Phase Cancellation in a Gaussian Noise Environment

The problem of phase concellation of two sinusoidal signals in the presence of Gaussian noise is considered for two types of decision schemes: comparison and threshold decision. The receiver is made up of several channels, each consisting of a narrow-band filter, envelope detecter, and decision circuit. In the case of comparison decision, the cancellation probability as a function of signal-to-noise ratio is derived for a two-channel receiver and then extended to
m
channels. The results derived are exact. In the case of threshold decision, the cancellation probability as a function of signal-to-noise ratio and threshold level is derived for the equal signal level case, then extended to the near-equal signal level case. The results obtained are approximate with an accuracy of better than 1 percent for signal-to-noise ratios greater than about 3 dB. In addition, exact results are derived for the noisefree case.