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In this paper, a new approach to study the effect of carrier frequency offset (CFO) due to the mismatch between the transmitter and receiver oscillators on the bit error rate (BER) performance of asynchronous multicarrier code division multiple access (MC-CDMA) systems is proposed. The closed form BER expression when the maximum ratio combining (MRC) is used is derived. The correctness and effectiveness of the proposed approach is verified through computer simulations. Numerical results show that small CFO has insignificant effect on the BER performance of MC-CDMA systems.