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Medium Access Control (MAC) protocols with transmission power control, rate control and modulation control have been proposed to improve the performance of ad hoc networks and provisioning of differentiated service in wireless networks. However, its effectiveness is reduced in the presence of strong noise over the wireless channels. It is further aggravated in wireless mesh networks (WMN) due to the need to traverse multiple-hops from source to destination. To further improve the performance of the WMNs, network traffic can be spread across multiple vacant channels to reduce the node density per transmission channel. Cognitive radio technique can be used to identify the vacant channel. In this paper, we proposed the cognitive power-controlled rate-adaptive MAC protocol (CPCRA) based on cognitive radio technology, which combines power control, rate control, and modulation control with dynamic spectrum access. Simulation results demonstrate that CPCRA can achieve better performance in terms of lower delay and higher throughput.