Sensing performance analysis of GLRT detector with multiple antennas: Does correlation help?

Abstract-In cognitive radio networks (CRN), the generalized likelihood ratio test (GLRT) has been widely used in multiantenna based spectrum sensing applications. The potential advantages of GLRT detector in detecting correlated primary signal has also been illustrated in prior work. However, the positive effect of the antenna correlation has not been theoretically studied up to now. In this paper, the false-alarm probability and the detection probability for GLRT detector with multi-antenna are firstly derived. The detection performance improvement due to the antenna correlation is then theoretically investigated. Numerical results are presented to verify the effectiveness of the analysis. Therefore, the results indicate that there is a tradeoff between the sensing performance and the spectral efficiency, because the fading signal correlation does reduce the channel capacity in the multiple antennas CRN.