Multiple-channel detection of a Gaussian time series over frequency-flat channels

This work addresses the problem of deciding whether a set of realizations of a vector-valued time series with unknown temporal correlation are spatially correlated or not. Specifically, the spatial correlation is induced by a colored source over a frequency-flat single-input multiple-output (SIMO) channel distorted by independent and identically distributed noises with temporal correlation. The generalized likelihood ratio test (GLRT) for this detection problem does not have a closed-form expression and we have to resort to numerical optimization techniques. In particular, we apply the successive convex approximations approach which relies on solving a series of convex problems that approximate the original (non-convex) one. The proposed solution resembles a power method for obtaining the dominant eigenvector of a matrix, which changes over iterations. Finally, the performance of the proposed detector is illustrated by means of computer simulations showing a great improvement over previously proposed detectors that do not fully exploit the temporal structure of the source.