Extreme Eigenvalues-Based Detectors for Spectrum Sensing in Cognitive Radio Networks

Abstract

This paper focuses on the design of the optimal or near-optimal detector resorting to extreme eigenvalues. A general framework for detector design involving model-driven and data-driven approaches is introduced. Specifically, the extreme eigenvalues based likelihood ratio test (LRT) is derived via the model-driven approach. Merging the model-driven and data-driven approaches, the Naive Bayesian detector is proposed based on the extreme eigenvalues, which converts the design of test statistic into a two-class decision boundary construction problem, and a solution is provided by the Naive Bayesian classifier. To render the detectors more practical, two near-optimal detectors called <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-sum and <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-product of maximum and minimum eigenvalues (<inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-SMME, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-PMME) are further designed, in which <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> is a weight coefficient. Furthermore, the theoretical performance analysis of the <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-SMME and <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-PMME algorithms is provided, and the optimal weight selection is further obtained by solving an optimization problem under the Neyman-Pearson criterion. Finally, simulation experiments demonstrate that the proposed detectors achieve performance improvements over the state-of-the-art detectors using extreme eigenvalues, and almost coincide with the detection performance of the LRT detector.