Asymptotic non-null distribution of the generalized coherence estimate

The use of the generalized coherence estimate as a statistic for detection of a common signal in multiple independent channels of additive gaussian noise has been studied in several papers. This work has relied on simulations to evaluate detector performance because the distribution of the generalized coherence estimate with signal present is unknown. This paper derives an asymptotic expression for the non-null distribution of the estimate as the length of the sample sequences approaches infinity, develops an asymptotic performance analysis based on this distribution, and compares the receiver operating characteristics derived from this theoretical approach to those obtained using simulations with large sample sequence lengths