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 used for mitigating the effects of phase noise. This scheme renders a repetition coding approach where the transmitter sends multiple replicas of each data bit. 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. 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 using (delay) differential demodulation (as DPSK and CP-FSK, or continuous phase frequency-shift keying), is exemplified and explicit results for the considered time-diversity DPSK scheme are provided. The optimum design of the diversity level is discussed and it is concluded that power efficient transmission is feasible even at bit rates comparable with the signal linewidth