The traditional approach to the design of adaptive beamformers assumes that the desired signal components are not present in training data, and the robustness of beamformer is known to depend essentially on the availability of signal-free training data. However, in many important applications such as mobile communications, passive location, microphone array speech processing, medical imaging, and radio astronomy, the signal-free training data cells are unavailable. In such scenarios, the desired signal is always present in the training snapshots, and the adaptive beamforming methods become very sensitive to any violation of underlying assumptions on the environment, sources, or sensor array. In fact, the performances of the existing adaptive array algorithms are known to degrade substantially in the presence of even slight mismatches between the actual and presumed array responses to the desired signal [10]-[12]. Similar types of degradation can take place when the array response is known precisely but the training sample size is small, namely the mismatch between the actual and the estimated covariance matrix [13]-[15]. Therefore, robust approaches to adaptive beamforming appear to be of primary importance in these cases [16][17].