Adaptive Equalization for Frequency-Selective Channels of Unknown Length

Abstract

This paper studies adaptive equalization for time-dispersive communication channels whose impulse responses have unknown lengths. This problem is important, because an adaptive equalizer designed for an incorrect is suboptimal; it often estimates an unnecessarily large number of parameters. Some solutions to this problem exist (e.g., attempting to estimate the channel length and then switching between different equalizers); however, these are suboptimal owing to the difficulty of correctly identifying the and the risk associated with an incorrect estimation of this length. Indeed, to determine the is effectively a model order selection problem, for which no optimal solution is known. We propose a novel systematic approach to the problem under study, which circumvents the estimation of the length. The key idea is to model the impulse response via a mixture Gaussian model, which has one component for each possible length. The parameters of the mixture model are estimated from a received pilot sequence. We derive the optimal receiver associated with this mixture model, along with some computationally efficient approximations of it. We also devise a receiver, consisting of a bank of soft-output Viterbi algorithms, which can deliver soft decisions. Via numerical simulations, we show that our new method can outperform conventional adaptive Viterbi equalizers that use a fixed or an estimated length.