This paper introduces the generalized coherence (GC) estimate and examines its application as a statistic for detecting the presence of a common but unknown signal on several noisy channels. The GC estimate is developed as a natural generalization of the magnitude-squared coherence (MSC) estimate-a widely used statistic for nonparametric detection of a common signal on two noisy channels. The geometrical nature of the GC estimate is exploited to derive its distribution under the H0 hypothesis that the data channels contain independent white Gaussian noise sequences. Detection thresholds corresponding to a range of false alarm probabilities are calculated from this distribution. The relationship of the H0 distribution of the GC estimate to that of the determinant of a complex Wishart-distributed matrix is noted. The detection performance of the three-channel GC estimate is evaluated by simulation using a white Gaussian signal sequence in white Gaussian noise. Its performance is compared with that of the multiple coherence (MC) estimate, another nonparametric multiple-channel detection statistic. The GC approach is found to provide better detection performance than the MC approach in terms of the minimum signal-to-noise ratio on all data channels necessary to achieve desired combinations of detection and false alarm probabilities.
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering