Detection of Modulated Gaussian Signals in Noise

A method using Hermite polynomials is utilized for analyzing the outputs of νth-law devices for inputs of modulated Gaussian signals and zero-mean Gaussian noise. New results are developed for the output correlation functions, and techniques for obtaining closed-form expressions are pointed out. Output signal-to-noise ratios for various input carrier-to-noise-power ratios are calculated, and plots are shown for a single sinusoidal modulating signal. Results are derived to show the existence of a theoretical maximum for the output signal-to-noise ratio. The method can be directly applied for the case of general Fourier expandable signals modulating a Gaussian carrier.