Maximum-likelihood estimation of FIR channels excited by convolutionally encoded inputs

If error correcting coding is present in the information symbols, the channel estimation procedure may be further complicated, since the encoder introduces a nonlinear operation on the information symbols (in the field of reals). Moreover, because of the encoder's memory, the input to the channel may not be i.i.d. Therefore classical blind channel equalization methods may not be suitable for systems with coding. In this letter, a blind stochastic maximum-likelihood channel estimation algorithm is proposed for convolutionally coded signals transmitted through a multipath channel. The performance of the estimator is explored, based on the evaluation of approximate Cramer-Rao bounds. The CRB's are used in turn to obtain approximate expressions for the probability of error. Finally, some illustrative simulations are presented.