An EM algorithm for path delay and complex gain estimation of slowly varying fading channel for CPM signals

International audienceThis paper addresses the joint path delay and time-varying complex gain estimation for continuous phase modulation (CPM) over a time-selective slowly varying flat Rayleigh fading channel. We propose an expectation-maximization (EM) algorithm for path delay estimation in a Kalman smoother framework. The time-varying complex gain is modeled by a first order autoregressive (AR) process. Such a modeling yields to the representation of the problemby a dynamic bayesian system in a state-space form that allows the application of EMalgorithm in the context of unobserved data for obtaining an estimate of the path delay. This is used with Kalman smoother for state estimation. We derive analytically a closed form expression of the modified hybrid Cram'er-Rao bound (MHCRB) for path delay and complex gain parameters. Finally, some numerical examples are presented to illustrate the performance of the proposed algorithm compared to the conventional generalized correlation method and to the MHCRB