Generic error probabilities

This paper presents new forms for an error probability associated with the phase angle between two vectors perturbed by Gaussian noise. An interesting consequence of the underlying generic form is a new expression for the symbol error rate in MDPSK that is very similar to its counterpart for MPSK, The generic error probability is further shown to contain as special cases MPSK, MDPSK, CPFSK, and digital FM; and to give a new expression for the Marcum Q-function. The generic error probability also 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.