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In this paper, we consider a joint design of energy-efficient sensing and transmission durations for a cognitive radio (CR) system in which the primary user (PU) is protected. The design problem is formulated as a function of two variables, which are sensing and transmission durations, subject to the interference to the PU. The optimal solutions are analyzed and a sub-optimal algorithm that maximizes the energy efficiency for the CR system is presented. The performance of the proposed energy-efficient design for the CR system is also evaluated.