Bayesian multi-antenna sensing in cognitive radio networks using Fractional Bayes Factor

This paper proposes a Bayesian detector for spectrum sensing in a multi-antenna cognitive radio (CR) network in which no channel state information (CSI) is available. The Bayesian approach for detection necessitates a prior distribution of the CSI in terms of the spatial covariance matrix, and unfortunately it is often improper and cannot be applied directly. We shall introduce the use of the Fractional Bayes Factor (FBF) approach to handle improper prior, which in turn yields a well-defined Bayes factor as the test statistic for detection. A number of priors of the CSI are examined and a closed-form expression for the test statistics is derived. The developed Bayesian detector is compared with those by using the conjugate priors for both hypotheses and the generalized likelihood ratio test (GLRT), and it yields considerable improvement in detection performance.