Huang Gongping, Benesty Jacob, Chen Jingdong
Center of Intelligent Acoustics and Immersive Communications and School of Marine Science and Technology, Northwestern Polytechnical University, 127 Youyi West Road, Xi'an 710072, China.
INRS-EMT, University of Quebec, 800 de la Gauchetiere Ouest, Montreal, QC H5A 1K6, Canada.
J Acoust Soc Am. 2017 May;141(5):3236. doi: 10.1121/1.4983122.
Circular differential microphone arrays (CDMAs) have been extensively studied in speech and audio applications for their steering flexibility, potential to achieve frequency-invariant directivity patterns, and high directivity factors (DFs). However, CDMAs suffer from both white noise amplification and deep nulls in the DF and in the white noise gain (WNG) due to spatial aliasing, which considerably restricts their use in practical systems. The minimum-norm filter can improve the WNG by using more microphones than required for a given differential array order; but this filter increases the array aperture (radius), which exacerbates the spatial aliasing problem and worsens the nulls problem in the DF. Through theoretical analysis, this research finds that the nulls of the CDMAs are caused by the zeros in the denominators of the filters' coefficients, i.e., the zeros of the Bessel function. To deal with both the white noise amplification and deep nulls problems, this paper develops an approach that combines different rings of microphones together with appropriate radii. The resulting robust concentric circular differential microphone arrays (CCDMAs) can mitigate both problems. Simulation results justify the superiority of the robust CCDMA approach over the traditional CDMAs and robust CDMAs.
圆形差分麦克风阵列（CDMA）因其转向灵活性、实现频率不变方向性图的潜力以及高方向性因子（DF），在语音和音频应用中得到了广泛研究。然而，由于空间混叠，CDMA在DF和白噪声增益（WNG）中都会出现白噪声放大和深零点的问题，这在很大程度上限制了它们在实际系统中的应用。最小范数滤波器可以通过使用比给定差分阵列阶数所需更多的麦克风来提高WNG；但这种滤波器会增加阵列孔径（半径），从而加剧空间混叠问题，并使DF中的零点问题恶化。通过理论分析，本研究发现CDMA的零点是由滤波器系数分母中的零点，即贝塞尔函数的零点引起的。为了解决白噪声放大和深零点这两个问题，本文提出了一种将不同环的麦克风与适当半径相结合的方法。由此产生的鲁棒同心圆形差分麦克风阵列（CCDMA）可以减轻这两个问题。仿真结果证明了鲁棒CCDMA方法相对于传统CDMA和鲁棒CDMA的优越性。
