Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference

TLDR

The Viterbi algorithm is easier to implement than earlier optimum nonlinear processors and its performance can be straightforwardly and accurately estimated. A maximum‑likelihood sequence estimator for a digital pulse‑amplitude‑modulated sequence in the presence of finite intersymbol interference and white Gaussian noise is developed. The estimator uses a sampled linear filter, the whitened matched filter, followed by the Viterbi algorithm, and a simplified but effectively optimum variant is presented for popular partial‑response schemes. The whitened matched filter outputs form sufficient statistics for sequence estimation, and the resulting performance is effectively optimal, matching any.

Abstract

A maximum-likelihood sequence estimator for a digital pulse-amplitude-modulated sequence in the presence of finite intersymbol interference and white Gaussian noise is developed, The structure comprises a sampled linear filter, called a whitened matched filter, and a recursive nonlinear processor, called the Viterbi algorithm. The outputs of the whitened matched filter, sampled once for each input symbol, are shown to form a set of sufficient statistics for estimation of the input sequence, a fact that makes obvious some earlier results on optimum linear processors. The Viterbi algorithm is easier to implement than earlier optimum nonlinear processors and its performance can be straightforwardly and accurately estimated. It is shown that performance (by whatever criterion) is effectively as good as could be attained by any receiver structure and in many cases is as good as if intersymbol interference were absent. Finally, a simplified but effectively optimum algorithm suitable for the most popular partial-response schemes is described.