A GEOMETRIC APPROACH TO MULTIPLE-CHANNEL SIGNAL-DETECTION

This paper introduces the generalized coherence (GC) estimate and exam ines its application as a statistic for detecting the presence of a co mmon but unknown signal on several noisy channels, The GC estimate is developed as a natural generalization of the magnitude-squared coheren ce (MSG) estimate-a widely used statistic for nonparametric detection of a common signal on two noisy channels. The geometrical nature of th e GC estimate is exploited to derive its distribution under the No hyp othesis that the data channels contain independent white Gaussian nois e sequences. Detection thresholds corresponding to a range of false al arm probabilities are calculated from this distribution, The relations hip of the Ho distribution of the GC estimate to that of the determina nt of a complex Wishart-distributed matrix is note. The detection perf ormance of the three channel GC estimate is evaluated by simulation us ing a white Gaussian signal sequence in white Gaussian noise, Its perf ormance is compared with that of the multiple coherence (MC) estimate, another nonparametric multiple-channel detection statistic, The GC ap proach is found to provide better detection performance than the MC ap proach in terms of the minimum signal-to-noise ratio on all data chann els necessary to achieve desired combinations of detection and false a larm probabilities.