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Cognitive radio (CR) is considered as one of the most promising solutions to the problem of overcrowded spectrum by allowing secondary users (SUs) to access the spectrum dynamically. Most related previous work on CR networks with primary users' (PUs') participation ignores the SU selection scheme when the spectrum holes cannot satisfy the requirements of all SUs. In this paper, we propose an optimal SU selection scheme with the optimization goals of maximizing the PU's reward, which is defined as the summation of rent collected from the SUs. To solve this problem, a restless bandit approach is used, which dramatically simplifies the computational complexity. Furthermore, extensive simulation results are presented to show the significant performance improvement of the proposed scheme compared to the existing ones.