On the Binary DPSK Communication Systems in Correlated Gaussian Noise

Using the recently developed probability density function we obtain "directly" the error rate expressions for the binary differential phase-shift keyed (DPSK) systems when the noise values at the sampling instants in adjacent time slots are statistically dependent. Two cases are considered: One corresponding to equal SNR at each of the two sampling instants, and the other to unequal SNR\´s. The consideration of the former case, together with the assumption of unequal a priori symbol probabilities P0and P1results in an error rate expression where ρ is the noise correlation coefficient, and h²is the SNR. This expression shows clearly why PEis independent of noise correlation when the source symbols are equi-probable provided intersymbol interference is assumed absent. We then obtain the error probability expression in terms of unequal SNR\´s (at the two sampling instants) and the correlation coefficient ρ. Since intersymbol interference in a binary DPSK system gives rise to unequal SNR\´s, this expression provides a useful formula for estimating the system performance under such circumstances.