Adaptive equalization for frequency-selective channels of unknown length

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 channel length 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 channel length and the risk associated with an incorrect estimation of this length. Indeed, to determine the channel length 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 channel length. The key idea is to model the channel impulse response via a mixture Gaussian model, which has one component for each possible channel 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 channel length.