Eigenvalue-based Detection Techniques Using Finite Dimensional Complex Random Matrix Theory: A Review

Detection of primary users without requiring information of signal is of great importance in spectrum sensing (SS) in Cognitive Radio. Therefore, in recent years, eigenvalue based spectrum sensing algorithms are under the spotlight. Many primary user detection techniques have been proposed for use in Cognitive Radio (CR) and their drawbacks and benefits have been examined. However, among the various methods proposed, only some of them can survive in an antagonistic environment. Therefore, another appealing side of eigenvalue based primary user detection algorithms is the fact that they are totally immune to uncertain noise levels so they are called robust detectors. Random matrix theory (RMT) is a useful tool which is applicable across a large number of fields and in the last decade, a considerable applications in signal detection has emerged. In this paper, the detection performances of the eigenvalue based techniques are analyzed based on the exact threshold formulations using RMT. As opposed to the threshold estimations with large number of samples and antennas presented in the literature, the exact thresholds are used for finite number of samples and antennas. The importance of accurate decision threshold selection in spectrum sensing is emphasized. It is shown that the accurate threshold computations enable the achievement of higher detection performances than asymptotic analyses reported in the literature.