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Although the medium access control (MAC) protocol and the physical layer have been well-defined in the IEEE 802.16 specifications, resource allocation and management schemes, which are crucial components to guarantee quality of service (QoS) performances, still remain as open issues. In this paper, we focus on the problem of the utility-based resource allocation in the IEEE 802.16 OFDMA systems. The utility is used in our study to balance the efficiency and fairness of resource allocation. We formulate the optimization problem as one that maximizes the system utility of all active users subject to certain conditions, which are determined by adaptive resource allocation schemes. To maximize the system utility, a near optimal multiuser resource allocation algorithm with low complexity is proposed. Numerical results show that the proposed algorithm can achieve a system performance very close to the optimal solution obtained by the exhaustive method with a low computational complexity and offer a more preferable tradeoff via the predesigned fairness factor between the spectral efficiency and the fairness than existing approaches.