Generalized Real-Valued Weighted Covariance-Based Detection Methods for Cognitive Radio Networks With Correlated Multiple Antennas

This paper is concerned with the spectrum sensing problem for cognitive radio networks with correlated receiving multiple antennas in the time-varying fading channel. We first consider the scenario that all the antennas have the same noise variance and present a generalized real-valued weighted-covariance-based detection (GRWCD) method. In particular, we derive the distribution of the GRWCD statistic under the null hypothesis, which allows us to develop the theoretical decision threshold for a given false alarm probability. Besides, we derive the distribution of the GRWCD statistic under the alternative hypothesis, which enables us to provide a mathematical expression for the detection probability as well as the theoretical receiver operating characteristic. Meanwhile, we consider a more general scenario of unequal per-antenna noise variances and present a modified GRWCD method as well as the theoretical expressions of the decision threshold. The simulation results are provided to verify the accuracy of the derived results and show that the proposed two methods are capable of providing performance improvement over several advanced methods in the literature.