{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:45:17Z","timestamp":1760150717731,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,25]],"date-time":"2023-12-25T00:00:00Z","timestamp":1703462400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62022091","61921001"],"award-info":[{"award-number":["62022091","61921001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Target misalignment can cause beam pointing deviations and degradation of sidelobe performance. In order to eliminate the effect of target misalignment, we formulate the jamming sub-space recovery problem as a linearly modified atomic norm-based optimization. Then, we develop a deep-unfolding network based on the alternating direction method of multipliers (ADMM), which effectively improves the applicability and efficiency of the algorithm. By using the back-propagation process of deep-unfolding networks, the proposed method could optimize the hyper-parameters in the original atomic norm. This feature enables the adaptive beamformer to adjust its weight according to the observed data. Specifically, the proposed method could determine the optimal hyper-parameters under different interference noise matrix conditions. Simulation results demonstrate that the proposed network could reduce computational cost and achieve near-optimal performance with low complexity.<\/jats:p>","DOI":"10.3390\/rs16010096","type":"journal-article","created":{"date-parts":[[2023,12,25]],"date-time":"2023-12-25T23:00:12Z","timestamp":1703545212000},"page":"96","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["ADMM-Net for Beamforming Based on Linear Rectification with the Atomic Norm Minimization"],"prefix":"10.3390","volume":"16","author":[{"given":"Zhenghui","family":"Gong","sequence":"first","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Xinyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Mingjian","family":"Ren","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4015-6531","authenticated-orcid":false,"given":"Xiaolong","family":"Su","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1233-1494","authenticated-orcid":false,"given":"Zhen","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/PROC.1969.7278","article-title":"High-resolution frequency-wavenumber spectrum analysis","volume":"57","author":"Capon","year":"1969","journal-title":"Proc. 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