An adaptive hidden Markov model approach to FM and M-ary DPSK demodulation in noisy fading channels

In this paper extended Kalman filtering (EKF) and hidden Markov model (HMM) signal processing techniques are coupled in order to demodulate frequency modulated signals in noisy fading channels. The demodulation scheme presented is applied to both digital M-ary differential phase shift keyed (MDPSK) and analog frequency modulated (FM) signals. Adaptive state-and-parameter estimation schemes are devised based on the assumption that the transmission channel introduces time-varying gain-and-phase changes, modelled by a stochastic linear system, and has additive Gaussian noise, An adaptive HMM approach is formulated which consists of a continuous state Kalman filter (KF) coupled with finite-discrete state HMM filters. The technique used is to represent MDPSK and FM signals with state space signal models for which the KF/HMM coupled filters are derived. A key to this approach is that complete information-states are used, instead of the maximum a posteriori estimates of the traditional matched filter approach, or maximum likelihood estimates of the Viterbi algorithm. The case of white observation noise is considered, as well as a generalisation to cope with coloured noise. Simulation studies are also presented.