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Multiuser detection (MUD) for code-division multiple-access (CDMA) systems usually relies on some a priori channel estimates, which are obtained either blindly or by using training sequences, and the covariance matrix of the received signal, usually replaced by the sample covariance matrix. However, such prior estimates are often affected by errors that are typically ignored in subsequent detection. In this paper, we present robust channel estimation and MUD techniques for multicarrier (MC) CDMA by explicitly taking into account such estimation errors. The proposed techniques are obtained by optimizing the worst case performance over two bounded uncertainty sets pertaining to the two types of estimation errors. We show that although the estimation errors associated with the prior channel estimate and the sample covariance matrix are generally not bounded, it is beneficial to optimize the worst case performance over properly chosen bounded uncertainty sets determined by a parameter called bounding probability. At a slightly higher computational complexity, our proposed robust detectors are shown to yield improved performance over the standard detectors that ignore the prior estimation errors.