Computationally Efficient Maximum Likelihood Sequence Estimation and Activity Detection for $M$ -PSK Signals in Unknown Flat Fading Channels

In this letter, we develop a computationally efficient algorithm for the Maximum Likelihood (ML) sequences estimation (MLSE) of an M-ary Phase Shift keying (M -PSK) signal transmitted over a frequency non-selective slow fading channel with an unknown complex amplitude and an unknown variance additive white Gaussian noise. The proposed algorithm also provides the ML estimates of the complex amplitude and the noise variance that are critical in signal activity detection and demodulation in the modern cognitive communication receivers. We prove the optimality of the proposed algorithm and compare its performance via simulation with a recent suboptimal algorithm.