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An adaptive parallel interference cancellation (PIC) scheme is proposed for the multicarrier direct sequence code division multiple access (MC-DS-CDMA) system. By taking advantage of the combining techniques before and after the PIC stage, the diversity provided by the MC-DS-CDMA system can be exploited to improve further the bit error probability performance and increase the user/data capacity. An adaptive MAI estimation algorithm is applied before the PIC stage to improve the accuracy of the MAI cancellation. The performance behaviour of our proposed detector is investigated and the analytic bit error probabilities for the matched filter (MF), the conventional PIC and our proposed adaptive PIC are derived. The theoretical results agree well with simulations. It is shown that the adaptive PIC receiver outperforms the MF and the conventional PIC receiver for MC-DS-CDMA systems in a frequency selective fading channel.