{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T13:15:41Z","timestamp":1775913341592,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,1,20]],"date-time":"2023-01-20T00:00:00Z","timestamp":1674172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology Project of Sichuan Province","award":["2023YFG0176"],"award-info":[{"award-number":["2023YFG0176"]}]},{"name":"Science and Technology Project of Sichuan Province","award":["62231006"],"award-info":[{"award-number":["62231006"]}]},{"name":"Science and Technology Project of Sichuan Province","award":["2022D009"],"award-info":[{"award-number":["2022D009"]}]},{"name":"National Natural Science Foundation of China","award":["2023YFG0176"],"award-info":[{"award-number":["2023YFG0176"]}]},{"name":"National Natural Science Foundation of China","award":["62231006"],"award-info":[{"award-number":["62231006"]}]},{"name":"National Natural Science Foundation of China","award":["2022D009"],"award-info":[{"award-number":["2022D009"]}]},{"name":"Municipal Government of Quzhou","award":["2023YFG0176"],"award-info":[{"award-number":["2023YFG0176"]}]},{"name":"Municipal Government of Quzhou","award":["62231006"],"award-info":[{"award-number":["62231006"]}]},{"name":"Municipal Government of Quzhou","award":["2022D009"],"award-info":[{"award-number":["2022D009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In this paper, we study the multiple-input multiple-output (MIMO) radar transmit waveform design method for beampattern matching. The purpose is to design the beampattern to approximate the actual one and minimize the cross-correlation sidelobes under the constant modulus constraint (CMC). Due to the CMC, the problem is non-convex, and the existing methods solve it with relaxation, resulting in performance degradation. Different from these methods, we notice that the CMC is the product of complex circles (CC). Based on this physical characteristic, the direct beampattern matching without relaxation (DBMWR) method is proposed. To be specific, we first formulate the original problem as an unconstrained quartic problem over the CC and then solve it by the proposed method without relaxation. Simulation results show that the proposed method can achieve a balance in terms of accuracy and computation complexity compared with other methods.<\/jats:p>","DOI":"10.3390\/rs15030633","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T04:19:22Z","timestamp":1674447562000},"page":"633","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["MIMO Radar Transmit Waveform Design for Beampattern Matching via Complex Circle Optimization"],"prefix":"10.3390","volume":"15","author":[{"given":"Weijie","family":"Xiong","sequence":"first","affiliation":[{"name":"Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324003, China"},{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinfeng","family":"Hu","sequence":"additional","affiliation":[{"name":"Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324003, China"},{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Zhong","sequence":"additional","affiliation":[{"name":"Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324003, China"},{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yibao","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering and Computer Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangqing","family":"Xiao","sequence":"additional","affiliation":[{"name":"Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324003, China"},{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gangyong","family":"Zhu","sequence":"additional","affiliation":[{"name":"Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324003, China"},{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1109\/TAES.2018.2847958","article-title":"Fast Angle Estimation for MIMO Radar With Nonorthogonal Waveforms","volume":"54","author":"Liao","year":"2018","journal-title":"IEEE Trans. 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