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This paper addresses the problem of signal cancellation in adaptive beamforming for microphone arrays due to snapshot-deficient spatial correlation matrix estimation in dynamic acoustic environments. They propose an adaptive diagonal loading method that leverages the Kantorovich inequality to bound the condition number of the correlation matrix, ensuring the White Noise Gain (WNG) stays within specified limits. The method includes three estimation techniques for the adaptive loading level with varying computational complexities, achieving stable beamforming under rapidly changing interference.
Guaranteeing stable beamforming in dynamic acoustic environments is now possible with a novel adaptive diagonal loading method that strictly bounds White Noise Gain.
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.
