{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:39:38Z","timestamp":1760240378278,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T00:00:00Z","timestamp":1558656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006606","name":"Natural Science Foundation of Tianjin City","doi-asserted-by":"publisher","award":["16JCQNJC01100","17JCYBJC16400"],"award-info":[{"award-number":["16JCQNJC01100","17JCYBJC16400"]}],"id":[{"id":"10.13039\/501100006606","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Doctor Foundation of Tianjin Normal University","award":["52XB1203"],"award-info":[{"award-number":["52XB1203"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671394"],"award-info":[{"award-number":["61671394"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>An underdetermined direction of arrival (DOA) estimation method of wideband linear frequency modulated (LFM) signals is proposed without grid mismatch. According to the concentration property of LFM signal in the fractional Fourier (FRF) domain, the received sparse model of wideband signals with time-variant steering vector is firstly derived based on a coprime array. Afterwards, by interpolating virtual sensors, a virtual extended uniform linear array (ULA) is constructed with more degrees of freedom, and its covariance matrix in the FRF domain is recovered by employing sparse matrix reconstruction. Meanwhile, in order to avoid the grid mismatch problem, the modified atomic norm minimization is used to retrieve the covariance matrix with the consecutive basis. Different from the existing methods that approximately assume the frequency and the steering vector of the wideband signals are time-invariant in every narrowband frequency bin, the proposed method not only can directly solve more DOAs of LFM signals than the number of physical sensors with time-variant frequency and steering vector, but also obtain higher resolution and more accurate DOA estimation performance by the gridless sparse reconstruction. Simulation results demonstrate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/s19102383","type":"journal-article","created":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T11:20:46Z","timestamp":1558696846000},"page":"2383","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Underdetermined DOA Estimation of Wideband LFM Signals Based on Gridless Sparse Reconstruction in the FRF Domain"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8912-3573","authenticated-orcid":false,"given":"Yue","family":"Cui","sequence":"first","affiliation":[{"name":"College of Computer and Information Engineering, Tianjin Normal University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junfeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Tianjin University of Technology, Tianjin 300384, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Electronic Science and Technology, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhanying","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Computer and Information Engineering, Tianjin Normal University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinqi","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Computer and Information Engineering, Tianjin Normal University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18574","DOI":"10.1109\/ACCESS.2019.2892113","article-title":"A novel smeared synthesized LFM TC-OLA radar system: Design and performance","volume":"7","author":"Youssef","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1109\/TAES.2017.2696318","article-title":"Robust LFM target detection in wideband sonar systems","volume":"53","author":"Lee","year":"2017","journal-title":"IEEE Trans. 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