A Second Order Statistical Analysis of the Operation of a Limiter-Phase Detector-Filter Cascade

In some coherent communication systems, such as the Apollo Unified S-band system,1 where information is transmitted by phase modulating a carrier, bandpass limiters2 are used in the IF channels preceding the coherent demodulators. Ideally the bandpass limiter removes any amplitude modulation that might exist before the signal is demodulated. 233 234 T H E BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1969 Figure 1 shows a typical coherent phase demodulator used in such a system. This demodulator consists of a multiplication operation (a phase detector) with post-video filtering. The phase modulated signal is multiplied by a coherent carrier reference to yield a video signal containing the desired information. The signal into the limiter is usually accompanied by noise that is frequently assumed to be additive and gaussian. The presence of the noise affects the performance of the demodulator in a very complicated way because of the nonlinearity of the limiter. Thus it is difficult to evaluate the corruptive effect of the noise on the demodulated information. One criterion of performance at points in a communication system is the signal-to-noise power ratio (S/N). For the cascade in Fig. 1, a problem of interest to the systems engineer is the video filter output S/N as a function of the input S/N to the limiter when the input noise is additive, stationary, and gaussian. The relationship is known between input and output S/N for an ideal bandpass limiter where the input is the sum of a stationary gaussian noise and a signal Pit) cos (ccet + ) (see Ref.