Adaptive Diagonal Loading for Norm Constrained Beamforming

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.

The minimum variance distortionless response (MVDR) beamformer is widely used for multichannel speech enhancement due to strong noise suppression while preserving target signals. In practice, its performance is sensitive to microphone self-noise and array mismatches. Existing approaches typically rely on fixed, manually tuned WNG thresholds or diagonal loading, leading to suboptimal performance under unknown or time-varying acoustic conditions. This paper proposes a data-driven MVDR framework that adaptively estimates the WNG constraint using a deep neural network. The network jointly predicts a time-frequency noise mask for covariance estimation and a frequency-dependent WNG threshold, enabling dynamic robustness-directivity control. A differentiable robust MVDR layer is integrated into the framework, allowing end-to-end optimization. Experiments demonstrate consistent improvements in speech quality and intelligibility over conventional fixed-WNG MVDR methods.

Adaptive beamforming is a cornerstone of array signal processing, yet its performance often collapses in the face of complex, rapidly changing interference. When interferers appear or move unpredictably, conventional estimators encounter a fundamental memory trade-off: short windows enable rapid tracking but suffer from high estimation variance, while long windows provide stable rejection but fail to adapt to shifts. This challenge is resolved by introducing the Universal Switching Beamformer (USB), which integrates competitive sequential prediction into the beamforming architecture. By employing a linear transition diagram, the USB implicitly maintains an exponentially large family of candidate covariance histories and dynamically re-weights them based on their cumulative output power. This mechanism allows the beamformer to automatically vary its effective memory length without explicit change detection or heuristic parameter tuning. A theoretical upper bound is proven on the regret relative to an omniscient oracle that selects the best piecewise-stationary covariance model in hindsight. Extensive simulations and experiments on the SwellEx-96 dataset demonstrate that the USB achieves the agility of short-window estimators and the precision of long-term integration, providing a principled solution for tracking highly non-stationary scenes.