Cascaded coherent tracking systems with time-varying channels

A performance analysis is presented of a two-way coherent tracking system (of the type used for spacecraft tracking and navigation) in which the transmitted signals have pass through linear time-varying channels. The performance of the system is characterized by the steady state probability density function of the reduced phase error process in the second tracking loop, the system considered consisting of two first-order phase locked loops in cascade. While the log normal channel, which arises in communication through planetary atmospheres, was used as the channel model, the results can be extended to other channels, such as the Rice and Rayleigh channels.