A BAYESIAN MAXIMUM-LIKELIHOOD SEQUENCE ESTIMATION ALGORITHM FOR A-PRIORI UNKNOWN CHANNELS AND SYMBOL TIMING

It is well known that maximum-likelihood sequence estimation (MLSE), implemented using the Viterbi algorithm (VA), is the optimum demodulator for signals distorted by multipath and additive white Gaussian noise (AWGN). At low signal-to-noise ratios, however, it may be difficult to obtain the needed channel and symbol timing estimates, since any channel estimation algorithm itself relies on reliable symbol decisions. Here, we show that the optimum demodulator for the case of an a priori unknown channel and symbol timing can be approximated using a modified Viterbi algorithm, in which the branch metrics are obtained from the conditional innovations of a bank of extended Kalman filters (EKF). Each EKF computes channel and timing estimates conditioned on one of the survivor sequences in the trellis. It is also shown that the minimum-variance channel and timing estimates can be approximated by a sum of conditional EKF estimates, weighted by the VA metrics. Simulated bit error rate (BER) results and averaged-squared channel/timing error trajectories are presented, with estimation errors compared to the Cramer-Rao lower bound. The BER performance of the modified VA is also shown to be superior to that obtained using a decision-directed channel/timing estimation algorithm.