Training based maximum likelihood channel identification

In this paper, we address the problem of identifying convolutive channels in a maximum likelihood (ML) fashion when a constant training sequence is periodically inserted in the transmitted signal. We consider the case where the channel is quasi-static (i.e. the sampling period is several orders of magnitude below the coherence time of the channel). There are no requirements on the length of the training sequence and all the received symbols that contain contributions from the training symbols are exploited. We first propose an iterative method that converges to the ML estimate of the channel. We then derive a closed form expression of the ML channel estimate.