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This paper addresses the subcarrier and power allocation problem in the uplink of an OFDMA system under the cognitive radio environment. The objective is to maximize the sum-rate of secondary users, without causing adverse interference to the primary users. We formulate the optimization problem subject to the individual power constraints and the interference constraints. Since the problem cannot be solved easily, we make continuous relaxation and give the optimality conditions for the relaxed problem. Based on the conditions, an integer-valued solution for the original problem is obtained and an efficient iterative subcarrier and power allocation algorithm is developed. Simulation results show that our proposed algorithm significantly improves the sum-rate performance, and provides good convergence.