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The performance of blind multiuser detection methods is known to degrade severely in the presence of even small mismatches between the actual and the presumed desired user signatures. Such mismatches may occur in practical situations due to an imperfect knowledge of the channel impulse response. We propose a new robust approach to blind multiuser detection in the presence of unknown arbitrary-type mismatches of the desired user signature. Two different formulations of a robust multiuser receiver are considered. The proposed formulations are based on the explicit modeling of uncertainties in the covariance matrix of the desired user signature and/or data covariance matrix and optimization of the worst-case performance. Simple closed-form solutions to the considered robust multiuser detection problems are derived. The proposed methods have a computational complexity comparable to that of the traditional blind multiuser detection algorithms, and, at the same time, offer an improved robustness and faster convergence rates.