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Beamformer design using measured microphone directivity patterns: Robustness to modelling error

The design process for time-invariant acoustic beamformers often assumes that the microphones have an omni-directional directivity pattern, a flat frequency response in the range of interest, and a 2D environment in which wavefronts propagate as a function of azimuth angle only. In this paper we investigate those cases in which one or more of these assumptions do not hold, considering a Minimum Variance Distortionless Response (MVDR)-based solution that is optimized using measured directivity patterns as a function of azimuth, elevation and frequency. Robustness to modelling error is controlled by a regularization parameter that produces a suboptimal but more robust solution. A comparative study is made with the 4-element cardioid microphone array employed in Microsoft Kinect for Windows, whose beamformer weights are calculated with directivity patterns using (a) 2D cardioid models, (b) 3D cardioid models and (c) 3D measurements. Speech recognition and PESQ results are used as evaluation criteria with a noisy speech corpus, revealing empirically optimal regularization parameters for each case and up to a 70% relative improvement in word error rate comparing (a) and (c).