Blind and semi-blind equalization of CPM signals with the EMV algorithm

We apply the expectation-maximization Viterbi algorithm (EMVA) introduced in a previous paper to the blind or semi-blind maximum-likelihood equalization of continuous-phase modulated (CPM) signals transmitted over a noisy linear finite impulse response (FIR) channel. The EMVA is a computationally efficient technique for simultaneously performing system identification and signal detection whenever the transmission system admits a hidden Markov model (HMM) description. The convergence properties of the EMVA are examined and a method for monitoring the EMVA convergence rate online is presented. It is shown that the order of the FIR channel can be estimated by applying the order-incrementing (OI) and fixed-order (FO) methods proposed previously. A Cramer-Rao bound is derived for the channel impulse response, and it is shown via simulations that the EMVA approaches this bound as the SNR increases. Finally, an EMVA-based technique is described for estimating the error covariance matrix for the system parameters for the case of long observation blocks.