A New Formula for MDPSK Symbol Error Probability

This letter presents an extremely compact new formula for the symbol error probability in M-ary differential phase shift keying (MDPSK) that is extraordinarily similar to its counterpart for M-ary phase shift keying (MPSK). This result follows from a new form for a generic error probability associated with the phase angle between two vectors perturbed by Gaussian noise. The new form also leads to a new expression for the Marcum Q-function. As special cases, the generic error probability is noted to also contain MPSK, CPFSK, and digital FM. Finally, it is pointed out that the generic error probability simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum-likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK.