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The cognitive radio (CR) technology will allow a group of potential users to identify and access available spectrum resources provided that the interference to the users for whom the band has been licensed is kept below a prescribed level. However, this research area is at a very immature stage because various research challenges have to be addressed and solved. In this paper our objective is to present an overview of some research issues for CR networks. Specifically, we present some research and development in CR networks with focus on i) information- theoretic aspects, ii) spectrum sensing, iii) link adaptation, iv) advanced transceiver design, and v) admission control. We also discuss some important research problems related to these specific topics that needs to be addressed before deployment of CR systems in practice.