{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:14:01Z","timestamp":1760242441391,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,8,24]],"date-time":"2017-08-24T00:00:00Z","timestamp":1503532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61601504","61501504"],"award-info":[{"award-number":["61601504","61501504"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation Research Project of Shanxi province, China","award":["2016JQ6020"],"award-info":[{"award-number":["2016JQ6020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes an improved spatial differencing (ISD) scheme for two-dimensional direction of arrival (2-D DOA) estimation of coherent signals with uniform rectangular arrays (URAs). We first divide the URA into a number of row rectangular subarrays. Then, by extracting all the data information of each subarray, we only perform difference-operation on the auto-correlations, while the cross-correlations are kept unchanged. Using the reconstructed submatrices, both the forward only ISD (FO-ISD) and forward backward ISD (FB-ISD) methods are developed under the proposed scheme. Compared with the existing spatial smoothing techniques, the proposed scheme can use more data information of the sample covariance matrix and also suppress the effect of additive noise more effectively. Simulation results show that both FO-ISD and FB-ISD can improve the estimation performance largely as compared to the others, in white or colored noise conditions.<\/jats:p>","DOI":"10.3390\/s17091956","type":"journal-article","created":{"date-parts":[[2017,8,24]],"date-time":"2017-08-24T11:16:52Z","timestamp":1503573412000},"page":"1956","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Improved Spatial Differencing Scheme for 2-D DOA Estimation of Coherent Signals with Uniform Rectangular Arrays"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9910-0663","authenticated-orcid":false,"given":"Junpeng","family":"Shi","sequence":"first","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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\/0000-0002-8893-0856","authenticated-orcid":false,"given":"Fenggang","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Binfeng","family":"Zong","sequence":"additional","affiliation":[{"name":"Unit-94710 of the PLA, Wuxi 214000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Wang","sequence":"additional","affiliation":[{"name":"Unit-94259 of the PLA, Penglai 265600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3197","DOI":"10.1109\/TSP.2011.2144591","article-title":"Computationally efficient subspace-based method for two-dimensional direction estimation with L-shaped array","volume":"59","author":"Wang","year":"2011","journal-title":"IEEE Trans. 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