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The performance of adaptive beamforming methods is known to degrade in the presence of even small mismatches between the actual and presumed array responses to the desired signal. We propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary-type mismatches of the desired signal array response. Our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both rank-one and higher-rank desired signal models. The proposed beamformer is based on an explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst-case performance optimization. A simple closed-form solution to this robust adaptive beamforming problem is obtained. This solution naturally combines two different types of diagonal loading which are applied to the sample and presumed signal covariance matrices. Our new robust beamformer has a computational complexity comparable to that of the traditional adaptive beamforming algorithms while it offers a greatly improved robustness and faster convergence rate as compared to existing robust beamformers.