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Multicarrier code-division multiple access (MCCDMA) system with adaptive frequency hopping (AFH) has attracted attention of researchers due to its excellent spectral efficiency. A suboptimal water-filling (WF) channel allocation algorithm was previously proposed for the reverse link of this system. To overcome the limitations of the WF algorithm in the presence of fading-induced near-far problem, a new allocation algorithm is proposed and demonstrated to improve performance when the conventional matched filter (MF) receiver is employed. Moreover, the allocation methods are extended to accommodate multiuser detectors (MUDs) at the receiver for MC-CDMA system with AFH. It is demonstrated that the combination of the improved allocation algorithm and the linear MUDs is very efficient in mitigating the fading and multi-access interference (MAI) for realistic mobile radio channels with correlated subcarriers, channel state information (CSI) mismatch, and imperfect power control. Numerical results show that the proposed adaptive transmission method has much greater system capacity than conventional non-adaptive MC direct-sequence (DS)-CDMA system.