Adaptive Diagonal Loading using Krylov Subspaces for Robust Beamforming

2026-05-11

AI Summary

This work addresses the challenge of degraded white noise gain and target signal suppression in adaptive beamforming with large microphone arrays under dynamic acoustic conditions and limited snapshot availability, where inaccurate estimation of the spatial correlation matrix undermines performance. To overcome this, the authors propose an efficient Krylov subspace–based adaptive diagonal loading method that employs Lanczos iteration to construct a low-dimensional tridiagonal matrix. By leveraging Ritz values to rapidly approximate the extreme eigenvalues of the correlation matrix, the approach stabilizes white noise gain and achieves robust beamforming. The method reduces computational complexity from O(M³) to O(kM²), significantly lowering computational cost with negligible performance loss, and demonstrates near-optimal interference suppression and stringent white noise gain control across diverse dynamic interference scenarios—comparable to that achieved by exact eigendecomposition.

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 degrades the White Noise Gain (WNG), leading to severe target signal cancellation. To ensure stable and robust beamforming, we previously proposed an adaptive diagonal loading method that leverages the Kantorovich inequality to guarantee the WNG remains strictly within specified bounds. However, accurately determining the smallest necessary loading level requires calculating the extreme eigenvalues of the spatial correlation matrix, a computationally expensive $\mathcal{O}(M^3)$ operation for large arrays. In this paper, we introduce a highly efficient $\mathcal{O}(kM^2)$ estimation technique using Lanczos iterations to build a small Krylov subspace. By projecting the correlation matrix onto a tridiagonal matrix of dimension $k \ll M$, we extract Ritz values that rapidly converge to the exact extreme eigenvalues. Our evaluations demonstrate that this Lanczos-accelerated approach achieves performance identical to exact Eigenvalue Decomposition (EVD), ensuring optimal interference suppression and strict WNG adherence at a fraction of the computational cost.

Problem

• adaptive beamforming
• snapshot-deficient
• White Noise Gain
• spatial correlation matrix
• eigenvalue estimation

Innovation

• Krylov subspace
• Lanczos iteration
• adaptive diagonal loading
• robust beamforming
• White Noise Gain