Bayesian EM-based demodulators for frequency-selective fading channels

In this paper, the problem of adaptive MAP symbol detection in the uncoded transmission as well as the problem of adaptive APP demodulation in the coded transmission of data symbols over the frequency-selective Rayleigh fading channel are explored within the framework of the Bayesian expectation-maximization (BEM) algorithm. In particular, two novel versions of the BEM-based detection and demodulation algorithms are derived. In contrast to the earlier developments of BEM algorithms, the formulations derived in this paper lead to the computationally efficient algorithms which avoid the matrix inversions while using sequential processing over the time and trellis branch indexes. In addition, it is shown how the recursive versions of the BEM algorithms can be combined with the well-known forward-backward processing soft-input soft-output (SISO) algorithms resulting in adaptive SISOs with soft decision directed (SDD) channel estimators. An application of the proposed algorithms to the iterative "turbo-processing" receivers illustrates how these SDD channel estimators can efficiently exploit the extrinsic information obtained from the SISO decoder in order to enhance their estimation accuracy.