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.>

A design and analysis of a coherent frequency-hopped (C-FH) spread-spectrum system operating in the presence of both jamming and a nonideal channel response is presented. A simple channel equalizer and a joint maximum-likelihood RF and C-FH phase track loop operate simultaneously. By assuming that the channel response is smooth over every slot, and that the effect of decision error is negligible, the convergence properties of the equalizer are analyzed in the presence of jamming. The numerical results are shown for the average error probability, the steady-state mean-square-error, and the convergence time when the system is operating in the presence of both frequency error and arbitrary channel phase response. The overall performance is very close to that of an ideally synchronized system, except when a coherent multitone jammer is present having the same phase of the received signal. In this latter case, the system experiences slightly more degradation.>