SEP Bounds for MPSK With Low SNR

Abstract

We derive new bounds on the symbol error probability (SEP) of $M$ -ary phase-shift keying (MPSK) with $M>4$ , in additive white Gaussian noise. The exact SEP expressions require numerical integration or the computation of a two-dimensional function. Differently, the new SEP bounds only depend on simple one-dimensional functions and hence are easier to compute than the exact SEP. We show that the new bounds are tighter than the existing SEP bounds for MPSK at low signal-to-noise ratio (SNR), while preserving accuracy at large SNR. In addition, simple and accurate SEP approximations for MPSK with $M>4$ are derived.