Reverberation and noise have a significant effect on the intelligibility of speech in rooms. The detection of clear speech in highly reverberant and noisy enclosures is an extremely difficult task. Recently, spherical microphone arrays have been studied for processing of sound fields in three-dimensions, with applications ranging from acoustic analysis to speech enhancement. This paper presents the derivation of a model that facilitates the prediction of spherical array configurations that guarantee an acceptable level of speech intelligibility in reverberant and noisy environments. A spherical microphone array is employed to generate a spatial filter that maximizes speech intelligibility according to an objective measure that combines the effects of both reverberation and noise. The spherical array beamformer is designed to enhance the speech signal while minimizing noise power and maintaining robustness over a wide frequency range. The paper includes simulation and experimental studies with a comparison to speech transmission index based analysis to provide initial validation of the model. Examples are presented in which the minimum number of microphones in a spherical array can be determined from environment conditions such as reverberation time, noise level, and distance of the array to the speech source.
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