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In this paper, we consider the uplink transmission in multicarrier code-division multiple-access (MC-CDMA) systems. As other multicarrier signals, MC-CDMA signals have high envelope fluctuations and a high peak-to-mean envelope power ratio (PMEPR), which leads to amplification difficulties. This is particularly important for the uplink transmission, since an efficient low-cost power amplification is desirable at the mobile terminals (MTs). Moreover, the transmission over time-dispersive channels destroys the orthogonality between spreading codes, which might lead to significant multiple-access interference levels. To reduce the envelope fluctuations of the transmitted signals, while maintaining the spectral efficiency, the MC-CDMA signal associated to each MT is submitted to a clipping device, followed by a frequency-domain filtering operation. However, the nonlinear distortion effects can be high when an MC-CDMA transmitter with reduced envelope fluctuations is intended (e.g., a small clipping level and/or when successive clipping and filtering operations are employed). In this paper, we define an iterative receiver that jointly performs a turbo multiuser detection and the estimation and cancellation of the nonlinear distortion effects. Our performance results show that the proposed receiver structure allows good performances, very close to the linear receiver ones, even for high system load and/or when a PMEPR as low as 1.7 dB is intended for each MT.