Performance analysis of noncoherent sequence detection of M-ary PSK

In this paper, we present a theoretical performance analysis of recently proposed noncoherent schemes for the combined sequence detection and decoding of coded M-ary phase shift keying (M-PSK) signals [1]. Based on the classical union bound, we describe a method for the numerical evaluation of the pairwise error probability, for which no closed-form expressions exist, and compare results with computer simulations. We also present an upper bound to this pairwise error probability which may be effectively used for an exhaustive search of optimal codes. This bound allows us to prove that the noncoherent sequence detection schemes proposed in [1] perform as well as an optimal coherent receiver when an implicit phase memory parameter is sufficiently large. In the case of differentially encoded MPSK, we derive a simple expression for the asymptotic bit error probability which is in agreement with simulations for high as well as low signal-to-noise ratio.