A simple tight upper bound on the BEP of 2DPSK over the AWGN channel w
ith phase noise in the received signal is obtained. The phase is model
ed as a Gaussian random process which is slowly varying compared to th
e bit rate so that a piecewise-constant approximation can be made. The
bound is verified by computer simulations, and it provides good estim
ates of the error probability. It shows that for high SNR the error pr
obability decreases as the reciprocal of the square-root of the SNR. T
he results are applicable in particular to heterodyne optical communic
ations.