Journal of Beijing University of Posts and Telecommunications. Blind CFR Estimation for SC2FDE Systems

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1 Journal of Beijing University of Posts and Telecommunications Aug. 29 Vol. 32 No. 4 : (29) CFR 1,2, 3, 3, 1 (1., 1876 ; 2., 413 ; 3., 3615) :.,,.,,.. : ; ; ; : TN : A Blind CFR Estimation for SC2FDE Systems I Meng2xing 1,2, HUAN G ong2yang 3, CHEN G En 3, IU Ze2min 1 (1. School of Telecommunication Engineering, Beijing University of Posts and Telecommunications, Beijing 1876, China ; 2. Department of Physics and Telecommunication Engineering, Hunan City University, Hunan Yiyang 413, China ; 3. Key aboratory of Underwater Acoustic Communication and Marine Information Technology, Ministry of Education, Fujian Xiamen 3615, China) Abstract : A blind scheme to estimate channel f requency response ( CFR) in oversampled single2carrier f requency2domain equalization ( SC2FDE) systems based on linear prediction algorit hm ( PA) is devel2 oped. Compared wit h conventional PA based time2domain channel estimation approach, t his met hod obtains the closed2form solution for CFR directly from tap weights of the prediction filter, rather than cross2correlation of innovation and measurement s. The proposal is robust to channel order overestima2 tion. It s performance is better t han t hat of conventional PA based time2domain channel estimation approach. Fut hermore, it ensures t hat t he channel estimation in time2domain appears finite support2 ing. Simulations confirm our analysis. Key words : single2carrier f requency2domain equalization ; channel f requency response ; blind estima2 tion ; linear prediction algorit hm ( SC2FDE), [1 ],. ( PA) SC2 FDE CFR. Slock [2 ], A. M. Karim [3 ],. ( [4 ] ), PA,,. PA,, : : (26AA9Z18) ; (8C196) : (1972 ),,, E2mail : cn ; (1927 ),,,.

2 78 32,. PA,. CFR,. [ 526 ]. [ 5 ] 2 ; [ 6 ] 1 1, 2. 1, SC2FDE,CIR, CFR. SC2FDE,,,, ( ),. [ 7 ], 9 db. CFR. CIR. 1 SC2FDE N,.,. q, x k = [ x k () x k (1) x k ( N - 1) ] T k ; h l = [ h l () h l (1) h l ( M ) ] T ( l - 1) T/ q + n T, l [ l, q ], T, ; y k, l ( n) = y ( ( l - 1) T/ q + n T), y k, l = [ y k, l () y k, l (1) y k, l ( ) ] T ; w, w k, l ( n) w k, l y k, l ( n) y k, l, SC2FDE y k, l = x k g h l + w k, l (1) Y k, l X k W k, l y k, l, x k w k, l N DFT, H l h l N DFT,(1) Y k, l ( i) = H l ( i) X k ( i) + W k, l ( i), i [, N - 1 ], : (2) 1),, 2. 2), 1. 2 CFR,,. 211 CFR l [ l, q ], y k ( n) = [ y k,1 ( n) y k,2 ( n) y k, q ( n) ] T h ( i) = [ h 1 ( i) h 2 ( i) h q ( i) ] T Y k ( i) = [ Y k,1 ( i) Y k,2 ( i) Y k, q ( i) ] T H ( i) = [ H 1 ( i) H 2 ( i) H q ( i) ] T y k ( n) = h ( i) x k ( n - i) i = (3) Y k ( i) = H ( i) X k ( i) (4) y k ( n) r y ( n, m) = E[ y k ( n) y H k ( n - m ) ] r y ( n, m ) n, r y ( n, m ) r y ( m ). (3) 2),E[ y k ( n) ] =,n, { y ( n), n [, N - 1 ]},y k ( n) 1. h ( z) = h ( i) z - i, h ( z), Bezout, y k ( n) AR. [3 ], { y ( n) } 1, h () x ( n).,,, y ( n) = y^ ( n) + h () x ( n) = A H i y ( n - l) + h () x ( n) (5) i = 1

3 4 : CFR 79, A i q q ; y^ k ( n ) y k ( n). 2 R = RA = r (6) r y () r y (1) r y ( ) r y ( - 1) r y () r y ( - 1) ω ω r y ( - ) r y ( - 1) r y () A = q A 1, r = A r y () - h () h H () r y ( - 1) r y ( - ) (6), r y ( i), i, A i h () h H (). h () h H () 1,h () h H () h () h H () = ( u 1 ) ( u 1 ) H (7),; u 1. (7) h () =( u 1 ) (8),. (3) (5), l - 1, h (1) x ( l - 1) + + h ( l) x () + h ( l + 1) x ( N - 1) + + h ( ) x ( N - + l) = A H 1 y ( l - 1) + + A H l y () + A H l + 1 y ( - 1) + + A H y ( - + l) (9) (9) x 3 k, ( N - 1) h ( l + 1) = A H 1 E[ y ( l - 1) x 3 ( N - 1) ] + A H 2 E[ y ( l - 2) x 3 ( N - 1) ] + + A H l + 1 E[ y ( - 1) x 3 ( N - 1) ] (1) h ( l + 1) = A H 1 h ( l) + A H 2 h ( l - 1) + + A H l + 1 h () = l +1 A H i h ( l - i + 1), l - 1 (11) i = 1 (3) (5), A H i h - i + c =, c [1, ] (12) i = c N N + 1 N, (13) (14) : h () h (1) h ( ) = > h N q q A H A H 2 A H 1 A H 1 q q A H A H 2 ω ω ω ω ω A H - 1 A H 1 q q A H A H A H - 1 A H 1 q q ω ω ω ω ω q A H A H - 1 A H 1 q > ( A H ) h () h (1) h ( ) + h () N q 1 h N =( A H ) h N + [ h T () ] T (13) ( A H ). F N q N Fourier, (13) F N H N = diag ( A F, A F,1 A F, N - 1) H N + [ h T () h T () h T () ] T (14) H N h N q N DFT, A F, i F N [ q A 1 A q q ] H N q q i q q,(16) H N ( i) = A F, i H N ( i) + h (), H H N ( i) = ( I q - A F, i) - 1 h () (15) DFT, g (,) I q g (, N ) I q g ( N,) I q g ( N, N ) I q > G H N = GH N (16) H h = [ h ( ) h ( 1) h ( ) q 1 q 1 ] T N q 1q N DFT, g ( k, m ) = 1 N N - 1 n = j2( rm - k) n/ N e,(18) CFR.

4 CFR, 1 2, 1 r y () - 2 I q,.,, (13) (14),(18) CFR., ^ h () h^ H (),.,(18) CFR H^ h^ l [ N, N - 1 ] ^ h ( l) =,,, h^ ( + 1) h^ ( N - 1), [7 ]., CFR,., PA, SNR. 3, N = 1 24,6, 8PSK,q = 2. [8 ] = 3, h ( z) = j j j j j j j j z z z - 3 z + [ 9 ] = arg ( h () / h^ () ). 1 Monte Carlo.,MMSE SC2FDE,K = 2., 2.,[7 ]S BER. 1,, S, SNR 6 db, S., S. SNR 14 db,ber , PA [ 5 ]. CFR ( RMSE). 2, PA,, S. 212, SNR,, PA. SNR,, 16 db,.,,[ 5 ]. [ 5 ] 2 PA RMSE (98 )

5 98 32 l. ] : IEEE Press, 27 : [7 ] Zarrin S, Gazor S. Analysis of partial phase combining, hybrid and transmit antenna selection schemes under channel estimation errors and feedback delay[ C] CWIT 7. Canada : [ s. n. ], 27 : [8 ] Cui J, Sheikh A U H, Falconer D D. BER analysis of optimum combining and maximal ratio combining with channel correlation for dual antenna systems [ C ] 1997 IEEE 47th V TC. Phoenix : IEEE Press, 1997 : [9 ] Gradshteyn I S, Ryzhik I M. Table of integrals, series, and products [ M ]. 6th ed. ondon : Academic Press, [ 1 ] Goldsmith A. Wireless communication[ M ]. New York : Cambridge University Press, (8 ) CIR. SNR,, RMSE ; SNR 16 db,rmse, RMSE. 4 SC2FDE CFR,, CFR, SNR PA. CIR,.. : [1 ],,. [J ]., 25, 28 (2) : Sun Weijun, Zou Yongzhong, i Daoben. Blind channel estimation performance analysis[j ]. Beijing University of Posts and Telecommunications, 25, 28 (2) : [2 ] Slock D. Blind fractionally2spaced equalization, perfect2 reconstruction filter banks and multi2channel linear pre2 diction[ C] 1994 IEEE Inter2 national Conference on A2 coustics, Speech, and Signal Processing. Adelaide : [ s. n. ], 1994 : [3 ] Karim A M, Eric M, Philippe. Prediction error method for second2order blind identification [ J ]. IEEE Transactions on Signal Processing, 1997, 45 ( 3) : [4 ],. [J ]., 28, 31 (3) : Yu ei, Yang Xinyuan. Blind and semi2blind channel es2 timation based on subspace [ J ]. Beijing University of Posts and Telecommunications, 28, 31 (3) : [ 5 ] i X H, Fan H. Direct estimation of blind zero2forcing e2 qualizers based on second2order statistics [ J ]. IEEE Transactions on Signal Processing, 2, 48 ( 8) : [6 ] i X H, Fan H. inear prediction methods for blind frac2 tionally spaced equalization [ J ]. IEEE Transactions on Signal Processing, 2, 48 (6) : [7 ],,. SC2FDE S [J ]., 27, 29 (4) : Du Yan, Zhang Yongsheng, Wang Xinzheng. On the S channel estimation of SC2FDE systems based on data aid2 ed method [ J ]. Journal of Electronics and Information Technology, 27, 29 (4) : [8 ] Roy S, i C Y. A subspace blind channel estimation method for OFDM systems without cyclic prefix [ J ]. IEEE Transactions on Wireless Communications, 23, 2 (1) : [9 ] Tugnait J K, uo W. inear prediction error method for blind identification of periodically time2varying chan2 nels[j ]. IEEE Transactions on Signal Processing, 22, 5 (12) :

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