Maximum likelihood sequence estimators: a geometric view

Abstract

Communication issues are described in terms of 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. An approach to the maximum-likelihood sequence estimator based on a sufficient statistic derived from these concepts is proposed. 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