The analysis of a coherent frequency hopped spread spectrum system

A digital joint phase/timing tracking loop for a coherent frequency-hopped spread-spectrum system is analyzed for both training mode and tracking performance. Under minor assumptions, the phase error is modeled as a homogeneous finite Markov chain. The length of the training period, the approximate probability of entering the tracking range, the steady-state average error probability, and the mean-time to loss-of-lock are derived. The effects of both nonzero RF phase error and cubic channel phase response are presented. It is shown that the performance of the system can be designed to be close to that of a perfectly synchronized system.<>