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This paper considers the problem of radio resource allocation in an orthogonal frequency-division multiple access based cognitive radio (CR) network that opportunistically operates within the licensed primary users (PUs) spectrum. The resource allocation algorithm aims at maximizing the CR network throughput under PUs interference constraints. The CR interference introduced into PUs subbands is modeled as a composite that consists of the following two parts: 1) CR out-of-band emissions and 2) the interference that arises as a result of imperfect spectrum sensing. We consider both downlink and uplink subcarrier and power allocation. In both cases, the resource allocation problem is a mixed-integer nonlinear programming problem, for which obtaining the optimal solution is known to be NP-hard. Computationally efficient suboptimal algorithms are proposed for the downlink resource allocation problem, and then, they are extended to the uplink case. We show through simulation that the proposed algorithms exhibit near-optimal performance and significantly reduce the computational complexity compared to obtaining the optimal solution.