A geometrical approach to multiple-channel detection

Summary form only given, as follows. The generalized coherence (GC) estimate, a recently introduced detection statistic that forms the basis of a nonparametric test for a common but unknown signal on several noisy channels, is shown to be geometric in nature. This perspective is used to show that the GC estimate is the unique function of M ≥ 2 complex sample sequences having a desirable set of properties. Its distribution function is derived under the H₀ assumption that the sample sequences representing filtered data from M noisy channels are drawn from independent Gaussian processes. This is accomplished by exploiting the interpretation of the MSC estimate as the volume of a polytope in (real) 2M-dimensional space. The properties and performance of the GC estimate as a detection statistic are also discussed. Detection thresholds corresponding to different false alarm probabilities are derived for various numbers of channels and sequence lengths. The performance of the GC detector as a function of the signal-to-noise ratios on the noisy channels is evaluated by simulation, and the results are compared with performance data for other multiple-channel detection schemes.