Multiple-Channel Signal Detection using the Generalized Coherence spectrum

Recently, a generalization of the magnitude squared coherence (MSC) spectrum for more than two random processes has been proposed. The generalized MSC (GMSC) spectrum definition, which is based on the largest eigenvalue of a matrix containing all the pairwise complex coherence spectra, provides a frequency-dependent measure of the linear relationship among several stationary random processes. Moreover, it can be easily estimated by solving a generalized eigenvalue problem. In this paper we apply the GMSC spectrum for detecting the presence of a common signal from a set of linearly distorted and noisy observations. Specifically, the new statistic for the multiple-channel detection problem is the integral of the square root of the GMSC, which can be estimated as the sum of the $P$ largest generalized canonical correlations (typically $P=1$ is enough in practice). Unlike previous approaches, the new statistic implicitly takes into account the spectral characteristics of the signal to be detected (e.g., its bandwidth). Finally, the performance of the proposed detector is compared in terms of its receiver operating characteristic (ROC) curve with the generalized coherence (GC) showing a clear improvement in most scenarios.