE, Internatonal Conference on Electroncs and Informaton Engneerng, Vol.1, pp , [4] C. Chen and C. L, Hgh speed ral communcaton system: A survey, Computer Engneerng and Applcatons, Vol.46, No.34, pp.24 26, [5] 3GPP. Further Advancements for E-UTRA Physcal Layer Aspects, Techncal Report [OnlneAvalable]: org, [6] E. Telatar, Capacty of mult-antenna Gaussan channels, European Transactons on Telecommuncatons, Vol.10, No.6, pp , [7] S.M. Alamout, A smple transmt dversty technque for wreless communcatons, IEEE Journal on Selected Areas n Communcatons, Vol.16, No.8, pp , [8] V. Tarokh, H. Jafarkhan and A.R. Calderbank, Space-tme block codng for wreless communcatons: Performance results, IEEE Journal on Selected Areas n Communcatons, Vol.17, No.3, pp , [9] Y. L, X. Gao, Impact of co-channel MIMO nterference on desred downlnk recever usng STBC, Chnese Journal of Electroncs, Vol.18, No.3, pp , [10] L. Lu, C. Tao and W. Dong, Dscusson on the channel measurement and channel model under hgh speed ralway envronment, Telecommuncatons Scence, Vol.27, No.5, pp.54 60, [11] D. Tse and P. Vswanath, Fundamentals of Wreless Communcaton, Cambrdge Unversty Press, [12] Procedures. Thrd Generaton Partnershp Project, Techncal Specfcaton Group Rado Access Network Std. Rev. TS25, [13] J.J. Van de Beek, M. Sandell and P.O. Borjesson, ML estmaton of tme and frequency offset n OFDM systems, IEEE Transactons on Sgnal Processng, Vol.45, No.7, pp , [14] J. Guo, Y. Shang, S. Ren and H. Xa, Jont estmaton of synchronzaton parameters and channels for generalzed-ofdm uplnk, Chnese Journal of Electroncs, Vol.19, No.4, pp , [15] P.H. Moose, A technque for orthogonal frequency dvson multplexng frequency offset correcton, IEEE Transactons on Communcatons, Vol.42, No.10, pp , CAO Yuan receved hs B.S. degree n Electrc Engneerng and Automaton from Dalan Jaotong Unversty and Ph.D. degree n Traffc Informaton Engneerng and Control from Bejng Jaotong Unversty n 2004 and 2011 respectvely, where hs now an Assstant Professor. Snce 2006, he has partcpated n many engneerng practce, especally n the sgnal and communcaton system of hgh-speed ralway. He has taken part n several key natonal research projects n the feld of hgh-speed tran communcatons. Hs research nterests nclude the possblty and sutablty of new wreless communcatons, ncludng MIMO, OFDM, and LTE, n hgh-speed ralway systems. (Emal: ycao@bjtu.edu.cn) WEN Ynghong receved her Ph.D. degree n transportaton automaton and control n 1998 from North Jaotong Unversty, where she s currently the professor and Ph.D. supervsor. She s the drector of the EMC Laboratory of Bejng Jaotong Unversty, and also s the Senor Member of IEEE. Her research nterests nclude rado wave propagaton characterstcs n Hgh-Speed Ralway. XU We receved hs B.S. degree n Electrcal Engneerng n 2003 and hs M.S. and Ph.D. degrees n Communcaton and Informaton Engneerng n 2006 and2009, respectvely, all from Southeast Unversty, where he s currently an Assocate Professor. He s also a senor research fellow wth the Natonal moble communcatons research lab. (NCRL), Chna. Between 2009 and 2010, he was a post-doctoral research fellow wth the Department of Electrcal and Computer Engneerng, Unversty of Vctora, Vctora, BC, Canada. He has been nvolved n Techncal Program Commttee for many IEEE conferences ncludng Globecom, WCNC, VTC, etc. Hsre- search nterests nclude mult-antenna and mult-user channels, user schedulng, lmted feedback strateges, and relay cooperatve networks. XIE Xn receved hs M.S. degree n 2013 from Southeast Unversty, Nanjng, Chna. Hs research topc focuses on wreless communcatons for hgh speed ralways.