TIME DIVERSITY IN DPSK NOISY PHASE CHANNELS

Differential phase shift keying (DPSK) in the presence of both additive white Gaussian noise and a phase impairment, modeled by a Brownian motion is considered. A time-diversity scheme is employed for mitigating the effects of phase noise. This scheme renders a repetition coding approach where the transmitter sends multiple replicas of each data bit. The receiver decision is based on softly combining the demodulated outputs where the demodulation consists of a prefilter followed by a delay and multiply detector. An upper bound on the bit error probability, relying on a bivariate moment-generating function admitted by certain real functionals of the phase sample-path, is derived. Though this generating function is unknown, it is bounded using the available underlying univariate moments. The latter are computable in a straightforward manner using a recursive procedure. The approach taken yields a trackable analysis, which rigorously adheres the phase noise effects. The impact of an incomplete statistical characterization on the tightness of the resultant bound is addressed. The theory, which is applicable to assess the design and performance of general heterodyned lightwave systems employing (delay) differential demodulation (as DPSK and CP-FSK), is exemplified and explicit results for the considered time-diversity DPSK scheme are provided. We study the optimum design of the diversity level and conclude that power efficient transmission is feasible even at bit rates comparable with the signal linewidth.