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Speech recognition performance degrades significantly in distant-talking environments, where the speech signals can be severely distorted by additive noise and reverberation. In such environments, the use of microphone arrays has been proposed as a means of improving the quality of captured speech signals. Currently, microphone-array-based speech recognition is performed in two independent stages: array processing and then recognition. Array processing algorithms, designed for signal enhancement, are applied in order to reduce the distortion in the speech waveform prior to feature extraction and recognition. This approach assumes that improving the quality of the speech waveform will necessarily result in improved recognition performance and ignores the manner in which speech recognition systems operate. In this paper a new approach to microphone-array processing is proposed in which the goal of the array processing is not to generate an enhanced output waveform but rather to generate a sequence of features which maximizes the likelihood of generating the correct hypothesis. In this approach, called likelihood-maximizing beamforming, information from the speech recognition system itself is used to optimize a filter-and-sum beamformer. Speech recognition experiments performed in a real distant-talking environment confirm the efficacy of the proposed approach.