Generalized training based channel identification

In this paper, we address the general problem of identifying convolutive channels when several training sequences are inserted in the transmitted data symbols stream. We analyze the general situation where the training sequences differ from each other. We consider quasi-static channels (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 used for the identification. We first propose an iterative method that quickly converges to the maximum likelihood (ML) channel estimate. We also derive a simple closed form expression that approximates the ML channel estimate.