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

Abstract

This paper presents a second-order statistical analysis for the cascade of a bandpass limiter, and ideal phase detector and a video filter. This cascade forms an important subsystem in the mathematical model of some coherent communication systems where information is transmitted by phase or frequency modulation of the carrier. We derive the autocorrelation function R(t <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , t <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> ) of the video filter response when the bandpass limiter input is a fixed amplitude-phase modulated carrier plus stationary gaussian noise. The video filter response is wide sense stationary for some nontrivial cases; these include biphase, single tone, and stationary gaussian noise phase modulation. For these cases, we obtain the video filter output average power spectrum as the Fourier transform of R(τ) for all values of the limiter input signal-to-noise power ratio. An application of the results of this paper is the performance of a FM-PM demodulator for a set of parameters characteristic of one mode of operation of the Apollo Unified S-Band communications system. We present the performance as a family of curves of subcarrier channel output signal-to-noise power ratio as functions of the limiter input signal-to-noise ratio where subcarrier phase modulation index is a parameter. The approach is similar to the analysis by Davenport of the signal-to-noise ratio transfer characteristic of an isolated bandpass limiter.