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Maximizing the output signal-to-noise ratio (SNR) of a sensor array in the presence of spatially colored noise leads to a generalized eigenvalue problem. While this approach has extensively been employed in narrowband (antenna) array beamforming, it is typically not used for broadband (microphone) array beamforming due to the uncontrolled amount of speech distortion introduced by a narrowband SNR criterion. In this paper, we show how the distortion of the desired signal can be controlled by a single-channel post-filter, resulting in a performance comparable to the generalized minimum variance distortionless response beamformer, where arbitrary transfer functions relate the source and the microphones. Results are given both for directional and diffuse noise. A novel gradient ascent adaptation algorithm is presented, and its good convergence properties are experimentally revealed by comparison with alternatives from the literature. A key feature of the proposed beamformer is that it operates blindly, i.e., it neither requires knowledge about the array geometry nor an explicit estimation of the transfer functions from source to sensors or the direction-of-arrival.