Orthogonal frequency division multiplexing (OFDM) is a popular multicarrier modulation method for wireless systems. However, the OFDM communication system is sensitive to inter-carrier interference (ICI), which arises because of Doppler spread and carrier frequency offset. This study addresses the problem of resource management in the presence of ICI and multipath fading channels. This study developed a minimized average bit error rate-based method that adaptively allocates the subcarrier, bit, and power in OFDM systems to obtain minimum total transmission power under certain quality of service requirements (i.e., the minimum data rate and the bit error rate). The simulation results demonstrated that the proposed suboptimal algorithms can substantially improve the performance of the OFDM systems compared with the uniform power allocation algorithm or conventional water-filling algorithm. Furthermore, applying the proposed resource allocation algorithm was demonstrated to distribute the sum capacity more fairly and flexibly among users than the sum capacity maximization method did.