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The capacity maximisation problem of the secondary user subject to an interference constraint in orthogonal frequency division multiplexing-based cognitive radio systems is studied in this paper. A novel constant interference strategy to allocate power to subcarriers is derived, where all selected subcarriers are subject to the same interference constraint. It means all subcarriers have the same interference power. This strategy ensures the original interference constraint satisfied. The capacity loss of the proposed methods compared with the optimal solution is also analysed. An upper bound of the capacity loss is derived. Its value can determine the potential benefit of the proposed methods even if the optimal solution is not obtained. Therefore an advanced strategy to select subcarriers to allocate power becomes important, which affects the performance of the proposed methods and the upper bound. By using a proposed indicator, two novel power allocation methods were presented with a lower complexity to select subcarriers for allocating power, which outperforms the existing methods. Performances of the proposed methods are very near that of the optimal solution.