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A coherent symbol-by-symbol (SBS) diversity receiver for m-ary phase-shift keying (MPSK) and differentially encoded MPSK (MDPSK) signals transmitted over a nonselective Rayleigh fading channel is presented. It incorporates a new adaptive filter for channel estimation that does not require any prior knowledge of the fading process model. It estimates the fading gains through decision-feedback and recursive least squares adaptation of the filter coefficients. A novel forgetting-factor adaptation algorithm that enables the filter to react quickly to randomly changing fading statistics caused by shadowing and acceleration/deceleration is introduced. Simulations show that the receiver performs better than that of Adachi's ( IEEE Trans. Veh. Technol. vol. 47 p. 909, 1998), either without shadowing or under slow lognormal shadowing.