{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T16:10:09Z","timestamp":1775578209445,"version":"3.50.1"},"reference-count":63,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T00:00:00Z","timestamp":1722297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61701140"],"award-info":[{"award-number":["61701140"]}]},{"name":"National Natural Science Foundation of China","award":["SL20230204"],"award-info":[{"award-number":["SL20230204"]}]},{"name":"Songjiang Laboratory","award":["61701140"],"award-info":[{"award-number":["61701140"]}]},{"name":"Songjiang Laboratory","award":["SL20230204"],"award-info":[{"award-number":["SL20230204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Unlike uniform linear arrays (ULAs), coprime arrays require fewer physical sensors yet provide higher degrees of freedom (DOF) and larger array apertures. However, due to the existence of \u201choles\u201d in the differential co-array, the target detection performance deteriorates, especially in adaptive beamforming. To address these challenges, this paper proposes an efficient and robust adaptive beamforming algorithm leveraging coprime array interpolation. The algorithm eliminates unwanted signals and uses the Gauss\u2013Legendre quadrature method to reconstruct an Interference-plus-Noise Covariance Matrix (INCM), thereby obtaining the beamforming coefficients. Unlike previous techniques, we utilize a virtual interpolated ULA to expand the aperture, enabling the acquisition of a high-dimensional covariance matrix. Additionally, a projection matrix is constructed to eliminate unwanted signals from the received data, greatly enhancing the accuracy of INCM reconstruction. To address the high computational complexity of integral operations used in most INCM reconstruction algorithms, we propose an approximation based on the Gauss\u2013Legendre quadrature, which reduces the computational load while maintaining accuracy. This algorithm avoids the array aperture loss caused by using only the ULA segment in the difference co-array and improves the accuracy of INCM reconstruction. Simulation and experimental results show that the performance of the proposed algorithm is superior to the compared beamformers and is closer to the optimal beamformer in various scenarios.<\/jats:p>","DOI":"10.3390\/rs16152792","type":"journal-article","created":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T15:25:23Z","timestamp":1722353123000},"page":"2792","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Efficient and Robust Adaptive Beamforming Based on Coprime Array Interpolation"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6326-3417","authenticated-orcid":false,"given":"Siming","family":"Chen","sequence":"first","affiliation":[{"name":"The School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Xiaochuan","family":"Wu","sequence":"additional","affiliation":[{"name":"The School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Shujie","family":"Li","sequence":"additional","affiliation":[{"name":"The School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Weibo","family":"Deng","sequence":"additional","affiliation":[{"name":"The School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5423-5070","authenticated-orcid":false,"given":"Xin","family":"Zhang","sequence":"additional","affiliation":[{"name":"The School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1109\/TAES.2004.1310001","article-title":"Robust adaptive beamforming for HF surface wave over-the-horizon radar","volume":"40","author":"Fabrizio","year":"2004","journal-title":"IEEE Trans. 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