{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T08:25:24Z","timestamp":1773044724153,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2021,11,27]],"date-time":"2021-11-27T00:00:00Z","timestamp":1637971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a new radar signal modulated with a hybrid of the frequency shift keying (FSK) and the phase shift keying (PSK) signal\u2014i.e., the FSK-PSK signal\u2014is studied. Different phase encoding sequences are used to modulate the sub-pulses to obtain lower sidelobe levels and ensure signal orthogonality. In addition, to counter intra-pulse slice repeater jamming of specific length generated by the enemy jammer, an orthogonal waveform made of sub-pulses of equal length based on the FSK-PSK modulation scheme is designed. The simulation results show that the optimized discrete phase encoding sequence can significantly enhance the orthogonality of the sub-pulse in the FSK-PSK signal and effectively suppress the slice repeater jamming. Two algorithms are proposed: (1) the low sidelobe waveform optimization algorithm based on ADMM (LSW-ADMM); and (2) the anti-slice-repeater-jamming algorithm based on ADMM (ASRJ-ADMM). Both algorithms exhibit fast convergence speed and low computational complexity.<\/jats:p>","DOI":"10.3390\/s21237915","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T01:45:02Z","timestamp":1638323102000},"page":"7915","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Hybrid FSK-PSK Waveform Optimization for Radar Based on Alternating Direction Method of Multiplier (ADMM)"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7332-0898","authenticated-orcid":false,"given":"Zhiting","family":"Fei","sequence":"first","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"},{"name":"Research and Development Department, China Academy of Launch Vehicle Technology, Beijing 100076, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiachen","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5440-3556","authenticated-orcid":false,"given":"Zhe","family":"Geng","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohua","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jindong","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1049\/iet-rsn.2015.0063","article-title":"Design of multiple-input multiple-output transmit waveform and receive filter for extended target detection","volume":"9","author":"Karbasi","year":"2015","journal-title":"IET Radar Sonar Navig."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1109\/JSTARS.2018.2790987","article-title":"Subpixellic Methods for Sidelobes Suppression and Strong Targets Extraction in Single Look Complex SAR Images","volume":"11","author":"Abergel","year":"2018","journal-title":"IEEE J. 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