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To satisfy the requirement for high data rate and high frequency efficiency in future mobile radio communication systems, an MC-CDMA system using adaptive modulation is proposed in order both to achieve frequency diversity and to maximize the spectral efficiency. We also give a practical adaptive modulation algorithm with low computational complexity and small signaling overhead, which is suitable for MC-CDMA downlink transmission. Simulation results show that adaptive MC-CDMA systems outperform conventional MC-CDMA systems. The combining schemes at the receiver in MC-CDMA systems, which affect the efficiency of the adaptive modulation algorithm, are also analyzed, including multi-user interference.