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In this paper, we study the resource allocation problem in the downlink of an OFDMA system. Taking into account the constraint that each user can be assigned only one modulation and coding scheme (MCS), our goal is to maximize the system utility, which can be either the sum rate of users or certain fairness metric. The joint subcarrier, rate, and power allocation problem is formulated, and a straightforward suboptimal algorithm is proposed to solve this problem efficiently. Through computer simulation, our proposed algorithm is verified to be better in performance compared to the existing ones.