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We propose a new transmission and resource allocation technique based on multicarrier direct-sequence CDMA (MC-DS-CDMA). The proposed system allocates subcarriers and spreading codes to users by considering their current bandwidth requirements and frequency shifts caused by their movement. Through the use of low-correlation spreading codes in close subcarriers the scheme reduces the inter-carrier interference generated by high-speed users while keeping the inter-symbol interference at a low level due to the multicarrier transmission. The analysis and results show that a substantial mitigation of both the intercarrier interference and bit error ratio, without reducing the system bandwidth efficiency, can be achieved. That makes our proposed method a good candidate for future broadband highly-mobile networks.