MULTIPLE SYMBOL PARTIALLY COHERENT DETECTION OF MPSK

In this paper we show that by using the known (or estimated) value of carrier tracking loop SNR in the decision metric, it is possible to im prove the error probability performance of a partially coherent MPSK s ystem relative to that corresponding to the commonly used ideal cohere nt decision rule. Using a maximum-likehood approach, an optimum decisi on metric is derived and shown to take the form of a weighted sum of t he ideal coherent decision metric (i.e., correlation) and the noncoher ent decision metric which is optimum for differential detection of MPS K. The performance of a receiver based on this optimum decision rule i s derived and shown to provide continued improvement with increasing l ength of observation interval (data symbol sequence length). Unfortuna tely increasing the observation length does not eliminate the error fl oor associated with the finite loop SNR. Nevertheless, in the limit of infinite observation length, the average error probability performanc e approaches the algebraic sum of the error floor and the performance of ideal coherent detection, Le., at any error probability above the e rror floor, there is no degradation due to the partial coherence. Whil e the above is strictly speaking only true in the limit of infinite ob servation length, it is shown that one can virtually achieve this limi ting behavior with practical size observation lengths. Furthermore, th e 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.