Error rate bounds for differential PSK

Differential phase-shift keying (DPSK) and coherent phase-shift keying (CPSK) are two of the techniques widely used in digital communications over channels such as satellite, terrestrial radio, and voiceband telephone. Because of the linear nature of the demodulation process in CPSK, the error performance of CPSK with various sources of impariments has been exhaustively treated, but even with additive Gaussian noise, only asymptotic approximations are available to determine the detection performance of M-ary DPSK, M greater than 2. In this note, the error performance of nonbinary DPSK in additive Gaussian noise channels has been bounded in terms of tabulated functions and various approximations are then derived.