This letter focuses on the design of selective receivers for homogeneous scenarios where a very small number of secondary data are available. To this end, at the design stage it is assumed that the cell under test (CUT) contains a fictitious signal orthogonal to the nominal steering vector under the null hypothesis; the clutter covariance matrix is modeled as a random matrix with an inverse complex Wishart distribution. Under the above assumptions, we devise two Bayesian detectors based on the GLRT criterion, both one-step and two-step. It is shown that the proposed detectors have the same detection structure as their non-Bayesian counterparts, substituting the colored diagonal sample covariance matrix (SCM) for the classic one. Finally, a performance assessment, conducted by Monte Carlo simulations, has shown that our detectors ensure better rejection capabilities of mismatched signals than the existing Bayesian detectors, at the price of a certain loss in terms of detection of matched signals.

The sensing scheme based on the generalized likelihood ratio test (GLRT) technique has attracted a lot of research interest in the field of cognitive radios (CR). Although its potential advantages in detecting correlated primary signal have been illustrated in prior work, no theoretical analysis of the positive effects of the correlation has appeared in the literature. In this letter, we derive the theoretical false-alarm and detection probabilities of GLRT detector. The theoretical analysis shows that, in the low signal-to-noise ratio (SNR) region, the detector's performance can be improved by exploiting the high correlations between the primary signal samples. The conclusions of the analysis are verified by numerical simulation results.