Phase Cancellation Probabilities for Several Sinusoidal Signals in Gaussian Noise

The problem of the detection of a noncoherent sinusoidal signal in the presence of Gaussian noise plus several other interfering sinusoidal signals is considered. The receiver operation consists of envelope detection followed by threshold decision, and the signals are assumed to have equal amplitudes. The probability of phase cancellation, i.e., the probability that the envelope falls below threshold, is calculated as a function of threshold setting, signal-to-noise power ratio, and the number of simultaneous signals.