{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:37:55Z","timestamp":1760240275241,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T00:00:00Z","timestamp":1556236800000},"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":["61371169, 61601167, 61601504, 61631020"],"award-info":[{"award-number":["61371169, 61601167, 61601504, 61631020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the open research fund of State Key Laboratory of Millimeter Waves, Southeast University","award":["K201826"],"award-info":[{"award-number":["K201826"]}]},{"name":"the open research fund of State Key Laboratory of Complex Electromagnetic Environmental Effects of Electronic Information System, and the Fundamental Research Funds for the Central Universities","award":["NE2017103"],"award-info":[{"award-number":["NE2017103"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we derive the discrete Fourier transform (DFT) method for direction of arrival (DOA) estimation by generating the massive virtual difference co-array with the nested array. By contrast with the spatial smoothing (SS) subspace-based methods for nested array, which halve the array aperture, the proposed method can take full advantage of the total array aperture. Since the conventional DFT method is a non-parametric method and is limited by Rayleigh threshold, we perform the phase rotation operation to obtain the fine DOA estimates. Owing to the full utilization of the array aperture and phase rotation operation, the proposed method can achieve better performance than SS subspace-based methods for far-field sources especially with massive virtual difference co-arrays which possess a large number of virtual sensors. Besides, as the fast Fourier transform (FFT) is attractive in practical implementation, the proposed method lowers the computational cost, as compared with the subspace-based methods. Numerical simulation results validate the superiority of the proposed method in both estimation performance and complexity.<\/jats:p>","DOI":"10.3390\/s19091961","type":"journal-article","created":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T07:52:59Z","timestamp":1556265179000},"page":"1961","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computationally Efficient Sources Location Method for Nested Array via Massive Virtual Difference Co-Array"],"prefix":"10.3390","volume":"19","author":[{"given":"Wei","family":"Wu","sequence":"first","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"Institute of Manned Space System Engineering, China Academy of Space Technology, Beijing 100094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunfei","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space (Nanjing University of Aeronautics and Astronautics), Ministry of Industry and Information Technology, Nanjing 211106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space (Nanjing University of Aeronautics and Astronautics), Ministry of Industry and Information Technology, Nanjing 211106, China"},{"name":"State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfeng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"College of computer and information, Hohai University, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,26]]},"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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