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Speech signals recorded in real environments may be corrupted by ambient noise and reverberation. Therefore, noise reduction and dereverberation algorithms for speech enhancement are typically employed in speech communication systems. Although microphone arrays are useful in reducing the effect of noise and reverberation, existing methods have limited success in significantly removing both reverberation and noise in real environments. This paper presents a method for noise reduction and dereverberation that overcomes some of the limitations of previous methods. The method uses a spherical microphone array to achieve plane-wave decomposition (PWD) of the sound field, based on direction-of-arrival (DOA) estimation of the desired signal and its reflections. A multi-channel linearly-constrained minimum-variance (LCMV) filter is introduced to achieve further noise reduction. The PWD beamformer achieves dereverberation while the LCMV filter reduces the uncorrelated noise with a controllable dereverberation constraint. In contrast to other methods, the proposed method employs DOA estimation, rather than room impulse response identification, to achieve dereverberation, and relative transfer function (RTF) estimation between the source reflections to achieve noise reduction while avoiding signal cancellation. The paper includes a simulation investigation and an experimental study, comparing the proposed method to currently available methods.