Error performance of differentially coherent detection of binary DPSK data transmission on the hard-limiting satellite channel

The error performance of a differentially coherent detection method of binary differential phase-shift keying (DPSK) system operating over a hard-limiting satellite channel is derived. The main objective of our derivation was to observe the extent of error rate degradation of a DPSK system due to unequal power levels and noise correlations between the two adjacent time slot pulses. In practice, the power imbalance, or equivalently SNR imbalance, is induced by such phenomena as intersymbol interference and/or errors in phase delay in the 'one-bit-delayed' reference input. The noise correlation is a practical assumption since the noise is necessarily band limited in the system. Error probabilities are given as a function of uplink SNR with different levels of SNR imbalances and different downlink SNR as parameters. It is discovered that, while SNR imbalance affects error performance, the probability of error is independent of noise correlation if the symbol probabilities are equal.