Analysis of a coherent frequency-hopped spread-spectrum receiver in the presence of jamming

A digital phase/timing tracking loop for a coherent frequency-hopped spread-spectrum receiver is analyzed. A training period is introduced to aid the system in entering the tracking mode; once in this latter mode, decision-directed measurements are used. The S-curve, the conditional variance of the phase estimator, and the linear model of the loop are derived. Then, under minor assumptions, the phase error is modeled as a homogeneous finite Markov chain. Based on this model, the length of the training period and the approximate probability of entering the tracking range are obtained; in the tracking mode, the steady-state average probability of error and the mean-time to loss-of-lock are obtained. By limiting the maximum output magnitude of the phase estimator, it is shown that the tracking performance is close to that of coherent binary phase-shift keying (BPSK) in the absence of jamming, or that assuming perfect synchronization, in the presence of partial-band jamming. The mean-time to loss-of-lock is shown to be several orders of magnitude larger than the expected length of training period. The effects of a cubic channel phase response and a constant RF phase error are presented