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An efficient and flexible air interface is the necessary condition to achieve the ambitious goals of next generation broadband wireless networks. Multicarrier code division multiple access (MC-CDMA) is a practical answer to this need, but the considerable vulnerability to nonlinear distortions induced by high power amplifiers at the transmitter side hinders its appealing features, thereby demanding for adequate countermeasures. The current paper contributes to this issue with a novel multiuser data predistortion (MUDP) procedure aimed at mitigating the performance degradation of a MC-CDMA forward-link in the presence of a nonlinear channel. The proposed MUDP resides entirely at the transmitter of the base station, and simply requires a set of modified constellations, which are jointly and iteratively optimized so that the distortions experienced by each active user are significantly reduced. The required computational complexity is then kept at affordable levels by resorting to a suboptimal yet effective scheme based on the identification of the strongest interfering users combined with the set-partitioning and the symmetry properties of their constellations. Numerical simulation results corroborate the effectiveness of the MUDP in improving the link performance under typical demanding multiple-access operating conditions.