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We propose a new multi-user detection of slow frequency hopping multicarrier direct-sequence code division multiple access technique (multi-user detection of SFH/MC DS-CDMA). The frequency hopping pattern are controlled by asset of constant-weight code. Consequently, multirate communication can be implemented by selecting the correspondence set of constant-weight code. We assume the system operates in multipaths fading environment and a decorrelating receiver structure, The receiver has an explicit knowledge of the associated frequency-hopping (FH) patterns invoked. The system's performance is evaluated using Nakagami fading channels with numerical method. Furthermore the performance of the multi-user detection of SFH/MC DS-CDMA system is compared to the conventional Multi-user detection of direct-sequence code division multiple access system (multi-user detection of DS-CDMA).