Considerations of Nonlinear Effects in Phase-Modulation Systems

A class of "optimum" phase modulation (PM) system treated in the past is one wherein a sinusoidal carrier is phase modulated linearly by a Gaussian (baseband) random process and demodulation is performed by a phase-locked loop (PLL). This paper is concerned with PM systems in which the phase modulation is allowed to be nonlinear. In practice, most phase modulators are restricted to finite ranges of linear operations. The performance (SNR) of the PLL demodulator is degraded when the linear range is exceeded by an amplitude of the modulating waveform. The occurrence of performance degradation is a random event whose frequency depends on the linear range and the statistics of the waveform amplitude. By interpreting the nonlinear phase modulation as a saturation phenomenon, we determine in this paper the performances of PLL de modulator as a function of varying degree of saturation (or limiting) level for several cases of baseband spectrums. We model the "saturation" by an error function limiter. Our results are general, and it is shown that the previous results of linear modulations are special cases of our results. We then move on to assume that the baseband waveform is a composite signal of multichannel frequency division multiplexed (FDM) signals. As a result, we compute the lower bounds of slgnal-to-crosstalk power ratio for several cases of baseband spectrums.