{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:04:46Z","timestamp":1760241886591,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T00:00:00Z","timestamp":1539907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["PolyU. 152200\/14E"],"award-info":[{"award-number":["PolyU. 152200\/14E"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"name":"The Hong Kong Polytechnic University","award":["4-ZZGS and G-YBVQ"],"award-info":[{"award-number":["4-ZZGS and G-YBVQ"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In designing acoustic broadband beamformers, the complexity can grow significantly when the number of microphones and the filter length increase. It is advantageous if many of the filter coefficients are zeroes so that the implementation can be executed with less computation. Moreover, the size of the array can also be pruned to reduce complexity. These problems are addressed in this paper. A suitable optimization model is proposed. Both array pruning and filter thinning can be solved together as a two-stage optimization problem to yield the final sparse designs. Numerical results show that the complexity of the designed beamformers can be reduced significantly with minimal effect on performance.<\/jats:p>","DOI":"10.3390\/s18103536","type":"journal-article","created":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T10:08:02Z","timestamp":1539943682000},"page":"3536","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the Sparse Beamformer Design"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4499-5009","authenticated-orcid":false,"given":"Mingjie","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, South China Normal University, Guangzhou 510000 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7523-4069","authenticated-orcid":false,"given":"Ka Fai Cedric","family":"Yiu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8942-5328","authenticated-orcid":false,"given":"Sven","family":"Nordholm","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Curtin University, Perth 6102, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Brandstein, M., and Ward, D. (2001). Microphone Arrays: Signal Processing Techniques and Applications, Springer.","DOI":"10.1007\/978-3-662-04619-7"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Havelock, D., Kuwano, S., and Vorlander, M. (2008). Beamforming for speech and audio signals. Handbook of Signal Processing in Acoustics, Springer.","DOI":"10.1007\/978-0-387-30441-0"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/89.824702","article-title":"Array optimization applied in the near field of a microphone array","volume":"8","author":"Ryan","year":"2000","journal-title":"IEEE Trans. Speech Audio Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1109\/78.738237","article-title":"Nearfield beamforming using radial reciprocity","volume":"47","author":"Kennedy","year":"1999","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","first-page":"88","article-title":"The optimum design of one and two-dimensional FIR filters using the frequency response masking technique","volume":"40","author":"Lim","year":"1993","journal-title":"IEEE Trans. Circuits Syst. II"},{"key":"ref_6","first-page":"1522","article-title":"Minimax filters for microphone arrays","volume":"46","author":"Lau","year":"1999","journal-title":"IEEE Trans. Circuits Syst. II"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1109\/TSP.2006.882109","article-title":"Uniform concentric circular arrays with frequency-invariant characteristics-theory, design, adaptive beamforming and DOA estimation","volume":"55","author":"Chan","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","first-page":"141","article-title":"Chebyshev approximation for the design of broadband beamformers in the near field","volume":"45","author":"Nordholm","year":"1998","journal-title":"IEEE Trans. Circuits Syst. II"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1109\/LSP.2002.802109","article-title":"A new design method for broadband microphone arrays for speech input in automobiles","volume":"9","author":"Yiu","year":"2002","journal-title":"IEEE Signal Proc. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1109\/TSA.2003.815527","article-title":"Near-field broadband beamformer design via multidimensional semi-infinite linear programming techniques","volume":"11","author":"Yiu","year":"2003","journal-title":"IEEE Trans. Speech Audio Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3647","DOI":"10.1109\/TSP.2011.2133490","article-title":"A two-stage method for the design of near-field broadband beamformer","volume":"59","author":"Feng","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.dsp.2014.02.012","article-title":"The design of multi-dimensional acoustic beamformers via window functions","volume":"29","author":"Feng","year":"2014","journal-title":"Digit. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1007\/s10957-014-0543-5","article-title":"Performance limit of broadband beamformer designs in space and frequency","volume":"164","author":"Feng","year":"2015","journal-title":"J. Optim. Theory Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1109\/TSP.2009.2036471","article-title":"Linear programming algorithms for sparse filter design","volume":"58","author":"Baran","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","unstructured":"Lim, Y., Kwan, H.K., and Siu, W.C. (2016). Recent advances in sparse FIR filter design using l0 and l1 optimization techniques. Trends in Digital Signal Processing, Pan Stanford Publishing."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2959","DOI":"10.1137\/090767133","article-title":"Optimizing floating point units in hybrid FPGAs","volume":"20","author":"Zhang","year":"2010","journal-title":"SIAM J. Optim."},{"key":"ref_17","first-page":"3755","article-title":"Design of near-field broadband beamformer using semi-definite programming","volume":"8","author":"Yiu","year":"2012","journal-title":"Int. J. Innov. Comput. Inf. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3800","DOI":"10.1109\/TAP.2009.2027243","article-title":"Linear array thinning exploiting almost difference sets","volume":"57","author":"Oliveri","year":"2009","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2259","DOI":"10.1163\/156939310793699136","article-title":"Fast array thinning using global optimization methods","volume":"24","author":"Iglesias","year":"2010","journal-title":"J. Electromagn. Waves Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1109\/TSP.2011.2178491","article-title":"Placement design of microphone arrays in near-field broadband beamformers","volume":"60","author":"Feng","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1486","DOI":"10.1016\/j.asoc.2012.02.027","article-title":"A hybrid descent method with genetic algorithm for microphone array placement design","volume":"13","author":"Li","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1109\/18.391241","article-title":"Blind adaptive multiuser detection","volume":"41","author":"Honig","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_23","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_24","first-page":"15","article-title":"A perturbation exchange algorithm for convex semi-infinite programming with applications in sparse beamformer","volume":"14","author":"Gao","year":"2018","journal-title":"Pac. J. Optim."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3536\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:26:41Z","timestamp":1760196401000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3536"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,19]]},"references-count":24,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["s18103536"],"URL":"https:\/\/doi.org\/10.3390\/s18103536","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,10,19]]}}}