The Effect of Loop Stress on the Performance of Phase-Coherent Communication Systems

In phase-coherent communication systems which use phase-locked loops to provide synchronization of the data detector, the communications engineer is frequently faced with the problem of determining the effects which noisy timing has upon detection efficiency. This paper is concerned with determining these effects when second-order phase-locked loops, operating in the presence of frequency detuning, are used as a means of providing phase synchronization. The results are also applicable to the problem of establishing noisy reference losses in a broad class of coherent PCM telemetry systems, e.g., PCM/PSK/PM. Also presented are results which can be used to determine steady-state statistical dynamics of second-order loops.