{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T05:21:22Z","timestamp":1781155282358,"version":"3.54.1"},"reference-count":28,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2024,10,22]],"date-time":"2024-10-22T00:00:00Z","timestamp":1729555200000},"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":["61831009"],"award-info":[{"award-number":["61831009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>High-frequency surface wave radar (HFSWR) is widely used for detecting sea surface or low-altitude targets due to its all-weather operation and over-the-horizon detection capability. To further enhance the maneuverability and detection range of HFSWR, shipborne HFSWR has been developed. However, compared to shore-based platforms, shipborne platforms face challenges such as a small array aperture and reduced Direction of Arrival (DOA) estimation performance due to their limited size. The traditional time\u2013domain virtual aperture extension method, based on the principle of space-time equivalence, aims to improve the array aperture but has limitations when used for HFSWR background or multiple targets with different speeds. To address these issues, this paper proposes a range-Doppler domain (RD-domain) virtual aperture extension method for the uniform linear array, based on the uniform motion model. The contributions of this work include (1) a continuous motion model for shipborne HFSWR, (2) a virtual aperture processing flowchart for shipborne HFSWR, and (3) an RD-domain aperture extension method suitable for HFSWR background or multiple targets with varying speeds. Through simulation and experimental data, we validate the proposed method and analyze its performance.<\/jats:p>","DOI":"10.3390\/rs16213929","type":"journal-article","created":{"date-parts":[[2024,10,22]],"date-time":"2024-10-22T11:31:57Z","timestamp":1729596717000},"page":"3929","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["An RD-Domain Virtual Aperture Extension Method for Shipborne HFSWR"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-4361-2909","authenticated-orcid":false,"given":"Youmin","family":"Qu","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Marine Environmental Monitoring and Information Processing, Ministry of Industry and Information Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingpeng","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Marine Environmental Monitoring and Information Processing, Ministry of Industry and Information Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuguan","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Key Laboratory of Marine Environmental Monitoring and Information Processing, Ministry of Industry and Information Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xue","family":"Li","sequence":"additional","affiliation":[{"name":"The 22nd Research Institute of China Electronics Technology Group Corporation, Xinxiang 453003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,22]]},"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. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/TASSP.1985.1164583","article-title":"Adaptive beamforming for coherent signals and interference","volume":"33","author":"Shan","year":"1985","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1109\/TASSP.1985.1164649","article-title":"On spatial smoothing for direction-of-arrival estimation of coherent signals","volume":"33","author":"Shan","year":"1985","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1109\/TASSP.1985.1164700","article-title":"Multiple source location\u2014A matrix decomposition approach","volume":"33","author":"Di","year":"1985","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_6","unstructured":"Di, A.Z., and Tian, L.S. (1984, January 19\u201321). Matrix decomposition and multiple source location. Proceedings of the ICASSP\u201984. IEEE International Conference on Acoustics, Speech, and Signal Processing, San Diego, CA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ren, Q.S., and Willis, A.J. (1997, January 14\u201316). Extending MUSIC to single snapshot and on line direction finding applications. Proceedings of the Radar 97 (Conf. Publ. No. 449), Edinburgh, UK.","DOI":"10.1049\/cp:19971783"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/LGRS.2020.2967387","article-title":"Ship Detection and Direction Finding Based on Time-Frequency Analysis for Compact HF Radar","volume":"18","author":"Cai","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_9","first-page":"1","article-title":"A Two-Stage Hierarchical One-Class Classification Structure for HFSWR Ship-Target Detection","volume":"61","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, W., Yang, Y., and Liu, T. (2024). Coarse-to-Fine Target Detection for HFSWR with Spatial-Frequency Analysis and Subnet Structure. IEEE Trans. Multimed., 1\u201312.","DOI":"10.1109\/TMM.2024.3453044"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1109\/IRET-MIL.1962.5008415","article-title":"Some Early Developments in Synthetic Aperture Radar Systems","volume":"MIL-6","author":"Sherwin","year":"1962","journal-title":"Ire Trans. Mil. Electron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1121\/1.381049","article-title":"Creating an acoustic synthetic aperture in the ocean","volume":"60","author":"Williams","year":"1976","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1121\/1.396837","article-title":"Passive synthetic arrays","volume":"84","author":"Autrey","year":"1988","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/48.126953","article-title":"A circular passive synthetic array: An inverse problem approach","volume":"17","author":"Yen","year":"1992","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1121\/1.398335","article-title":"Extended towed array processing by an overlap correlator","volume":"86","author":"Stergiopoulos","year":"1989","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2128","DOI":"10.1121\/1.399181","article-title":"Optimum bearing resolution for a moving towed array and extension of its physical aperture","volume":"87","author":"Stergiopoulos","year":"1990","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1109\/48.725227","article-title":"Super-resolution processing for HF surface wave radar based on pre-whitened MUSIC","volume":"23","author":"Xie","year":"1998","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sun, M., Xie, J., Hao, Z., and Yi, C. (2012, January 21\u201325). Target detection and estimation for shipborne HFSWR based on oblique projection. Proceedings of the 2012 IEEE 11th International Conference on Signal Processing, Beijing, China.","DOI":"10.1109\/ICoSP.2012.6491681"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhang, B., Xie, J., and Hao, Z. (2016, January 10\u201313). Super-resolution processing for shipborne HFSWR based on an improved IMP. Proceedings of the 2016 CIE International Conference on Radar (RADAR), Guangzhou, China.","DOI":"10.1109\/RADAR.2016.8059405"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Shi, C., Zhang, L., Niu, J., Wu, M., and Zhang, J. (2021, January 20\u201323). DOA Estimation for Shipborne HFSWR: Model and Analysis. Proceedings of the OCEANS 2021: San Diego\u2013Porto, San Diego, CA, USA.","DOI":"10.23919\/OCEANS44145.2021.9706003"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4703","DOI":"10.1109\/TGRS.2020.3023025","article-title":"Analysis and Estimation of Shipborne HFSWR Target Parameters Under the Influence of Platform Motion","volume":"59","author":"Yang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2023.3335484","article-title":"Accurate Direction Finding for Shipborne HFSWR Through Platform Motion Compensation","volume":"61","author":"Wang","year":"2023","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, Y., Yu, H., Zhang, L., and Li, G. (2023). APO-ELM Model for Improving Azimuth Correction of Shipborne HFSWR. Remote. Sens., 15.","DOI":"10.3390\/rs15153818"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ji, Y., Zhang, J., Wang, Y., Yue, C., Gong, W., Liu, J., Sun, H., Yu, C., and Li, M. (2020). Coast\u2013Ship Bistatic HF Surface Wave Radar: Simulation Analysis and Experimental Verification. Remote. Sens., 12.","DOI":"10.3390\/rs12030470"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ji, Y., Wang, Y., Huang, W., Sun, W., Zhang, J., Li, M., and Cheng, X. (2021). Vessel Target Echo Characteristics and Motion Compensation for Shipborne HFSWR under Non-Uniform Linear Motion. Remote. Sens., 13.","DOI":"10.3390\/rs13142826"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Chen, M., Niu, J., Li, M., Zhang, L., Ji, Y., Wan, W., and Wu, Q.M.J. (2022). A Motion Compensation Method for Shipborne HFSWR by Using Dual Reference RF Signals Generated Onshore. Remote. Sens., 14.","DOI":"10.3390\/rs14051055"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yang, L., Zhang, H., Gao, L., and Bai, Y. (2021, January 15\u201319). DOA estimation of compact HFSWR by the virtual array synthesis algorithm. Proceedings of the 2021 CIE International Conference on Radar (Radar), Haikou, China.","DOI":"10.1109\/Radar53847.2021.10028101"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Bai, Y., Zhang, H., Zhou, M., and Yang, L. (2022, January 25\u201327). DOA estimation using shipborne HFSWR based on virtual synthetic array. Proceedings of the 2022 41st Chinese Control Conference (CCC), Hefei, China.","DOI":"10.23919\/CCC55666.2022.9902308"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/21\/3929\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:17:57Z","timestamp":1760113077000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/21\/3929"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,22]]},"references-count":28,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["rs16213929"],"URL":"https:\/\/doi.org\/10.3390\/rs16213929","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,22]]}}}