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This paper presents an uplink radio resource allocation algorithm for multicarrier based cognitive radio systems. The algorithm allocates the subcarriers to the users in the first step. In the second step, the power is allocated to these subcarriers in order to maximize the total data rate of the system without causing excessive interference to the primary user. The performance of the proposed algorithm is investigated using computer simulations to prove that it achieves a very good performance in comparison with optimal and outperforms other existing algorithms. Moreover, the throughput of Orthogonal frequency division multiplexing (OFDM) and filter bank multicarrier system (FBMC) based cognitive radio systems are compared to show the efficiency of using FBMC in future cognitive radio systems.