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Cognitive radio technology is an effective method to alleviate the spectrum scarcity. The fundamental challenge is how to allocate the primary channels to secondary users (SUs) to maximize the network utility without making interference to primary users (PUs). We propose a joint random access and power control algorithm to address this problem in the context of cognitive radio ad hoc networks. A non-convex optimization problem is formulated based on realistic SINR model. Furthermore, sensing error is considered in the formulation since the accuracy of spectrum sensing is important. Geometric programming and subgradient projection method are used to obtain the optimal solution to the problem. Analytical and simulation results show the effectiveness of the proposed algorithm.