Probability distribution of differential phase perturbed by tone interference and its application

Differential phase shift keying (DPSK) is widely used in communication systems where simplicity and robustness are desired. One such system is slow frequency hopped DPSK (SFH/DPSK) which can sustain a much higher data rate than a fast frequency hopped system while having the same hop rate. In the detection of SFH/DPSK, differentially coherent detection is often employed. This is because it is impossible to maintain the phase coherence between different hops. Differentially coherent detection can take advantage of phase coherence within a hop and thus outperforms noncoherent detection. In this paper we present a study of the probability distribution of a received differential phase perturbed by tone jamming and Gaussian noise. The intent is to study the effects of jamming against SFH/DPSK and to provide some tools for the analysis such a system.