This paper addresses the problem of adaptive detection of a signal of interest in presence of Gaussian disturbance with unknown covariance matrix. The covariance matrices of the primary and the secondary data share a common structure while having different power levels. A Bayesian approach is proposed here, where the structure are assumed to be random, with an appropriate distribution. Moreover, we assume that the cell under test (CUT) contains a fictitious signal orthogonal to the nominal steering vector under the null hypothesis. Under above assumptions, we devise a Bayesian detector based on the generalized likelihood ratio test (GLRT). Interestingly, it is shown that the proposed detector coincides with the knowledge-aided adaptive coherence estimator (KA-ACE) previously designed in a previous paper by Wang et al. The result provides an alternative explanation of the good selectivity properties exhibited by the KA-ACE.
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