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In this paper, we propose a joint subcarrier power allocation (SPA) and code assignment scheme for the synchronous multirate multicarrier direct-sequence code-division multiple-access (MC-DS-CDMA) system with time- and frequency-domain spreadings. Based on the newly defined metric multiple-access interference (MAI) coefficient, the proposed code assignment strategy can quantitatively predict the incurred MAI before assigning a spreading code. The SPA mechanism aims to maximize the received signal power. In addition to lowering the MAI, the proposed code assignment strategy further considers the compactness of the assigned codes in the entire 2-D tree structure. The simulation results show that the proposed joint SPA and code assignment strategy not only can reach a better received signal quality but can also achieve a high call admission rate.