A framework for diffuseness evaluation using a tight-frame microphone array configuration

This work presents a unified framework for estimating both sound-field direction and diffuseness using practical microphone arrays with different spatial configurations. Building on covariance-based diffuseness models, we formulate a velocity-only covariance approach that enables consistent diffuseness evaluation across heterogeneous array geometries without requiring mode whitening or spherical-harmonic decomposition. Three array types -- an A-format array, a rigid-sphere array, and a newly proposed tight-frame array -- are modeled and compared through both simulations and measurement-based experiments. The results show that the tight-frame configuration achieves near-isotropic directional sampling and reproduces diffuseness characteristics comparable to those of higher-order spherical arrays, while maintaining a compact physical structure. We further examine the accuracy of direction-of-arrival estimation based on acoustic intensity within the same framework. These findings connect theoretical diffuseness analysis with implementable array designs and support the development of robust, broadband methods for spatial-sound-field characterization.