Introduction

MAP sequence estimation is widely used in digital communication systems to estimate the transmitted data sequence observed over noisy, multipath channels. This objective becomes particularly challenging when the channel is unknown and fast-fading. If the channel is slow time-varying, effective algorithms [1,2,3,4] have been developed to estimate the transmitted data sequence and/or identify the channel blindly. For fast time-varying unknown channels, adaptive MLSE approaches have been developed. These algorithms usually estimate the transmitted data sequence based on the current estimate of the channel coefficients, while the channel coefficients are estimated using an estimate of the transmitted data sequence. One method of channel estimation [5] is to make tentative decisions which are obtained by truncating the surviving path in the Viterbi algorithm [6] to a fixed delay. Another channel estimator is realized by an adaptive decision-feedback equalizer (DFE) embedded in the MLSE structure [7]. Due to the decision delay in the former method and the error propagation caused by the DFE in the latter, these two methods have difficulty in tracking fast time-varying intersymbol interference (ISI) channels.

In [8] we have developed a maximum a posterior (MAP) sequence estimator for unknown, fast fading ISI channels for which the channel is modeled as FIR with a first-order Gauss-Markov coefficient vector. We derived a closed-form MAP cost function by marginalizing over the channel coefficients. For a small number of symbols n this cost can be exhaustively searched to obtain the MAP solution. For large n we proposed a Per Survivor Processing (PSP) algorithm. PSP has been successfully applied for suboptimal sequence estimation and channel identification. For example, Raheli et al. proposed PSP-based MLSE [9] for fast time-varying channels. A PSP based algorithm was proposed in [10], in which a Viterbi algorithm is used to identify survivor sequences, and a data-assisted channel estimator is employed for each survivor. For each survivor Viterbi path, the corresponding sequence was used for LMS or RLS based channel estimation. Although this adaptive MLSE approach can result in good tracking performance for fast time-varying ISI channels, it is a suboptimal sequence estimator approach. The PSP algorithm we proposed, being based on MAP estimator which marginalizes over the channel, avoids the limitations associated with suboptimal LMS or RLS channel estimation. In [8] we illustrated that it provides close to optimal results for a practical level of computation.

In this paper we employ this estimator to study the advantage realized by incorporating knowledge of the channel into a channel model and marginalizing over the channel coefficients. We will explore the degree of this advantage as a function of channel fading rate. We also study the sensitivity of this MAP estimator to inaccuracies in the assumed values of parameters of the Gauss-Markov model.