Abstract—The theory of adaptive sequence detection incorpo- rating estimation of channel and related parameters is studied in the context of maximum-likelihood (ML) principles in a general framework based on the expectation and maximization (EM) algorithm. A generalized ML sequence detection and estimation (GMLSDE) criterion is derived based on the EM approach, and it is shown how the per-survivor processing and per-branch processing methods emerge naturally from GMLSDE. GMLSDE is developed into a real time detection/estimation algorithm using the online EM algorithm with coupling between estimation and detection. By utilizing Titterington’s stochastic ap- proximation approach, different adaptive ML sequence detection and estimation (MLSDE) algorithms are formulated in a unified manner for different channel models and for different amounts of channel knowledge available at the receiver. Computer simu- lation results are presented for differentially encoded quadrature phase-shift keying in frequency flat and selective fading channels, and comparisons are made among the performances of the various adaptive MLSDE algorithms derived earlier.

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