Optimal and Approximate Methods for Detection of Uncoded Data with Carrier Phase Noise

Previous results in the literature have shown that derivation of the optimum maximum-likelihood (ML) receiver for symbol-by-symbol (SBS) detection of an uncoded data sequence based on all received signals in the presence of random phase noise is an intractable problem. This is because it involves the computation of the conditional probability distribution function (PDF) of the phase noise process. In this paper, we seek to minimize symbol error probability (SEP), which is achieved by SBS detection of the sequence based on all received signals. We show that the ML detector for this problem can be formulated as a weighted sum of central moments of the conditional PDF of phase noise. Given that the central moments of the conditional PDF of phase noise can be estimated, this new optimal structure is tractable with respect to the previously known optimal ML receiver. Furthermore, based on the new receiver structure, we propose a simple approximate method for SBS detection and investigate its scope and applicability. Simulation results demonstrate that SEP performance close to optimality can be obtained through the proposed method for a wide range of phase noise variances and low signal-to-noise ratio (SNR).