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Kernel-based learning (KBL) methods have recently become prevalent in many engineering applications, notably in signal processing and communications. The increased interest is mainly driven by the practical need of being able to develop efficient nonlinear algorithms, which can obtain significant performance improvements over their linear counterparts at the price of generally higher computational complexity. In this article, an overview of applying various KBL methods to statistical signal processing-related open issues in cognitive radio networks (CRNs) is presented. It is demonstrated that KBL methods provide a powerful set of tools for CRNs and enable rigorous formulation and effective solutions to both long-standing and emerging design problems.