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A C hannel-Whit ening Blind Sequence Estimation Algorithm. Yi Sun and Lang Tong' ... where Dmin is the minimum distance of sequence of symbol correlationĀ ...
ISlT 1998. Cambridge. MA, USA. August 16 - August 21

A Channel-Whitening Blind Sequence Estimation Algorithm Yi Sun and Lang Tong' Dept. of Electrical and Systems Engineering University of Connecticut, U-157 Storrs, C T 06269 E-mail: yisunObrc.uconn.edu, [email protected] MSE of W and CRE M=100

Abstract - In this paper, we propose the channelwhitening blind sequence estimation (CW-BSE) algorithm followed by a least square estimator for blind channel estimation, and analyze the performance of the CW-BSE algorithm. Simulation shows that when signal-to-noise ratio is larger than 8 dB, the mean squared error of estimated channel parameters achieves the Cramer-Rao bound for estimators using training sequence.

I. CW-BSE

ALGORITHM FOR CHANNEL ESTIMATION

Given the following signal model x ( t ) = Hs(t)

+ n(t)

SNR (dE)

(1)

where s ( t ) = ( S t - d + l , . . . ,s t ) E Cd is a symbol vector, H E CNxdis the multipath channel parameter matrix, n(t) E CN is the white Gaussian noise and x ( t ) E C N is the collected sample vector of received baseband signal. The purpose is to estimate H without knowing the transmitted sequence {sn}. The CW-BSE algorithm was originally proposed for blind sequence estimation [l]. It consists of a transform, which is usually channel-whitening (CW), followed by the Viterbi algorithm. The transform consists of the principal eigenvectors of HHN which can be estimated from data. In this paper, we propose to use the sequence obtained by the CW-BSE algorithm to estimate the channel matrix H based on the least square method. Fig. 1shows a simulation example of the proposed method. We consider the channel H obtained by taking the first, fifth and ninth rows of the channel parameter matrix used in the simulation of [l]. The BPSK signal is considered. In each trial, 100 bits are used. As shown in Fig. 1, when SNR2 8 dB, the MSE of the blind channel estimation is close to the Cramer-Rao bound of the estimator using known bit sequence.

11. PERFORMANCE

Fig. 1: MSE of blind channel estimation using channel whitening and Cramer-Rao bound for estimators utilizing known bit sequence.

Theorem 1 For the BPSK signal, the minimum distance of sequence of the symbol correlation function with correlation delay one is Dmin= 2 for all d^ 2 1. Theorem 1 shows that in the CW-BSE algorithm, the minimum distance of the sequence of symbol correlation function is small compared with the minimum distance of the original symbol sequence. If the orthogonal transformation matrix is used, J(T) is given by

where d^ is the number of principal eigenvectors used in t r a n s formation and Xi is the correspondent eigenvalues. Similarly, we can obtain the estimation error when the optimum t r a n s formation matrix is used. Ftom (2) and (3), we can obtain a lower bound of symbol error rate.

ANALYSIS

Since the estimated symbol sequence obtained by the CWBSE algorithm is used in the channel estimation, it is interesting to analyze the symbol error rate of the CW-BSE algorithm. The figure of merit is defined by

where Dminis the minimum distance of sequence of symbol correlation function used in estimation in trellis and J(T) is the variance of estimation error of the symbol correlation function. 'This work was supported in part by the National Science Foundation under Contract NCR-9321813 and by the Office of Naval

111. CONCLUSIONS The mean squared error of channel parameters estimated by the CW technique is fairly small compared with the Cramer-Rao bound for estimators using training sequence. However, to use the sequence of symbol correlation function in estimation reduces the minimum distance of paths in trellis. Hence, the CW-BSE algorithm is suitable for the initial channel acquisition of fading channels for blind channel equalization and sequence estimation.

REFERENCES [l] L. Tong, "Blind sequence estimation," IEEE "hns. on Comm., vol. 43, no. 12, pp. 2986-2994, Dec. 1995.

Research under Contract N00014-96-1-0895.

0-7803-5000-6/98/$10.00 0 1998 IEEE.

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