{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T14:23:39Z","timestamp":1775744619207,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,5,30]],"date-time":"2023-05-30T00:00:00Z","timestamp":1685404800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2022M723879"],"award-info":[{"award-number":["2022M723879"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Sparse arrays are of deep concern due to their ability to identify more sources than the number of sensors, among which the hole-free difference co-array (DCA) with large degrees of freedom (DOFs) is a topic worth discussing. In this paper, we propose a novel hole-free nested array with three sub-uniform line arrays (NA-TS). The one-dimensional (1D) and two-dimensional (2D) representations demonstrate the detailed configuration of NA-TS, which indicates that both nested array (NA) and improved nested array (INA) are special cases of NA-TS. We subsequently derive the closed-form expressions for the optimal configuration and the available number of DOFs, concluding that the DOFs of NA-TS is a function of the number of sensors and the number of the third sub-ULA. The NA-TS possesses more DOFs than several previously proposed hole-free nested arrays. Finally, the superior direction of arrival (DOA) estimation performance based on the NA-TS is supported by numerical examples.<\/jats:p>","DOI":"10.3390\/s23115214","type":"journal-article","created":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T07:21:51Z","timestamp":1685517711000},"page":"5214","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Hole-Free Nested Array with Three Sub-ULAs for Direction of Arrival Estimation"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7328-4815","authenticated-orcid":false,"given":"Yule","family":"Zhang","sequence":"first","affiliation":[{"name":"Graduate College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7939-4588","authenticated-orcid":false,"given":"Guoping","family":"Hu","sequence":"additional","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5284-7321","authenticated-orcid":false,"given":"Hao","family":"Zhou","sequence":"additional","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan","family":"Bai","sequence":"additional","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenghong","family":"Zhan","sequence":"additional","affiliation":[{"name":"Graduate College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuhan","family":"Guo","sequence":"additional","affiliation":[{"name":"Graduate College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research: The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. 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