Performance of Phase-Locked Loops in the Presence of Fading Communication Channels

An approach is presented for the analysis of phase-locked loops whose input signal has passed through time-varying channels. The specific channels considered in detail are the Rice-Nakagami, Rayleigh, and lognormal fading channels. Loop performance is characterized in terms of the steady-state probability density function of the reduced phase error process. The basic parameters which characterize performance include the loop signal-to-noise ratio (SNR) and the variance and bandwidth of the fading components introduced by the channel. Particular channel models are used to illustrate the theory for the firstorder loop. The results are also applied to the analysis of the PSK noisy reference problem in the presence of these time-varying channels.