Invariance of distribution of coherence estimate to second-channel statistics

When one of the two channels used in a coherence estimator contains only zero-mean stationary Gaussian noise, the probability distribution of the magnitude-squared-coherence estimate is utterly independent of the distribution in the other channel when the random variables in the two channels are statistically independent of each other. Thus, proper threshold settings for specified false alarm probabilities in a coherence-detector can be realized under complete ignorance of the statistics of the non-Gaussian channel.