Maximum-likelihood blind FIR multi-channel estimation with Gaussian prior for the symbols

We present two approaches to stochastic maximum likelihood identification of multiple FIR channels, where the input symbols are assumed Gaussian and the channel deterministic. These methods allow semi-blind identification, as they accommodate a priori knowledge in the form of a (short) training sequence and appears to be more relevant in practice than purely blind techniques. The two approaches are parameterized both in terms of channel coefficients and in terms of prediction filter coefficients. Corresponding methods are presented and some are simulated. Furthermore, Cramer-Rao Bounds for semi-blind ML are presented: a significant improvement of the performance for a moderate number of known symbols can be noticed.

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