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This paper investigates the problem of uplink subcarrier and power allocation in a Cognitive Radio (CR) network that operates opportunistically within vacant licensed Primary Users (PUs)spectrum. The resource allocation algorithm aims to maximize the CR network throughput under PUs interference constraints. In this paper, CR interference introduced into PUs sub-bands is modeled as a composite of two parts; CR Out-of-Band (OOB) emissions and the interference arising as a result of imperfect spectrum sensing. The uplink subcarrier and power allocation is a Mixed Integer Nonlinear Programming (MINLP) problem, for which obtaining the optimal solution is known to be NP-Hard. In this paper, we propose a three steps heuristic solution to the uplink resource allocation problem. We show through simulation that the proposed algorithm exhibits near-optimal performance and comes with a significant reduction in computational complexity when compared to that of obtaining the optimal solution.