TY - JOUR
T1 - Fundamental Approaches to Robust Differential Beamforming With High Directivity Factors
AU - Huang, Gongping
AU - Benesty, Jacob
AU - Chen, Jingdong
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2022
Y1 - 2022
N2 - Differential beamforming, which measures the spatial derivatives of the acoustic pressure field, can be used in a wide range of small devices that require high-fidelity sound and speech acquisition as it can achieve frequency-invariant spatial responses with high directivity factors (DFs). The most challenging problem in the design of any differential beamformer is how to achieve the maximum possible DF while maintaining a proper level of robustness for practical usage. This paper is devoted to dealing with this challenging problem. It presents a study on theory and methods to achieve the optimal and fundamental compromise between the white noise gain (WNG), which quantifies how robust is the beamformer, and the DF in differential beamforming. The major contributions of this work are as follows. 1) We show and prove that any null constrained fixed beamformer can be decomposed as the sum of two orthogonal filters, i.e., the maximum WNG (MWNG) beamformer and a reduced-rank one. Based on this decomposition, we develop three kinds of differential beamformers from the WNG perspective, which can achieve a flexible and optimal compromise between DF and WNG. 2) We show that a transformed null constrained beamformer can also be decomposed as the sum of two orthogonal filters, i.e., the transformed maximum DF (MDF) beamformer and another reduced-rank one. Based on this decomposition, we also develop three kinds of differential beamformers, which can obtain the desired level of DF while using the rest of the degrees of freedom to maximize the WNG.
AB - Differential beamforming, which measures the spatial derivatives of the acoustic pressure field, can be used in a wide range of small devices that require high-fidelity sound and speech acquisition as it can achieve frequency-invariant spatial responses with high directivity factors (DFs). The most challenging problem in the design of any differential beamformer is how to achieve the maximum possible DF while maintaining a proper level of robustness for practical usage. This paper is devoted to dealing with this challenging problem. It presents a study on theory and methods to achieve the optimal and fundamental compromise between the white noise gain (WNG), which quantifies how robust is the beamformer, and the DF in differential beamforming. The major contributions of this work are as follows. 1) We show and prove that any null constrained fixed beamformer can be decomposed as the sum of two orthogonal filters, i.e., the maximum WNG (MWNG) beamformer and a reduced-rank one. Based on this decomposition, we develop three kinds of differential beamformers from the WNG perspective, which can achieve a flexible and optimal compromise between DF and WNG. 2) We show that a transformed null constrained beamformer can also be decomposed as the sum of two orthogonal filters, i.e., the transformed maximum DF (MDF) beamformer and another reduced-rank one. Based on this decomposition, we also develop three kinds of differential beamformers, which can obtain the desired level of DF while using the rest of the degrees of freedom to maximize the WNG.
KW - Beampattern
KW - differential beamforming
KW - directivity factor
KW - microphone arrays
KW - quadratic eigenvalue problem
KW - robust beamforming
KW - white noise gain
UR - http://www.scopus.com/inward/record.url?scp=85139464743&partnerID=8YFLogxK
U2 - 10.1109/TASLP.2022.3209935
DO - 10.1109/TASLP.2022.3209935
M3 - 文章
AN - SCOPUS:85139464743
SN - 2329-9290
VL - 30
SP - 3074
EP - 3088
JO - IEEE/ACM Transactions on Audio Speech and Language Processing
JF - IEEE/ACM Transactions on Audio Speech and Language Processing
ER -