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A novel adaptive coherent receiver for TCM signals transmitted over randomly time-variant frequency-selective fast-fading wireless links is presented. Its main feature is that the three different tasks of channel-estimation, equalization and decoding are jointly carried out in an optimal way. The last two operations are jointly accomplished by a symbol-by-symbol (SbS) Abend-Fritchman like detector (Proakis, 1989) which delivers both hard-decisions and suitably defined soft-output statistics. The latter directly feed a nonlinear Kalman-type estimator for channel tracking. Using the more informative soft-statistics in place of usual hard statistics for channel estimation constitutes the novel attractive feature of the proposed receiver; in this way, the channel estimator is able to fully exploit the coding redundancy so to enhance the tracking capability.