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.

翻译：可靠的适应性波束成形对于在高度动态声学环境中运行的大型麦克风阵列至关重要。在说话者和干扰源快速移动的场景中，可用于估计空间相关矩阵的样本支持往往稀疏不足。这种不足，加之阵列缺陷，会降低白噪声增益，导致严重的目标信号抵消。为确保稳定且鲁棒的波束成形，我们提出了一种新颖的自适应对角加载方法，该方法能保证白噪声增益严格保持在指定边界内。通过利用康托罗维奇不等式，我们将期望的白噪声增益映射为相关矩阵条件数的严格上界。此外，我们提出了三种自适应加载水平的估计技术，范围从基于迹的边界估计到精确特征值分解，分别提供可扩展的计算复杂度$\mathcal{O}(M)$、$\mathcal{O}(M^2)$和$\mathcal{O}(M^3)$。我们的方法在快速变化的干扰下展现了高度稳定的波束成形性能。