A note on power-law devices and their effect on signal-to-noise ratio

The effect of power-law devices, used as either band-pass nonlinear amplifiers or envelope detectors, on the signal-to-noise ratio is determined for both limiting cases of very large and very small input signal-to-noise ratio. Expressions are derived for the degradation in signal-to-noise ratio in terms of the envelopes and phases of the signal and noise. The results are general, applying to Gaussian and non-Gaussian noises and modulated and unmodulated signals, and allow important conclusions to be reached concerning the value of power-law devices in communications systems in various signal and noise environments. It is found that band-pass nonlinear amplifiers can generally be chosen to improve the signal-to-noise ratio if the input signal-to-noise ratio is small and the noise is non-Gaussian. Envelope detectors usually degrade the signal-to-noise ratio since they exhibit a "small-signal suppression" effect in all noise environments except for the special case of unmodulated sine-wave interference.