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In this study, the authors have investigated a dynamic spectrum access method for cognitive radio (CR) networks by using polychromatic sets (PS) theory. First, a power control model is proposed in which the transmission power at a CR node can be calculated by considering both the primary radio (PR)-to-CR and PR-to-PR interference under a specific outage probability. In order to allocate the available spectrum among the CR nodes in a spectrum overlay scenario, the authors further propose a channel selection algorithm based on PS. This study also gives a framework of the PS-based method and concludes with future work describing the practical implementation of the proposed framework. Effectiveness of proposed method is demonstrated through an example application.