Center of Intelligent Acoustics and Immersive Communications, School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi'an 710021, China.
Shaanxi Joint Laboratory of Artificial Intelligence, Shaanxi University of Science and Technology, Xi'an 710021, China.
Sensors (Basel). 2023 Apr 4;23(7):3733. doi: 10.3390/s23073733.
The differential microphone array, or differential beamformer, has attracted much attention for its frequency-invariant beampattern, high directivity factor and compact size. In this work, the design of differential beamformers with small inter-element spacing planar microphone arrays is concerned. In order to exactly control the main lobe beamwidth and sidelobe level and obtain minimum main lobe beamwidth with a given sidelobe level, we design the desired beampattern by applying the Chebyshev polynomials at first, via exploiting the structure of the frequency-independent beampattern of a theoretical th-order differential beamformer. Next, the so-called null constrained and least square beamformers, which can obtain approximately frequency-invariant beampattern at relatively low frequencies and can be steered to any direction without beampattern distortion, are proposed based on planar microphone arrays to approximate the designed desired beampatterns. Then, for dealing with the white noise amplification at low-frequency bands and beampattern divergence problems at high-frequency bands of the null constrained and least square beamformers, the so-called minimum norm and combined solutions are deduced, which can compromise among the white noise gain, directivity factor and beampattern distortion flexibly. Preliminary simulation results illustrate the properties and advantages of the proposed differential beamformers.
差分麦克风阵列，或差分波束形成器，因其频率不变的波束图案、高指向性因子和紧凑尺寸而受到广泛关注。在这项工作中，我们关注的是具有小单元间距平面麦克风阵列的差分波束形成器的设计。为了精确控制主瓣波束宽度和旁瓣电平，并在给定的旁瓣电平时获得最小的主瓣波束宽度，我们首先通过利用理论 th 阶差分波束形成器的频率无关波束图案的结构，应用切比雪夫多项式来设计所需的波束图案。接下来，基于平面麦克风阵列，提出了所谓的零约束和最小二乘波束形成器，它们可以在相对较低的频率下获得近似频率不变的波束图案，并且可以在不产生波束图案失真的情况下指向任何方向，以逼近设计的期望波束图案。然后，为了解决零约束和最小二乘波束形成器在低频带的白噪声放大和高频带的波束图案发散问题，推导出了所谓的最小范数和组合解，它们可以灵活地在白噪声增益、指向性因子和波束图案失真之间进行权衡。初步的仿真结果说明了所提出的差分波束形成器的特性和优势。
