Maximum likelihood sequence estimation of CPM signals transmitted over Rayleigh flat-fading channels

A method for the sequential updating of log-likelihood functions for maximum-likelihood sequence estimation is presented. It is shown that, in a general case, this method can be implemented using Kalman filtering techniques. For the special case of Rayleigh flat fading and continuous phase modulation (CPM) signaling, this approach is shown to lead to an attractive receiver structure. This type of receiver, called the linear predictive receiver, can be implemented in the form of the Viterbi algorithm with the trellis updates being computed using a bank of finite pulse response (FIR) filter and square operations. Simulation results are presented that demonstrate the superiority of the linear predictive receiver over receivers employing differential detection, in the presence of fast fading. It is shown that the optimal linear predictive receiver does not possess an irreducible error rate for a class of Rayleigh fading channels used to model terrestrial mobile channels