Objective Bayesian Detection Under Spatially Correlated Gaussian Observations for Multi-Antenna Cognitive Radio Network

This paper develops an objective Bayesian detector for asserting the presence of primary user (PU) signal buried in additive noise/interference using a sequence of complex vector samples from a multi-antenna spectrum sensing system. The PU signal is zero mean Gaussian and the noise/interference is Gaussian with possibly non-zero mean and spatial correlation. No prior knowledge is available except the signal has non-zero power when present. For the noise only hypothesis, we propose a uniform prior for the mean, and a mix of the conjugate and uniform priors for the covariance matrix inverse in terms of the Cholesky factorization. For the signal presence hypothesis, we propose a class of objective priors that includes Jeffreys, independent Jeffreys, left-Haar measure and right-Haar measure priors. The test statistic is derived in closed-form and the setting of hyperparameter is devised to ensure the test is meaningful for the detection problem. Numerical results support the promising performance of the proposed detector over other state-of-the-art methods.