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

The error performance of differentially coherent detection of a binary differential phase-shift keying (DPSK) system operating over a hard-limiting satellite channel is derived. The main objective is to show the extent of error rate degradation of a DPSK system when a power imbalance exists between the two symbol pulses that are used in a bit decision interval. Consideration is also given to the DPSK error rate performance for the special case of {\em uncorrelated} uplink and {\em correlated} downlink noises at the sampling instants in adjacent time slots. Error probabilities are given as functions of uplink signal-to-noise ratio (SNR) and downlink SNR with different levels of SNR imbalance and different downlink SNR and uplink SNR as parameters, respectively. Our numerical results show that 1) as long as the symbols are equiprobable, the error probability is not dependent upon the downlink noise correlation, regardless of whether there is a power imbalance; 2) error performance is definitely affected by the power imbalance for all cases of symbol distributions; and 3) the error probability does depend upon downlink noise correlation for all levels of power imbalance if the symbol probabilities are not equal.