An Invariance Property of the Generalized Coherence Estimate

The distribution of the M-channel generalized coherence estimate is shown not to depend on the statistical behavior of the data on one channel provided that the other M \Gamma 1 channels contain only white gaussian noise and all channels are independent. This confirms a recently published conjecture and extends the utility of the GC estimate as a detection statistic to include active as well as passive scenarios. I. Introduction The ability to determine whether a common signal is present on two or more noisy channels is desirable for a variety of applications, particularly in situations where an unknown signal source is to be detected and localized from measurements made at several sensors. In the case of two channels, a commonly used method is to compare the magnitude-squared coherence (MSC) estimate computed using sample sequences from the two channels to a threshold. Because the distribution of the MSC estimate is known under specific H 0 assumptions, detection thresholds correspon..