Adaptive Diagonal Loading for Norm Constrained Beamforming

Reliable adaptive beamforming remains a challenge for large microphone arrays in highly dynamic acoustic environments. When talkers and interferers move quickly, the available sample support for estimating the spatial correlation matrix is often snapshot-deficient—sometimes just one snapshot. This deficiency, combined with array imperfections, degrades the White Noise Gain (WNG), leading to severe target signal cancellation. To address this, Manan Mittal, Ryan M. Corey, John R. Buck, and Andrew C. Singer introduce a novel adaptive diagonal loading method that guarantees the WNG stays strictly within specified bounds. Their key insight is leveraging the Kantorovich inequality to map the desired WNG to a strict upper bound on the condition number of the correlation matrix, ensuring numerical stability.

The paper presents three estimation techniques for the adaptive loading level: a trace-based method (O(M) complexity), a partial eigenvalue approach (O(M²)), and a full eigenvalue decomposition (O(M³)). This range allows practitioners to trade off accuracy for computational cost depending on their array size and real-time requirements. Experiments demonstrate highly stable beamforming even under fast-changing interference scenarios. The method is particularly relevant for applications like smart conference rooms, voice-controlled devices, and acoustic surveillance systems where large microphone arrays must operate reliably despite rapidly shifting acoustic scenes.