Error Rate Approximations for Differential Phase-Shift Keying

In this paper, we present an analysis of the performance of a model of the Differential Phase Shift Keying (DPSK) system. The method employed consists of deriving the test statistic for choosing between any two phases when an arbitrary phase is transmitted. The characteristic function of the test statistic is derived, and from this, the decision probability, i.e., the probability of choosing between any two phases conditional on the transmitted phase, is expressed as an integral. Curves are drawn of this probability applicable to any -phase system. An approximate expression is also derived which requires only the well-tabulated error function integral. The probability of a character (phase) error is upper and lower bounded based on the geometric interpretation of the decision probabilities. For a specified phase coding, we also relate the probability of a binary digit error to the decision probabilities. The exact expression for the probability of a binary digit error in a four-phase system is derived.