Probability distribution of DPSK in tone interference and applications to SFH/DPSK

The probability distribution of the received DPSK (differential phase-shift keying) signal under tone jamming is studied. The results should facilitate the analysis of the SFH/DPSK (slow frequency-hopped DPSK) system. The results given are more general than those previously published, in several aspects. First, the differential phase of the transmitted DPSK signal can assume any value. Second, probability distributions are derived instead of a set of probabilities calculated over certain symmetrical regions. This allows analyzing performance for arbitrary selected decision regions as well as determining optimum decision regions for demodulating the DPSK signal. Third, the joint probability distribution of both the magnitude and differential phase of the jammed DPSK signal is given. This can be used in the analysis where both tone jamming and Gaussian noise are considered. These results are used to analyze the error probability performance of a general uncoded SFH/DPSK signal under worst-case tone jamming and Gaussian noise