Multiple symbol partially coherent detection of MPSK

The authors show that by using the known (or estimated) value of carrier tracking loop SNR in the decision metric, it is possible to improve the error probability performance of a partially coherent MPSK system relative to that corresponding to the commonly used ideal coherent decision rule. Using a maximum-likelihood approach, an optimum decision metric is derived and shown to take the form of a weighted sum of the ideal coherent decision metric (i.e., correlation) and the noncoherent decision metric which is optimum for differential detection of MPSK. The performance of a receiver based on this optimum decision rule is derived and shown to provide continued improvement with increasing length of observation interval (data symbol sequence length). Unfortunately increasing the observation length does not eliminate the error floor associated with the finite loop SNR. Nevertheless, in the limit of infinite observation length, the average error probability performance approaches the algebraic sum of the error floor and the performance of ideal coherent detection, i.e., at any error probability above the error floor, there is no degradation due to the partial coherence. While the above is strictly speaking only true in the limit of infinite observation length, it is shown that one can virtually achieve this limiting behavior with practical size observation lengths. Furthermore, the performance is quite insensitive to mismatch between the estimate of loop SNR (e.g., obtained from measurement) fed to the decision metric relative and its true value