针对麦克风阵列在动态环境中的波束成形稳定性问题，提出自适应对角加载方法。
Adaptive Diagonal Loading for Norm Constrained Beamforming
- 基于Kantorovich不等式，将白噪声增益约束转化为相关矩阵条件数上限。
- 三种计算复杂度分别为O(M)、O(M²)、O(M³)的自适应加载估计方法。
- 适用于快速变化干扰场景，特别适合大规模麦克风阵列系统。
在高动态声学环境中，大型麦克风阵列的可靠自适应波束成形至关重要。当说话者和干扰源快速移动时，用于估计空间相关矩阵的样本数量常严重不足。这种样本不足与阵列误差共同导致白噪声增益（WNG）下降，引发目标信号严重衰减。为确保波束成形的稳定性和鲁棒性，本文提出一种新型自适应对角加载方法，保证WNG始终严格处于指定范围内。通过利用Kantorovich不等式，将期望的WNG映射为相关矩阵条件数的严格上界。此外，提出了三种自适应加载水平的估计技术：基于迹的边界法、精确特征值分解等，分别具有O(M)、O(M²)和O(M³)的可扩展计算复杂度。实验表明，该方法在快速变化的干扰条件下仍能实现高度稳定的波束成形。
原文摘要 · Abstract (English)
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.
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