Humanoid robots require to use microphone arrays to acquire speech signals from the human communication partner while suppressing noise, reverberation, and interferences. Unlike many other applications, microphone arrays in humanoid robots have to face the restrictions in size and geometry. To address these challenges, this paper presents an approach to differential beamforming with arbitrary planar array geometries. The major contributions of this work are as follows: (1) a method is presented to design differential beamformers, which works for regular geometries such as linear, circular, and concentric circular ones, as well as irregular geometries, as long as the sensors’ positions are given or can be measured; (2) fundamental requirements for the design of different orders of linear differential microphone arrays (DMAs), partially steerable DMAs, fully steerable DMAs, and robust DMAs are discussed; (3) the validity and limitations of the Jacobi-Anger expansion approximation is analyzed, where we discuss how to achieve an optimal approximation by properly choosing the reference point; and (4) we show how to design an Nth-order DMA with 2N microphones using the Jacobi-Anger expansion.

中文翻译：

---

具有平面麦克风阵列的可控差分波束形成器

仿人机器人需要使用麦克风阵列从人类通信伙伴那里获取语音信号，同时抑制噪声、混响和干扰。与许多其他应用不同，仿人机器人中的麦克风阵列必须面临尺寸和几何形状的限制。为了应对这些挑战，本文提出了一种具有任意平面阵列几何形状的差分波束成形方法。这项工作的主要贡献如下：（1）提出了一种设计差分波束形成器的方法，该方法适用于规则几何形状，例如线性、圆形和同心圆形几何形状，以及不规则几何形状，只要传感器的位置是给定的或可以测量的；(2) 不同阶线性差分麦克风阵列 (DMA) 设计的基本要求，讨论了部分可控 DMA、完全可控 DMA 和稳健 DMA；（3）分析了Jacobi-ange扩展近似的有效性和限制，在那里我们讨论如何通过正确选择参考点来实现最佳逼近; (4) 我们展示了如何使用 Jacobi-Anger 扩展设计带有 2N 个麦克风的 N 阶 DMA。