EasyChair Preprint. Time-Domain Channel Estimation for the LTE-V System Over High-Speed Mobile Channels

Transcription

1 EasyChair Preprint 184 Time-Domain Channe Estimation for the LTE-V System Over High-Speed Mobie Channes Qu Huiyang, Liu Guanghui, Wang Yanyan, Wen Shan and Chen Qiang EasyChair preprints are intended for rapid dissemination of research resuts and are integrated with the rest of EasyChair. May 30, 2018

2 Time-Domain Channe Estimation for the LTE-V System Over High-Speed Mobie Channes Huiyang Qu, Guanghui Liu, Yanyan Wang, Shan Wen, Qiang Chen University of Eectronic Science and Technoogy of China, Chengdu , P.R. China Emai: {hyqu, yywang, shanwen, Abstract Deveoped from the LTE upink, the LTE-V2X standard, widey used as LTE-V, increases the overhead of piot symbos in order to acquire channe information robusty. In this paper, we propose to estimate time-varying pieces of channe rays for piot symbos based on the basis expansion mode BEM), and subsequenty to reconstruct time-domain channe response for data symbos by utiizing Sepian sequences based piece-wise interpoation SS-PWI). To demonstrate the precision of channe estimation CE), the Cramer Rao ower bound CRLB) is derived. The simuations are impemented on the LTE-V patform, on which we consider the extended vehicuar A mode EVA) channe with 2800 Hz maximum Dopper shift. The proposed time-domain CE schemes are we capabe of tracking the channe state information CSI), and the mean squared error MSE) of CE neary reaches the theoreticay derived CRLB. Index Terms Orthogona frequency division mutipe access OFDMA), singe carrier frequency division mutipe access SC-FDMA), ong term evoution vehicuar to everything LTE- V2X), CE, Sepian sequences I. INTRODUCTION Due to its advantage of ow peak to average power ratio, SC-FDMA technique has been adopted as the LTE upink transmission scheme for improving the power efficiency of mobie terminas [1]. With more piot overhead aiming for tracking time variations of extremey high-speed mobie channe, the LTE-V standard was specified on the basis of LTE upink framing configuration [2]. Traditionay, at the receiver side, precise CE is a necessary prerequisite for coherent demoduation, reying on inserted piots. When SC-FDMA is adopted by the LTE-V [3], we have to face the chaenges from the CE design, especiay in the vehice to vehice communication scenarios [4], [5]. In this case, the maxima reative veocity for the considered trias is 500 km/h, thus the maximum Dopper shift reaches 2800 Hz, given the carrier frequency of 5.9 GHz [6]. Even though much more piot overhead is considered in the LTE-V, the frequency-domain CE schemes [7] [9], may not capabe of tracking the channe with 2800 Hz Dopper spreading. In this paper, we address the CE chaenges of the SC- FDMA with appication to the LTE-V system. For the piot symbos, each ray i.e., path) is characterized by the basis expansion mode BEM) [10]. In the BEM, the band-imited Sepian sequences [11], are empoyed to express the timevarying fading channe in a ow-dimensiona space. Based on the estimated pieces of channe impuse response CIR), the Sepian sequences based piece-wise interpoation SS-PWI) is utiized for recovering the CIR of data symbos. The CRLB of the CIR estimation is derived for the proposed channe estimator as benchmarks. The proposed time-domain CE architecture is we capabe of tracking CSI whie preserving a reativey ow computationa compexity. The rest of this paper is organized as foows. We describe the transmission mode of SC-FDMA based LTE-V system in Sec. II. In Sec. III, the proposed CE schemes are presented, which is foowed by the CRLB derivation of CE in Sec. III-C. In Sec. IV, the proposed agorithms are investigated in the LTE-V receiver design and simuation resuts verify the proposed CE schemes. Finay, some concuding remarks are given in Sec. V. II. SYSTEM MODEL A discrete-time baseband SC-FDMA system with N subcarriers is considered, and idea synchronization is assumed at the receiver side for simpicity. Without oss of generaity, a singe-user SC-FDMA mode is considered in this paper, but the designed agorithms are appicabe to the mutiuser configuration. In the transmitter side shown in Fig. 1), compex data sequence d k) is moduated by inverse fast fourier transform IFFT) after channe encoding, consteation mapping, discrete fourier transform DFT) and subcarrier mapping. The moduation transforms the frequency-domain data into the time-domain sampes by y n) = 1 N 1 d k) e j2πnk/n, n [ N g, N), 1) N k=0 where j 2 = 1, and N g denotes the ength of the inserted the cycic prefix ). The gain of the th channe ray at the nth samping instant is assumed: h n, ), = 0, 1,, L 1, where the maxima time-deay spread L N g. At the receiver side, after removing, the received discrete-time signa is expressed as L 1 r n) = h n, ) y n ) + v n), n [0, N), 2) =0 where v n) is the zero-mean compex addictive Gaussian noise with variance σ 2. Defining r = [r0), r1),, rn 1)] T C N and y = [y ), y + 1),, y N 1)] T C N, the received signa is written in vector form as L 1 r = diag y )h + v, 3) =0

3 Data symbos Demoduation processing Encoded Data sequences DFT Subcarrier Mapping IFFT Add Data Rem. FFT Subcarrier Demapping FDE IDFT Demoduation Data MUX DE MUX Zadoff Chu sequences DFT Subcarrier Mapping IFFT Add Piot Rem. BEM Based DMRS-CE SS-PWI SS-MPI DFT Piot symbos CE processing Fig. 1. Baseband mode of the SC-FDMA Based LTE-V system. where v = [v0), v1),, vn 1)] T C N and h = [h 0, ), h 1, ),, h N 1, )] T represents L-path WS- SUS Rayeigh fading coefficients. As the is empoyed at the transmitter, y ) = y N ) for = 0, 1,, L 1. Assuming the Jake s mode, the covariance matrix of the th channe path is R h ), of which the eements are 12 REs Frequency 1 st sot 2 n d so t {R h )} m,n = σ 2 r m n ), m, n [0, N), 4) where r κ) = J 0 2πf d κt s ). The mentioned variabes J 0 ), σ 2, f d and T s represent the zeroth-order Besse function of the first kind, the normaized power of the th channe path, the maximum Dopper spreading and the samping period, respectivey. Let Y = diag y ), Y = [Y 0, Y 1,, Y L 1 ] and h = [ h T 0, h T 1,, h T L 1] C NL, 3) can be rewritten as the matrix form r = Yh + v. 5) III. THE PROPOSED TIME-DOMAIN CHANNEL ESTIMATION SCHEMES The LTE-V subframe structure, shown in Fig. 2, is evoved from the ong term evoution-device to device LTE-D2D), whie extra two DMRS symbos are added in one subframe. The first and ast symbos are used for the automatic gain contro AGC) and guard period GP), respectivey. The remained symbos are used to convey information data. From Fig. 2, the a-piot pattern in the DMRS symbos inspires us to estimate each channe ray, of which the response is characterized by the BEM. We further use this estimated CIR to interpoate the CIR of data symbos. In this paper, CE for the AGC and GP symbos are not considered in our agorithms. A. The Channe Estimation for Piot Symbos In the a-piot DMRS symbos, the th path of channe response within [0, N 1], is represented as the weighted sum of the orthogona basis functions {ϕ d } in a suitabe dimension D N): h = D 1 d=0 c d)ϕ d = Ψc. 6) AGC Data DMRS GP Fig. 2. Time Subframe structure of the LTE-V system. In 6), c = [c 0), c 1),, c D 1)] T C D denotes the th coefficient vector and Ψ C N D is the basisexpansion matrix consisting of Ψ=[ϕ 0, ϕ 1,, ϕ D 1 ] and ϕ d = [ϕ d 0), ϕ d 1),, ϕ d N 1)] T. The dimension D is imited by D D N, where D = 2f d T + 1, T is the symbo period and f d T is the maximum one-side Dopper bandwidth. Further, the channe with a taps is expressed as h = Φc, 7) where c = [ c T 0, c T 1,, c T L 1] T C DL, Φ = I L Ψ C NL DL, denotes kronecker product and I L is an L L identity matrix. Substituting 7) into 5), the received signa is rewritten as r = YΦc + v = Ac + v. 8) The desired BEM coefficient vector c is subject to Gaussian distribution, i.e., c N 0, Θ c ). The covariance matrix Θ c = bkdiag {Σ c 0),, Σ c L 1)} C LD LD, where Σ c ) = Φ T R h )Φ C D D and bkdiag means the bock diagona operator [12]. For improving the accuracy of coefficients estimation, c is obtained by the MMSE agorithm ĉ mmse = A H A + σ 2 Θ c ) 1) 1 A H r, 9) where ) H denotes the conjugate transpose. Based on the estimated expansion coefficient vector ĉ, the discrete-time

4 channe response coud be reconstructed by 7). In 1978, Sepian indicated that the discrete proate spheroida sequences, ater caed as Sepian sequences, demonstrated that the discrete proate spheroida sequences are bandimited and simutaneousy energy-concentrated in a finite time interva [11]. Specificay, the Sepian sequences are the eigenvectors of matrix Γ C M M Γϕ i = λ i ϕ i, 10) where the entries of Γ are {Γ} a,b = 2sinc {2π a b) f d T s } and a, b {0, 1,, M 1}. These Sepian sequences are douby orthogona on the finite set {0, 1,, M 1} and the infinite set {,, + } [13], definitey indicated as M 1 m=0 ϕ i [m] ϕ j [m] = λ i + m= ϕ i [m] ϕ j [m] = δ ij, 11) where i, j {0, 1,, M 1}. The eigenvaue λ i represents the energy concentration of the ith Sepian sequence. In the BEM, we seect the first D Sepian sequences as the basis functions, and simutaneousy adjust the ength to N. The basis functions based on the Sepian sequences are bandimited to [ f d T, f d T ] and time-concentrated during the symbo duration [0, N 1]. Given f d, the Sepian sequences are we capabe of characterizing the channe response of piot symbos. B. Sepian Sequences Based Piece-Wise Interpoation Inspired by the douby-orthogona and energy-concentrated properties, we extend the ength of Sepian sequences, and subsequenty approximate each channe ray with interpoation coefficients in the time interva [0, n 3 ]. Meanwhie, the dimension i.e., number) of the extended Sepian sequences is transformed into Q, and simiary satisfies 2f d T s n 3 + 1) + 1 Q n 3 + 1). The interpoation coefficients coud be acquired by means of the estimated CIR of interva [0, n 1 ] and [n 2, n 3 ], which are obtained by the BEM Cycic Prefix ) Data Piot Fig. 3. The simpified LTE-V subframe structure. Time entire interva: = p d. In the time domain, the th channe tap is denoted as the vector h C n3+1), and [ ) h = h T p1, h d ) T, h p2 ) T ] T. 12) The CIR estimates at piot symbos ĥ n, ), form the vector h pi, where {h pi } n = ĥ n, ), n pi, i = 1, 2. Utiizing h pi, the piece-wise interpoation is to recover the CIR of data symbos h d, where {h d } n = h n, ), n d. The th channe ray, varying during [0, n 3 ], is expanded by the extended Sepian sequences {ϕ e q} and the extended expansion parameters i.e., interpoation coefficients) as h Q 1 q=0 c e q) ϕ e q Ψ c e. 13) In 13), Ψ = [ ϕ e 0, ϕ e 1, ϕ e Q 1] C n 3+1) Q and c e = [c e 0), ce 1),, ce Q 1)]T C Q 1. Decomposing Ψ into Ψ p, the estimated CIR of piot symbos satisfies h p Ψ p c e, 14) where { Ψ }n,q p = ϕe q n), n p, q {0,, Q 1} and { } h p = h p1 h p2 C n3 n2+n1+2). The interpoation coefficient c e is obtained by using the LS method ĉ e = Ψ p) h p. 15) Therefore, the CIR of data symbos is recovered by ĥ d = Ψ dĉ e, 16) where { } Ψ d = n,q ϕe q n), n d, q {0,, Q 1}. C. Anaysis of the Channe Estimation Performance In this paper, the MMSE agorithm is utiized for the BEM coefficients estimation. Based on the anaysis of CIR estimation at piot symbos [14], in this section, we derive the CRLB of CIR estimation at data symbos based on SS-PWI. For the th channe tap, substituting 15) into 16), the SS- PWI can be simpy expressed as For simpicity, severa sets of discrete time indexing are introduced to describe the Sepian sequences based piecewise interpoation SS-PWI): time set of data symbos d = {n 1 + 1,, n 2 1}; time set of the first or eft piot symbo p1 = {0,, n 1 }; time set of the second or right piot symbo p2 = {n 2,, n 3 }, as shown in Fig. 3. The indexes of the two piot symbos are combined in one set as p = { p1 p2 }. Then, we have the time set of the h d = Ψ d Ψ p ) h p = Bhp. 17) For simpicity, we drop out the indexing sets d, p and use d, p to represent data and piot indexing sets, respectivey. Defining M = n 2 n 1 1 and 2N = n 1 + n 3 n 2 + 2, the channe with a taps is described as h d = B Wh p C ML 1, 18)

5 where B = I L B C ML NL, [ h h p p1 = ) T ) ], h p2 T T C 2NL 1, W = [ W0 T,, W T,, T L 1] WT C 2NL 2NL, [ h ) h d d T ) = 0, h d T ) ] 1,, h d T T L 1 C ML 1, [ ) T ) T ] T T h pi = h pi 0, h pi 1,, hl 1) pi C NL 1, [ ] 0 W = N N I N N 0 N 2L 1)N,. 0 N L+)N I N N 0 N L 1)N 19) Combining BEM and SS-PWI, 18) is rewritten as [ ] [ ] [ ] h d h p1 Φ 0 c1 = B W h p2 = B W. 20) Since the estimation errors exist in coefficients c 1, c 2, the interpoated CIR of data symbos is described as [ ] [ ] [ ] ĥ d Φ 0 Ξ1 0 c1 = B W, 21) 0 Ξ 2 c 2 where Ξ i = A H i A+σ2 Θ c ) 1) 1 A H i A; i = 1, 2. The interpoation errors consist of three parts: 1) The modeing error of subspace expanded by the Sepian sequences; 2) The bias of the BEM coefficients estimation; 3) The variance of the CIR estimation introduced by BEM. 1) The Modeing Error In Sec. III-B, Sepian sequences are utiized for expanding a ow dimensiona space to characterize channes variations. Apparenty, there is an modeing error between the rea and approximated channe response. The modeing error is defined as bias 2 M, which can be obtained from [13]. 2) Bias of the BEM coefficients estimation The estimation bias of the BEM coefficients wi aso infuence the Sepian interpoation. The error is defined as α, which is expressed as α =E{ĥ d [} h d Φ 0 =B W ] [ Ξ1 I 0 0 Ξ 2 I c 2 ] [ ] c1. c 2 3) The ower bound for the variance of interpoation 22) According to [14], the variance of the estimated BEM coefficients wi affect the ower bound of CIR estimation at piot symbos. Thereby, this variance shoud aso be considered into the SS-PWI. By defining c = [ ] c T 1, c T T 2 C 2DL 1, c A = [ Rec T ), Imc T ) ] T [ ] = c T R, c T T 23) I C 4DL 1, 21) can be rewritten as [ ĥ d Φ 0 = B W ] {[ ] Ξ1 0 + j 0 Ξ 2 [ ]} Ξ1 0 c 0 Ξ A. 2 24) The covariance matrix of estimated coefficients c A is C L ĉ A ) = E ĉ A E c A ) 2 = [ ca E ĉ A ) ] J 1 c A ) [ ca E ĉ A ) ] T, 25) where J c A ) is the Fisher information matrix and can be obtained from [15]. The ower bound of the covariance of the interpoation processing is C L ĥd ) = { B W [ Φ 0 ]} C L ĉ A ) { [ Φ 0 B W ]} H. 26) In summary, the ower bound of CE for data symbos is defined as CE CRLB, and CE CRLB bias 2 M + trace IV. SIMULATION RESULTS αα H + C L ĥd )). 27) In this section, simuation resuts are presented for assessing the performance of the proposed CE agorithms. The simuation patform is estabished based on the LTE-V standard. The signa bandwidth is 10 MHz, i.e., 1k system mode. The simuated channe is EVA, in which the carrier frequency is set as 5.9 GHz. Additionay, the power deay profie and parameter f d, for configuring the designed agorithm in this paper, can be acquired by using the methods in [16], [17]. From Sec. III-C, for the idea interpoation i.e., the CIR at piot symbos is idea), the interpoation accuracy is ony determined by the dimension Q. Nevertheess, in practice, the BEM based CE of piot symbos is a prerequisite for piece-wise interpoation. The CE accuracy at piot symbos wi significanty infuence the quaity of interpoation. For a tradeoff between the compexity and the estimation accuracy at piot symbos, we seect D = 5 as the order of the BEM. Subsequenty, we choose the optima interpoation order Q through the simuations. For obtaining the CIR in the whoe subframe duration, both the intraframe and the interframe interpoators need to be impemented, which has been described in Sec. III-C. Fig. 4 gives the MSE as a function of the SNR with different interpoation orders when f d = 2800 Hz, i.e., the normaized Dopper spreading is 18.6%. As shown in the figures, when considering the SNR ranging from 0 to 20 db, the interpoating order choices for intraframe and interframe cases are Q = 4 and Q = 6, respectivey. It s worth noting that, in the considered SNR range, the main estimation error is caused by the BEM. With the increasing of SNR, the MSE wi converge to the modeing error of the Sepian sequence based approximation of channe response. Additionay, we choose Q = 4 as intra/interframe interpoation order when f d = 2000 Hz. Fig. 5 demonstrates the MSE performance of the proposed CE agorithms, when the reative mobie speeds are 500 km/h and 357 km/h, respectivey. In these two cases, the SNR required by the scheme of BER+SS-PWI are about 15 db and 10 db at the MSE of As SNR increases, the MSE of BER+SS-PWI graduay approaches to the CRLB imit.

6 Fig. 5. MSE performance of CE when f d = 2800 Hz. Fig. 4. The MSE vs. SNR with different interpoation orders when f d = 2800 Hz. a) Intraframe interpoation. b) Interframe interpoation. V. CONCLUSION In this paper, we propose the time-domain channe estimation schemes for the LTE-V system over extremey highspeed channes. Due to the specia bock-type piots structure, the basis expansion mode BEM) is utiized to obtain the CIR of piot symbos. Subsequenty, the Sepian sequences based piece-wise interpoation SS-PWI) is empoyed to interpoate the CIR of data symbos. The CRLB of the CIR estimation based on the proposed estimator BEM+SS-PWI) is aso derived as benchmark for CE performance. The proposed interpoation agorithm, with the optimized orders, provides an idea MSE performance. REFERENCES [4] W. Zhuang, Emerging technoogies, appications, and standardizations for connecting vehices part II), IEEE Veh. Tech. Mag., vo. 12, no. 2, pp , May [5] H. Seo, K. D. Lee, S. Yasukawa, and Y. Peng, LTE evoution for vehice-to-everything services, IEEE Commun. Mag., vo. 54, no. 6, pp , June [6] S. Chen, J. Hu, Y. Shi et a., Vehice-to-everything V2X) services supported by LTE-based systems and 5G, IEEE Commun. Std. Mag., vo. 1, no. 2, pp , Juy [7] L. A. M. Ruiz, de Temino, C. Navarro, I. Manchon, C. Rom, and T. B. Sorensen, Iterative channe estimation with robust wiener fitering in LTE downink, in Proc. IEEE VTC 2008-Fa, Sept [8] O. Edfors, M. Sande, J. J. V. D. Beek, S. K. Wison, and P. O. Borjesson, OFDM channe estimation by singuar vaue decomposition, IEEE Trans. Commun., vo. 46, no. 7, pp , Juy [9] G. Liu, L. Zeng, H. Li, L. Xu, and Z. Wang, Adaptive interpoation for piot-aided channe estimator in OFDM system, IEEE Trans. Broadcast., vo. 60, no. 3, pp , June [10] Y. Zakharov and D. Zheng, Adaptive reguarization for BEM channe estimation in muticarrier systems, in Proc. IEEE ICASSP, Mar. 2016, pp [11] D. Sepian, Proate spheroida wave functions, fourier anaysis, and uncertainty-v: The discrete case, Be Syst. Tech. J., vo. 57, no. 5, pp , May [12] E. Panayirci, H. Seno, and H. V. Poor, Joint channe estimation, equaization, and data detection for OFDM systems in the presence of very high mobiity, IEEE Trans. Signa Process., vo. 58, no. 8, pp , Juy [13] T. Zemen and C. F. Meckenbrauker, Time-variant channe estimation using discrete proate spheroida sequences, IEEE Trans. Signa Process., vo. 53, no. 9, pp , Sept [14] M. F. Rabbi, S. W. Hou, and C. C. Ko, High mobiity orthogona frequency division mutipe access channe estimation using basis expansion mode, IET Commun., vo. 4, no. 3, pp , Jan [15] E. de Carvaho and D. Sock, Cramer-rao bounds for semi-bind, bind and training sequence based channe estimation, in Proc. SPAWC, Apr [16] Y. J. Kim and G. H. Im, Piot-symbo assisted power deay profie estimation for MIMO-OFDM systems, IEEE Commun. Lett., vo. 16, no. 1, pp , Jan [17] N. Linty and L. L. Presti, Dopper frequency estimation in GNSS receivers based on doube FFT, IEEE Trans. Veh. Techno., vo. 65, no. 2, pp , Feb [1] 3GPP, Evoved Universa Terrestria Radio Access EUTRA); Physica Channes and Moduation, Re. 10, TS Std., [2] S. Chen, J. Hu, Y. Shi, and L. Zhao, LTE-V: A TD-LTE-based V2X soution for future vehicuar network, IEEE Internet Things J., vo. 3, no. 6, pp , Sept [3] 3GPP, Study on enhancement of 3GPP Support for 5G V2X Services, Re. 15, TR V15.1.0) Std., 2017.