Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level
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....
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MDPI AG
2023-04-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/23/7/3733 |
| _version_ | 1827746427466416128 |
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| author | Xianghui Wang Mei Li Yingke Zhao Jiao Wang Xin Tan |
| author_facet | Xianghui Wang Mei Li Yingke Zhao Jiao Wang Xin Tan |
| author_sort | Xianghui Wang |
| collection | DOAJ |
| description | 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 <i>N</i>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. |
| first_indexed | 2024-03-11T05:25:10Z |
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| id | doaj.art-c41d148183574b12b22f7e8ae2e94411 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-11T05:25:10Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
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| series | Sensors |
| spelling | doaj.art-c41d148183574b12b22f7e8ae2e944112023-11-17T17:36:56ZengMDPI AGSensors1424-82202023-04-01237373310.3390/s23073733Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe LevelXianghui Wang0Mei Li1Yingke Zhao2Jiao Wang3Xin Tan4Center of Intelligent Acoustics and Immersive Communications, School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi’an 710021, ChinaCenter of Intelligent Acoustics and Immersive Communications, School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi’an 710021, ChinaCenter of Intelligent Acoustics and Immersive Communications, School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi’an 710021, ChinaCenter of Intelligent Acoustics and Immersive Communications, School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi’an 710021, ChinaShaanxi Joint Laboratory of Artificial Intelligence, Shaanxi University of Science and Technology, Xi’an 710021, ChinaThe 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 <i>N</i>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.https://www.mdpi.com/1424-8220/23/7/3733microphone arrayfixed beamformerdifferential beamformerfrequency-invariant beampatternmain lobe beamwidthsidelobe level |
| spellingShingle | Xianghui Wang Mei Li Yingke Zhao Jiao Wang Xin Tan Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level Sensors microphone array fixed beamformer differential beamformer frequency-invariant beampattern main lobe beamwidth sidelobe level |
| title | Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level |
| title_full | Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level |
| title_fullStr | Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level |
| title_full_unstemmed | Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level |
| title_short | Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level |
| title_sort | design of planar differential microphone array beampatterns with controllable mainlobe beamwidth and sidelobe level |
| topic | microphone array fixed beamformer differential beamformer frequency-invariant beampattern main lobe beamwidth sidelobe level |
| url | https://www.mdpi.com/1424-8220/23/7/3733 |
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