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Multicarrier direct sequence code division multiple access (MC DS-CDMA) is an attractive technique for achieving high data rate transmission. This is valid regardless of whether or not the potentially large peak-to-average power ratio (PAPR) is an important factor for its application. On the other hand, code select CDMA (CS-CDMA) is an attractive technique with constant amplitude transmission of multicode signal regardless of subchannels. This is achieved by introducing a code select method. In this paper, we propose a new multiple access scheme based on the combination of MC DS-CDMA and CS-CDMA. The proposed scheme, which we call MC CS-CDMA, includes as special cases the subclasses of MC DS-CDMA and CS-CDMA. This paper investigates the performance of these systems over a multipath frequency selective fading channel using a RAKE receiver with maximal ratio combiner. In addition, the PAPR of the proposed system is compared with that of both MC DS-CDMA and CS-CDMA. Simulation results demonstrate that the proposed system provides better PAPR reduction than MC DS-CDMA, at the expense of the complexity of the receiver and the number of available users. The numerical result demonstrates that the proposed system has better performance than MC DS-CDMA due to the increased processing gain and time diversity gain.