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This paper presents a multicarrier asynchronous direct-sequence code-division multiple-access (DS-CDMA) system wherein the output of a turbo product encoder modulates multiple band-limited DS-CDMA waveforms, which are transmitted in parallel at different carrier frequencies. The receiver detects and combines signals for the desired user and feeds an iterative decoder. The performance of this system is compared to that of a conventional single-carrier DS-CDMA system with a RAKE receiver, assuming a slowly varying frequency-selective Rayleigh fading channel. At roughly equivalent receiver complexity, results demonstrate similar performance in presence of additive white Gaussian noise and multiple-access interference and superior performance of the multicarrier system in the presence of partial-band interference.