M-ary PSK transmission for two-link channels with repeater nonlinearity and a noisy carrier reference

Earlier research on specifying the error probability for M-ary PSK transmission over a two-link channel with a nonlinear repeater is extended to include the effects of a noisy carrier reference. A convergent, infinite series for the error probability is presented. This representation is valid for a wide class of repeater nonlinearities and carrier reference error statistics. Numerical results are presented for well known models for the repeater and the carrier reference error. Both carrier reference loss and noise on the channel´s first link can cause the error probability to take an irreducible value in terms of the second link´s signal-to-noise ratio. Each impairment causes a similar phenomenon when acting alone and the results detail their combined effects.