Envelope Detector Performance for a Partially Coherent-Fading Sine Wave in Noise

The performance of a matched filter square-law envelope detector is investigated for a new signal-in-noise model, that of a partially coherent-fading random-phase sine wave in additive zero-mean noise. This model is of interest when analyzing the effects of random amplitude and/or phase channels on narrow-band input signals. The amplitude and the phase of the sine wave are assumed to be independent random processes with known bandwidths. This paper obtains deflection-criteria detection-performance results for the envelope detector as a function of the bandwidths of the amplitude and phase of the signal process, the noise process, the observation time, and the second-moment statistics of the amplitude, phase, and noise processes. The results show quantitatively that the detection performance of the envelope detector is much more sensitive to loss of phase coherence than to loss of amplitude coherence.