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Adaptive MLSDE using the EM algorithm

The theory of adaptive sequence detection incorporating 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 (1984) stochastic approximation 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 simulation 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.