Maximum Likelihood Sequence Estimators: A Geometric View

Communication issues are described via macro operations between the data and the observation spaces. The problem of recovering the data is related to the inversion of an operator (the channel mapping); for this reason results available in linear algebra and functional analysis are applicable. Traditional concepts in communications are identified with these operations. A new approach to the maximum likelihood sequence estimator based on a sufficient statistic derived from these concepts is proposed. With this approach, intersymbol interference is removed by linear equalization, and a Viterbi-like dynamic programming algorithm takes into account the correlated noise in the metric evaluation. The performance of suboptimal receivers obtained by means of metric simplification is analyzed. © 1989 IEEE