A generalized proof is presented that AM-to-PM conversion can only degrade, never improve, the intermodulation-noise performance of memoryless nonlinear systems with random input signals having even probability density functions, and a measure of degradation is defined. It is also shown for such signals that AM-to-PM conversion causes a deterministic constant phase shift to be added to the argument of the signal component at the output but has no other effect on its phase. This class of inputs includes one or the sum of several PSK signals, as well as large ensembles that can be modeled as Gaussian noise. The latter are dealt with by using Bussgang's theorem on input-output cross correlation. In the proof, Bussgang's theorem is extended to the complex case, to include phase as well as amplitude nonlinearities, yielding a complex version of the theorem. For Gaussian inputs it is shown that the undistorted signal and the intermodulation noise at the output of such systems are uncorrelated.

An analysis of SS/TDMA steady-state synchronization is presented, in which the need for reliable sync maintenance during periods of deep signal fades, beyond the point of communications outage, is considered. The time required for sync-maintenance measurements, together with impact on guard time requirements, will lead to degradation of SS/TDMA transmission efficiency. The need to ensure a sufficiently low rate of occurence of errors in the syncmaintenance measurements also impacts transmission efficiency. A generalized formulation relating the degree of immunity to signal fading, degradation in transmission efficiency, and rate of occurrence of measurement errors is developed. Numerical results are obtained for a typical satellite communications system of current interest. It is shown that sync-maintenance systems can be designed to operate reliably during severe signal fades, orders of magnitude beyond the point of communication outage, at the expense of minimal degradation of transmission efficiency. For this level of performance it is shown that, with proper choice of parameters, virtually error-free syncmaintenance operation can be achieved. Numerical values of typical design parameters are presented.