{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T23:21:07Z","timestamp":1778800867000,"version":"3.51.4"},"reference-count":19,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T00:00:00Z","timestamp":1557100800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61601370"],"award-info":[{"award-number":["61601370"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61425005"],"award-info":[{"award-number":["61425005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["576\/16"],"award-info":[{"award-number":["576\/16"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"name":"ISF-NSFC joint research program","award":["2514\/17 and 61761146001"],"award-info":[{"award-number":["2514\/17 and 61761146001"]}]},{"name":"Top International University Visiting Program for Outsanding Young scholars of Northwestern Polytechnical University","award":["2017"],"award-info":[{"award-number":["2017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Beamformers have been widely used to enhance signals from a desired direction and suppress noise and interfering signals from other directions. Constant beamwidth beamformers enable a fixed beamwidth over a wide range of frequencies. Most of the existing approaches to design constant beamwidth beamformers are based on optimization algorithms with high computational complexity and are often sensitive to microphone mismatches. Other existing methods are based on adjusting the number of sensors according to the frequency, which simplify the design, but cannot control the sidelobe level. Here, we propose a window-based technique to attain the beamwidth constancy, in which different shapes of standard window functions are applied for different frequency bins as the real weighting coefficients of microphones. Thereby, not only do we keep the beamwidth constant, but we also control the sidelobe level. Simulation results show the advantages of our method compared with existing methods, including lower sidelobe level, higher directivity factor, and higher white noise gain.<\/jats:p>","DOI":"10.3390\/s19092091","type":"journal-article","created":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T11:22:35Z","timestamp":1557400955000},"page":"2091","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Window-Based Constant Beamwidth Beamformer"],"prefix":"10.3390","volume":"19","author":[{"given":"Tao","family":"Long","sequence":"first","affiliation":[{"name":"Center of Intelligent Acoustics and Immersive Communications, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, Shaanxi, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2556-3972","authenticated-orcid":false,"given":"Israel","family":"Cohen","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Technion\u2014Israel Institute of Technology, Technion City, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baruch","family":"Berdugo","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Technion\u2014Israel Institute of Technology, Technion City, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Yang","sequence":"additional","affiliation":[{"name":"Center of Intelligent Acoustics and Immersive Communications, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, Shaanxi, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingdong","family":"Chen","sequence":"additional","affiliation":[{"name":"Center of Intelligent Acoustics and Immersive Communications, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, Shaanxi, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Benesty, J., Cohen, I., and Chen, J. (2018). Fundamentals of Signal Enhancement and Array Signal Processing, Wiley-IEEE Press.","DOI":"10.1002\/9781119293132"},{"key":"ref_2","unstructured":"Benesty, J., Chen, J., and Huang, Y. (2008). Microphone Array Processing, Springer."},{"key":"ref_3","unstructured":"Van Trees, H.L. (2004). Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory, John Wiley & Sons."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Benesty, J., Chen, J., and Cohen, I. (2015). Design of Circular Differential Microphone Arrays, Springer.","DOI":"10.1007\/978-3-319-14842-7"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5755","DOI":"10.1109\/TSP.2007.900087","article-title":"Minimum-Mean-Output-Energy Blind Adaptive Channel Shortening for Multicarrier SIMO Transceivers","volume":"55","author":"Darsena","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/97.481158","article-title":"FIR filter design for frequency invariant beamformers","volume":"3","author":"Ward","year":"1996","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3839","DOI":"10.1121\/1.2197606","article-title":"Steerable frequency-invariant beamforming for arbitrary arrays","volume":"119","author":"Parra","year":"2006","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.1016\/j.sigpro.2007.03.018","article-title":"Frequency invariant beamforming for two-dimensional and three-dimensional arrays","volume":"87","author":"Liu","year":"2007","journal-title":"Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1109\/TASL.2009.2016395","article-title":"Multichannel eigenspace beamforming in a reverberant noisy environment with multiple interfering speech signals","volume":"17","author":"Markovich","year":"2009","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2169","DOI":"10.1109\/TSP.2011.2106780","article-title":"Design of robust superdirective arrays with a tunable tradeoff between directivity and frequency-invariance","volume":"59","author":"Crocco","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2575","DOI":"10.1109\/TASL.2012.2208626","article-title":"Optimal real-weighted beamforming with application to linear and spherical arrays","volume":"20","author":"Tourbabin","year":"2012","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3891","DOI":"10.1121\/1.3701991","article-title":"A directionally tunable but frequency-invariant beamformer on an acoustic velocity-sensor triad to enhance speech perception","volume":"131","author":"Wu","year":"2012","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.sigpro.2016.07.019","article-title":"FIR-based symmetrical acoustic beamformer with a constant beamwidth","volume":"130","author":"Rosen","year":"2017","journal-title":"Signal Process."},{"key":"ref_14","first-page":"17","article-title":"Broadband microphone arrays for speech acquisition","volume":"26","author":"Ward","year":"1998","journal-title":"Acoust. Aust."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1002\/j.1538-7305.1961.tb03976.x","article-title":"Prolate spheroidal wave functions, Fourier analysis and uncertainty","volume":"40","author":"Slepian","year":"1961","journal-title":"Bell Labs Tech. J."},{"key":"ref_16","unstructured":"Kaiser, J.F. (, January April). Nonrecursive digital filter design using the I_0-sinh window function. Proceedings of the IEEE International Symposium on Circuits & Systems, San Francisco, CA, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1109\/JRPROC.1946.225956","article-title":"A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level","volume":"34","author":"Dolph","year":"1946","journal-title":"Proc. IRE"},{"key":"ref_18","unstructured":"Lyons, R.G. (2011). Understanding Digital Signal Processing, Pearson Education. [3rd ed.]."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2093","DOI":"10.1109\/TASLP.2015.2469142","article-title":"Theoretical analysis of differential microphone array beamforming and an improved solution","volume":"23","author":"Pan","year":"2015","journal-title":"IEEE Trans. Audio Speech Lang. Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/9\/2091\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:49:22Z","timestamp":1760186962000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/9\/2091"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,6]]},"references-count":19,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,5]]}},"alternative-id":["s19092091"],"URL":"https:\/\/doi.org\/10.3390\/s19092091","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,6]]}}}