Multiantenna GLR Detection of Rank-One Signals With Known Power Spectrum in White Noise With Unknown Spatial Correlation

Multiple-antenna detection of a Gaussian signal with spatial rank one in temporally white Gaussian noise with arbitrary and unknown spatial covariance is considered. This is motivated by spectrum sensing problems in the context of dynamic spectrum access in which several secondary networks coexist but do not cooperate, creating a background of spatially correlated broadband interference. When the temporal correlation of the signal of interest is assumed known up to a scale factor, the corresponding Generalized Likelihood Ratio Test is shown to yield a scalar optimization problem. Closed-form expressions of the test are obtained for the general signal spectrum case in the low signal-to-noise ratio (SNR) regime, as well as for signals with binary-valued power spectrum in arbitrary SNR. The two resulting detectors turn out to be equivalent. An asymptotic approximation to the test distribution for the low-SNR regime is derived, closely matching empirical results from spectrum sensing simulation experiments.