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Cognitive Radio (CR) is a promising concept for improving the utilization of scarce radio spectrum resource. OFDM is regarded as a potential technology for CR systems and resource allocation is a vital task in such systems. In this paper, a subcarrier and power allocation algorithm based on the linear waterfilling(LWF) scheme is proposed to maximize the downlink capacity of the CR systems while keeping both the total power budget and interference introduced to the primary user blow the pre-constraints. In the proposed algorithm, subcarrier allocation is first performed by assuming an equal power distribution. Secondly, the linear water-filling scheme under the interference constraint is proposed through searching for a rapid means for confirming the subcarriers which need not allocate power, then an iterative suboptimal power allocation algorithm based on LWF which have less complexity than the optimal algorithm is proposed. The proposed algorithm is shown to achieve a good performance which is close to the optimal algorithm.