Adaptive Diagonal Loading for Norm Constrained Beamforming

TL;DR

This paper introduces an adaptive diagonal loading method for robust beamforming in dynamic acoustic environments, ensuring stability and performance despite snapshot deficiencies and array imperfections.

Contribution

It proposes a novel approach using the Kantorovich inequality to adaptively control the correlation matrix condition number, with scalable estimation techniques for the loading level.

Findings

Ensures WNG remains within specified bounds for stability.

Demonstrates stable beamforming with fast-changing interference.

Provides computationally scalable estimation methods.

Abstract

Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the spatial correlation matrix is often snapshot-deficient. This deficiency, coupled with array imperfections, degrades the White Noise Gain (WNG), leading to severe target signal cancellation. To ensure stable and robust beamforming, we propose a novel adaptive diagonal loading method that guarantees the WNG remains strictly within specified bounds. By leveraging the Kantorovich inequality, we map the desired WNG to a strict upper bound on the condition number of the correlation matrix. Furthermore, we present three estimation techniques for the adaptive loading level, ranging from trace-based bounding to exact eigenvalue decomposition, offering scalable computational complexities of $\mathcal{O}(M)$, $\mathcal{O}(M^2)$, and $\mathcal{O}(M^3)$. Our approach demonstrates highly stable beamforming under fast-changing interference.