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Adaptive subcarrier, bit, and power allocation schemes for orthogonal frequency division multiple access (OFDMA) systems are considered. A low-complexity algorithm is proposed to minimize the overall transmit power under certain fairness constraints: Data rate and bit-error-rate (BER) requirements for each user. In the proposed algorithm, subcarrier allocation is first executed, which follows two steps: An initial subcarrier allocation to satisfy the individual data rate requirement; then a residual subcarrier allocation to further reduce the overall transmit power. After that, a single-user optimal bit and power allocation is performed for each user based on the water-filling strategy. The proposed heuristic subcarrier allocation algorithm has linear complexity in the number of users and subcarriers, as opposed to the combinatorial nature of the optimal solutions. More importantly, the proposed resource allocation scheme explores frequency diversity in a more efficient way compared with reference schemes of similar complexity, which makes it more preferable in highly frequency-selective fading channels.