Adaptive Diagonal Loading for Norm Constrained Beamforming

Fuente: arXiv

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Bibliographic Details
Main Authors:	Mittal, Manan, Corey, Ryan M., Buck, John R., Singer, Andrew C.
Format:	Preprint
Published:	2026
Subjects:	Systems and Control Information Theory Sound Applications
Online Access:	Acceder al recurso
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_version_	1866918485812051968
author	Mittal, Manan Corey, Ryan M. Buck, John R. Singer, Andrew C.
author_facet	Mittal, Manan Corey, Ryan M. Buck, John R. Singer, Andrew C.
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2605_04342
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Adaptive Diagonal Loading for Norm Constrained Beamforming Mittal, Manan Corey, Ryan M. Buck, John R. Singer, Andrew C. Systems and Control Information Theory Sound Applications 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.
title	Adaptive Diagonal Loading for Norm Constrained Beamforming
topic	Systems and Control Information Theory Sound Applications
url	https://arxiv.org/abs/2605.04342