John R. Buck

Manan Mittal, Ryan M. Corey, John R. Buck et al.

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.

Saurav R. Tuladhar, John R. Buck

The statistical behavior of the eigenvalues of the sample covariance matrix (SCM) plays a key role in determining the performance of adaptive beamformers (ABF) in presence of noise. This paper presents a method to compute the approximate eigenvalue density function (EDF) for the SCM of a \cin{} field when only a finite number of shapshots are available. The EDF of the ensemble covariance matrix (ECM) is modeled as an atomic density with many fewer atoms than the SCM size. The model results in substantial computational savings over more direct methods of computing the EDF. The approximate EDF obtained from this method agrees closely with histograms of eigenvalues obtained from simulation.

Manan Mittal, Ryan M. Corey, Diego Cuji et al.

In dynamic acoustic environments with time-varying interferers, effective beamforming requires identifying stationary regions over time. The Capon beamformer, a whitened matched filter constrained to maintain unity gain in the desired direction, theoretically relies on the instantaneous ensemble covariance matrix. Practical implementations rely on the batch Capon (or Sample Matrix Inversion), which estimates the sample covariance matrix (SCM) by averaging over a block of snapshots. This practical approach implicitly assumes that the data within the batch window is stationary and can be coherently combined. In non-stationary settings, a batch approach that averages over fixed or excessively long windows fails, as moving interferers smear the SCM and degrade the beamformer's nulling capabilities. To address this, this paper introduces a temporally segmented distortionless response beamformer. Inspired by the segmented least squares method, which fits piecewise polynomials to data while penalizing excessive segmentation to prevent overfitting, the framework extends practical Capon beamforming by incorporating data-driven temporal segmentation. This formulation minimizes output power while dynamically adapting the SCM estimation windows to local stationarity, offering a principled approach to tracking time-varying interferers.

Manan Mittal, Ryan M. Corey, John R. Buck et al.

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.

Manan Mittal, Ryan M. Corey, Diego Cuji et al.

In dynamic acoustic environments characterized by time-varying interferers and moving sources, effective beamforming requires accurately identifying stationary regions over time. Traditional Capon beamformers rely on the instantaneous ensemble covariance matrix, which is inaccessible in practice. Practical implementations overcome this by estimating the sample covariance matrix (SCM) through averaging over a block of temporal samples. However, in non-stationary settings, a naive batch approach fails. Moving interferers smear the SCM, causing the beamformer to place nulls in outdated locations while failing to track newly active interferers, thereby degrading its nulling capabilities. To address this fundamental limitation, an Online Segmented Beamformer is proposed. This algorithm incorporates data-driven temporal segmentation to causally minimize output power while dynamically adapting the SCM estimation windows to local stationarity. By framing the problem through the lens of dynamic programming, the proposed method tracks abrupt environmental changes and resets covariance estimates in real-time. We validate the performance of this framework in a complex, reverberant simulated acoustic environment and in highly reverberant real world experiments, demonstrating its superiority over fixed-window adaptive methods.