Geometry descriptors of irregular microphone arrays related to beamforming performance

Performance analysis for microphone arrays with irregular geometries typically requires direct computation of beamforming gains over the spatial and frequency ranges of interest. However, theses computations can be very consuming and limit synthesis methods for applications that require rapid answers, as in the case of surveillance and mobile platforms. A better understanding of microphone arrangements and their impact on performance can result in more efficient objective functions for optimizing array performance. This article, therefore, analyzes the relationship between irregular microphone geometries and spatial filtering performance with Monte Carlo simulations. Novel geometry descriptors are developed to capture the properties of irregular microphone distributions showing their impact on array performance. Performance metrics are computed from three-dimensional beam patterns through a delay and sum beamformer with a fixed number of microphones for irregular arrays and comparable regular arrays. Statistical analysis and Multi-way Analysis of Variance establish relationships between key performance metrics and proposed geometry descriptors. It is demonstrated that in conjunction with array centroid offset and dispersion, statistics of the microphone differential path distance can explain variations of performance metrics when steering at targets for immersive or near-field microphone applications.