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Cognitive radio (CR) and energy-efficient design have emerged as two promising techniques to achieve high spectrum efficiency (SE) and energy efficiency (EE), respectively. In this paper, we study energy-efficient opportunistic spectrum access strategies for an orthogonal frequency division multiplexing (OFDM)-based CR network with multiple secondary users (SUs). Both worst EE and average EE are considered and optimized for different emphases and application scenarios. Since the original optimization issues belong to nonconvex integer combinatorial fractional program and are essentially NP-hard for an optimal solution, we use continuous and convex relaxation to modify the problems for somewhat better mathematical tractability. For the relaxed worst-EE-based spectrum access problem, we first demonstrate the joint quasiconcavity of EE on subchannel and power allocation matrices and then develop a …