Analysis of the Tracking Loop of Phase Coherent Frequency Hopped Systems

This paper analyzes the behavior of frequency hopped systems that make use of an MSK-type waveform to obtain a continuous phase at each hop transition and that employ digital tracking loops at the receiver. It is shown that, for an AWGN channel, a steady state density function exists for the tracking error in the absence of frequency uncertainty. Also, the dynamics of the phase error can be obtained when there is uncertainty in the received frequency, and results for the probability distribution of the first time at which loss of lock occurs for a given initial frequency error are presented.