{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T10:21:21Z","timestamp":1774520481966,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T00:00:00Z","timestamp":1719964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China","award":["62271190"],"award-info":[{"award-number":["62271190"]}]},{"name":"Natural Science Foundation of China","award":["20220003"],"award-info":[{"award-number":["20220003"]}]},{"name":"Science and Technology on Electronic Information Control Laboratory","award":["62271190"],"award-info":[{"award-number":["62271190"]}]},{"name":"Science and Technology on Electronic Information Control Laboratory","award":["20220003"],"award-info":[{"award-number":["20220003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To solve the problem of aperture fill time (AFT) for wideband sparse arrays, variable fractional delay (VFD) FIR filters are applied to eliminate linear coupling between spatial and time domains. However, the large dimensions of the filter coefficient matrix result in high system complexity. To alleviate the computational burden of solving VFD filter coefficients, a novel multi\u2013regultion minimax (MRMM) model utilizing the sparse representation technique has been presented. The error function is constrained by the introduction of L2\u2013norm and L1\u2013norm regularizations within the minimax criterion. The L2\u2013norm effectively resolves the problems of overfitting and non\u2013unique solutions that arise in the sparse optimization of traditional minimax (MM) models. Meanwhile, the use of multiple L1\u2013norms enables the optimal design of the smallest sub\u2013filter number and order of the VFD filter. To solve the established nonconvex model, an improved sequential\u2013alternating direction method of multipliers (S\u2013ADMM) algorithm for filter coefficients is proposed, which utilizes sequential alternation to iteratively update multiple soft\u2013thresholding problems. The experimental results show that the optimized VFD filter reduces system complexity significantly and corrects AFT effectively in a wideband sparse array.<\/jats:p>","DOI":"10.3390\/s24134327","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T09:23:59Z","timestamp":1719998639000},"page":"4327","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Efficient Aperture Fill Time Correction for Wideband Sparse Array Using Improved Variable Fractional Delay Filters"],"prefix":"10.3390","volume":"24","author":[{"given":"Jie","family":"Gu","sequence":"first","affiliation":[{"name":"National Key Laboratory of Electromagnetic Space Security, Chengdu 610036, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Xu","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Electromagnetic Space Security, Chengdu 610036, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjing","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingwei","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Hohai University, Nanjing 210098, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"key":"ref_1","first-page":"278","article-title":"Using 1-D Variable Fractional-Delay Filters to Reduce the Computational Complexity of 3-D Broadband Multibeam Beamformers","volume":"61","author":"Edussooriya","year":"2014","journal-title":"IEEE Trans. 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