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One of the major challenges in the medium access control (MAC) protocol design over cognitive Ad Hoc networks (CAHNs) is how to efficiently utilize multiple opportunistic channels, which vary dynamically and are subject to limited power resources. To overcome this challenge, in this paper we first propose a novel diversity technology called Channel-Aggregation Diversity (CAD), allowing each secondary node to use multiple channels simultaneously with only one data radio per node under the upperbounded power. Using the proposed CAD, we develop a CAD based MAC (CAD-MAC) protocol, which can efficiently utilize available channel resources through joint power-channel allocation while guaranteeing the transmission-time fairness. Particularly, we convert the joint power-channel allocation to the Multiple-Choice Knapsack Problem, such that we can obtain the optimal transmission strategy to maximize the network throughput through dynamic programming. Simulation results show that our proposed CAD-MAC protocol can significantly increase the network throughput as compared to the existing protocols.