Optimum Sequence Estimation for Non-Gaussian Channels with Intersymbol Interference

In 1972, Forney proposed a maximum likelihood sequence estimator for digital PAM (pulse amplitude modulated) signals in the presence of nite intersymbol interference (ISI) and additive white Gaussian noise. This optimum scheme involves passing the received signal through a so-called whitened linear matched lter, sampling the lter output at the symbol rate, and processing the resulting sequence of samples using the Viterbi algorithm to estimate the transmitted sequence. In this paper, we derive a maximum likelihood sequence estimator for PAM signals in the presence of nite ISI, when the additive noise consists of i.i.d. samples following an arbitrary non-Gaussian distribution. Our optimal estimator consists of a so-called vector Viterbi algorithm that operates directly on the samples, many per symbol interval, of the (unnl-tered) received signal. We apply this algorithm to the special case of Laplacian noise, and obtain a particularly elegant receiver structure which is simple to implement.