On the simultaneous design of broadband beamformer filters and configuration

Mingjie Gao; Ka-Fai Cedric Yiu

doi:10.3934/naco.2022019

Article Contents

2023, Volume 13, Issue 2: 328-339. Doi: 10.3934/naco.2022019 open access

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On the simultaneous design of broadband beamformer filters and configuration

Mingjie Gao and
Ka-Fai Cedric Yiu^,

Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China

^*Corresponding author: Ka-Fai Cedric Yiu
^*Corresponding author: Ka-Fai Cedric Yiu

Received: May 2022

Revised: May 2022

Early access: July 2022

Published: January 2023

This paper is supported by RGC Grant PolyU. 152200/14E and 152245/18E, and PolyU grant G-UAHF. The first author is also supported by National Natural Science Foundation of China 12171168, Natural Science Foundation of Guangdong Province 2021A1515010368 and 2020A1515010489, the Foundation of Department of Education of Guangdong Province 2020ZDZX3004

Abstract / Introduction Full Text(HTML) Figure(11) / Table(1) Related Papers Cited by

Abstract

For signal enhancement, beamforming remains to be an essential technique for many applications. In the design process, the microphone locations are prescribed and the signal from a target location is being enhanced. While the filter coefficients can be readily optimized, it is found that the signal enhancement capability depends significantly on the array configuration. Therefore, it is advantageous to consider both filters and microphone positions as design variables. In this paper, this problem is addressed. We formulate the beamformer design problem as a non-linear least square problem and propose Gauss-Newton algorithm to update both filters and configuration simultaneously during iterations. We illustrate by several designs to demonstrate the effectiveness of the proposed method.

Keywords:

Beamformer optimization,
array configuration optimization.

Mathematics Subject Classification: Primary: 90C30, 65K05; Secondary: 68U99.

Citation:

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Figure 1. The structure of a near-field beamformer

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Figure 2.

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Figure 3. Initial array configuration (Ex1)

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Figure 4. Final array configuration (Ex1)

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Figure 5. Convergence history of the algorithm

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Figure 6. Amplitude of $ G({\boldsymbol{r}},f) $ where $ N = 5 $, $ L = 7 $ (Ex1) with considering microphone positions

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Figure 7. Amplitude of $ G({\boldsymbol{r}},f) $ where $ N = 5 $, $ L = 7 $ (Ex1) without considering microphone positions

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Figure 8. Initial array configuration (Ex2)

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Figure 9. Final array configuration (Ex2)

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Figure 10. Amplitude of $ G({\boldsymbol{r}},f) $ where $ N = 5 $, $ L = 26 $ (Ex2) with considering microphone positions

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Figure 11. Amplitude of $ G({\boldsymbol{r}},f) $ where $ N = 5 $, $ L = 26 $ (Ex2) without considering microphone positions

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Table 1. Comparison of the running times (Ex1)

Gauss-Newton Matlab Nonlinear LS

running time $ 8.7995 $(s) $ 1073.2 $(s)

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