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In this letter, we develop an optimal power allocation algorithm for the orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) systems with different statistical interference constraints imposed by different primary users (PUs). Given the fact that the interference constraints are met in a statistical manner, the CR transmitter does not require the instantaneous channel quality feedback from the PU receivers. A suboptimal algorithm with reduced complexity has been proposed and the performance has been investigated. Presented numerical results show that with our proposed optimal power allocation algorithm CR user can achieve significantly higher transmission capacity for given statistical interference constraints and a given power budget compared to the classical power allocation algorithms namely, uniform and water-filling power allocation algorithms. The suboptimal algorithm outperforms both water-filling algorithm and uniform power loading algorithm. The proposed suboptimal algorithm give an option of using a low complexity power allocation algorithm where complexity is an issue with a certain amount of transmission rate degradation.