Blind Equalization of Moving Average Channels Over Galois Fields

We consider the blind estimation / equalization of a Moving Average (MA) channel over a finite field. In this framework, the channel’s input and output signals, as well as its coefficients, belong to a finite (Galois) field, and all summation and multiplication operations are calculated modulo the field’s prime order. The input is assumed to be a sequence of independent, identically distributed (iid) samples with an unknown distribution, and the goal is to estimate the channel coefficients based on its observed output only. We derive two different estimation approaches: One is based on sequential identification of factors of the channel’s associated polynomial; The other is based on an attempted factorization of the empirical characteristic function of the channel’s output signal. We explain the trade-offs between the methods and demonstrate their performance by simulation.