The Extended-Window Channel Estimator for Iterative Channel-and-Symbol Estimation
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The Extended-Window Channel Estimator for Iterative Channel-and-Symbol Estimation Renato R. Lopes DSPCom, DECOM, FEEC, University of Campinas (UNICAMP), 400 Albert Einstein Avenue, 13083-970 Campinas, Sao Paulo, Brazil Email: [email protected]
John R. Barry School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, USA Email: [email protected] Received 29 April 2004; Revised 21 September 2004 The application of the expectation-maximization (EM) algorithm to channel estimation results in a well-known iterative channeland-symbol estimator (ICSE). The EM-ICSE iterates between a symbol estimator based on the forward-backward recursion (BCJR equalizer) and a channel estimator, and may provide approximate maximum-likelihood blind or semiblind channel estimates. Nevertheless, the EM-ICSE has high complexity, and it is prone to misconvergence. In this paper, we propose the extendedwindow (EW) estimator, a novel channel estimator for ICSE that can be used with any soft-output symbol estimator. Therefore, the symbol estimator may be chosen according to performance or complexity specifications. We show that the EW-ICSE, an ICSE that uses the EW estimator and the BCJR equalizer, is less complex and less susceptible to misconvergence than the EM-ICSE. Simulation results reveal that the EW-ICSE may converge faster than the EM-ICSE. Keywords and phrases: blind channel estimation, EM algorithm, maximum-likelihood estimation, iterative systems.
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INTRODUCTION
Channel estimation is an important part of communications systems. Channel estimates are required by equalizers that minimize the bit error rate (BER), and can be used to compute the coefficients of suboptimal but lowercomplexity equalizers such as the minimum mean-squared error (MMSE) linear equalizer (LE) [1], or the decisionfeedback equalizer (DFE) [1]. Traditionally, a sequence of known bits, called a training sequence, is transmitted for the purpose of channel estimation [1]. These known symbols and their corresponding received samples are used to estimate the channel. However, this approach, known as trained estimation, ignores received samples corresponding to the information bits, and thus does not use all the information available at the receiver. Alternatively, semiblind estimators [2] use every available channel output for channel estimation. Thus, they outperform estimators based solely on the channel outputs corresponding to training symbols, and require a shorter training sequence. Channel estimation is still This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
possible even if no training sequence is available, using a technique known as blind channel estimation. An important class of algorithms for blind and semiblind channel estimation is based on the iterative strategy depicted in Figure 1 [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], which we
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