Bayesian generalised likelihood ratio test-based multiple antenna spectrum sensing for cognitive radios

In this study, the authors address the problem of multiple antenna spectrum sensing in cognitive radios by exploiting the prior information about unknown parameters. Specifically, under assumption that unknown parameters are random with the given proper distributions, the authors use a Bayesian generalised likelihood ratio test (B-GLRT) in order to derive the corresponding detectors for three different scenarios: (i) only the channel gains are unknown to the secondary user (SU), (ii) only the noise variance is unknown to the SU, (iii) both the channel gains and noise variance are unknown to the SU. For the first and third scenarios, the authors use the iterative expectation maximisation algorithm for estimation of unknown parameters and the authors derive their convergence rate. It is shown that the proposed B-GLRT detectors have low complexity and besides are optimal even under the finite number of samples. The simulation results demonstrate that the proposed B-GLRT detectors have an acceptable performance even under the finite number of samples and also outperform the related recently proposed detectors for multiple antenna spectrum sensing.