{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T18:58:30Z","timestamp":1772823510667,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,24]],"date-time":"2019-12-24T00:00:00Z","timestamp":1577145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2016YFC1401100"],"award-info":[{"award-number":["2016YFC1401100"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","award":["61771352"],"award-info":[{"award-number":["61771352"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","award":["41474128"],"award-info":[{"award-number":["41474128"]}],"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 (HF SWR) plays an important role in marine stereoscopic monitoring system. Nevertheless, the congestion of external radio frequency interference (RFI) in HF band degrades its performance seriously. In this article, two novel fractional Fourier transform (FRFT)-based RFI suppression approaches are proposed. One is based on the orthogonal projection of sequences from fractional Fourier domain, and the other is based on singular value decomposition (SVD) of Hankel matrix of sequences from fractional inverse-Fourier domain. Simulation and experimental data collected by HF SWR from Wuhan University were used to test the effectiveness as well as the application condition of the proposed RFI suppression algorithms. The FRFT-based orthogonal projection algorithm is practicable for suppressing stationary RFI with unvaried carrier frequency, while the FRFT-based SVD algorithm is applicable equally for mitigating nonstationary RFI with time-varying carrier frequency or occasional duration time. The processing results may provide useful guidelines for interference suppression of HF SWR, and inspiring the further application of the FRFT-based methods for signal processing.<\/jats:p>","DOI":"10.3390\/rs12010075","type":"journal-article","created":{"date-parts":[[2019,12,24]],"date-time":"2019-12-24T10:28:43Z","timestamp":1577183323000},"page":"75","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Fractional Fourier Transform-Based Radio Frequency Interference Suppression for High-Frequency Surface Wave Radar"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5311-8972","authenticated-orcid":false,"given":"Qing","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Electronic Information, Wuhan University, Wuhan 430072, China"},{"name":"Collaborative Innovation Center for Geospatial Technology, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Electronic Information, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiongbin","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electronic Information, Wuhan University, Wuhan 430072, China"},{"name":"Collaborative Innovation Center for Geospatial Technology, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5733-9601","authenticated-orcid":false,"given":"Xianchang","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Electronic Information, Wuhan University, Wuhan 430072, China"},{"name":"Collaborative Innovation Center for Geospatial Technology, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhangyou","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic Information, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinxiong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic Information, Wuhan University, Wuhan 430072, China"},{"name":"Collaborative Innovation Center for Geospatial Technology, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1126\/science.198.4313.138","article-title":"Ocean Surface Currents Mapped by Radar","volume":"198","author":"Barrick","year":"1977","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1109\/TAP.1973.1140557","article-title":"Mapping of North Atlantic winds by HF radar sea backscatter interpretation","volume":"21","author":"Long","year":"1973","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1029\/RS012i003p00415","article-title":"Extraction of wave parameters from measured HF radar sea-echo Doppler spectra","volume":"12","author":"Barrick","year":"1977","journal-title":"Radio Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1049\/ip-rsn:19960153","article-title":"Automated propagation advice for OTHR ship detection","volume":"143","author":"Barnes","year":"1996","journal-title":"Proc. Inst. Elect. Eng. Radar Sonar Navigat."},{"key":"ref_5","first-page":"2362","article-title":"Computationally Efficient RF Interference Suppression Method with Closed-Form Maximum Likelihood Estimator for HF Surface Wave Over-The-Horizon Radars","volume":"54","author":"Yi","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Dzvonkovskaya, A., Dzvonkovsky, L., and Sobchuk, A. (2008, January 2\u20135). Adaptive Selection of HF Radar Operating Channels. Proceedings of the 2008 International Conference on Radar, Adelaide, Australia.","DOI":"10.1109\/RADAR.2008.4653923"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/LGRS.2015.2496223","article-title":"Transient Interference Excision in Over-the-Horizon Radar by Robust Principle Component Analysis with a Structured Matrix","volume":"13","author":"Ai","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1109\/TGRS.2008.916482","article-title":"Interference cancellation for high-frequency surface wave radar","volume":"46","author":"Guo","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1109\/7.722714","article-title":"Stochastic-constraints method in nonstationary hot-clutter cancellation. I. Fundamentals and supervised training applications","volume":"34","author":"Abramovich","year":"1998","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","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. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1109\/TAES.2013.6404105","article-title":"Adaptive Beamforming for Nonstationary HF Interference Cancellation in Skywave Over-the-Horizon Radar","volume":"49","author":"Su","year":"2013","journal-title":"IEEE Trans. Aerosp. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1109\/LGRS.2016.2560943","article-title":"Radio Frequency Interference Cancelation for Skywave Over-the-Horizon Radar","volume":"13","author":"Liu","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1109\/LSP.2005.845603","article-title":"Dense radio frequency interference suppression in HF radars","volume":"12","author":"Zhou","year":"2005","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1109\/LGRS.2011.2181817","article-title":"Radio frequency interference suppression in small-aperture high-frequency radars","volume":"9","author":"Zhou","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1109\/LGRS.2017.2775609","article-title":"Radio Frequency Interference Suppression Algorithm in Spatial Domain for Compact High-Frequency Radar","volume":"15","author":"Tian","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chen, Z., Xie, F., Zhao, C., and He, C. (2018). An Orthogonal Projection Algorithm to Suppress Interference in High-Frequency Surface Wave Radar. Remote Sens., 10.","DOI":"10.3390\/rs10030403"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1049\/iet-rsn.2010.0041","article-title":"Radio frequency interference cancellation for sea-state remote sensing by high-frequency radar","volume":"5","author":"Wang","year":"2011","journal-title":"IET Radar Sonar Navig."},{"key":"ref_18","unstructured":"Turley, M. (2003, January 3\u20135). Impulsive noise rejection in HF radar using a linear prediction technique. Proceedings of the 2003 Proceedings of Conference on Radar, Adelaide, Australia."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1109\/TGRS.2005.844291","article-title":"Transient interference excision in over-the-horizon radar using adaptive time-frequency analysis","volume":"43","author":"Guo","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"986","DOI":"10.1109\/LGRS.2018.2828990","article-title":"Radio Frequency Interference Mitigation for High-Frequency Surface Wave Radar","volume":"15","author":"Chen","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2568","DOI":"10.1109\/TSP.2009.2028095","article-title":"Short-Time Fractional Fourier Transform and Its Applications","volume":"58","author":"Tao","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3084","DOI":"10.1109\/78.330368","article-title":"The fractional Fourier transform and time-frequency representations","volume":"42","author":"Almeida","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1049\/iet-rsn.2014.0496","article-title":"Multi-frequency high frequency surface wave radar based on phase offset","volume":"9","author":"Zhang","year":"2015","journal-title":"IET Radar. Sonar. Navig."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1109\/LGRS.2017.2709816","article-title":"A new Algorithm for Surface Currents Inversion with High-Frequency Over-the-Horizon Radar","volume":"14","author":"Li","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1049\/el:20040085","article-title":"Method to suppress radio-frequency interference in HF radars","volume":"40","author":"Jun","year":"2004","journal-title":"Electron. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1421","DOI":"10.1109\/78.205747","article-title":"A singular value decomposition (SVD) based method for suppressing ocean clutter in high frequency radar","volume":"41","author":"Poon","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1109\/78.286957","article-title":"Signal processing applications of oblique projection operators","volume":"42","author":"Behrens","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1137\/S0895479897320824","article-title":"On Principal Angles between Subspaces of Euclidean Space","volume":"22","author":"Drmac","year":"2000","journal-title":"Siam J. Matrix Anal. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Gurgel, K.W., Barbin, Y., and Schlick, T. (2007, January 18\u201321). Radio Frequency Interference Suppression Technique in FMCW Modulated HF Radars. Proceedings of the OCEANS 2007-Europe, Aberdeen, UK.","DOI":"10.1109\/OCEANSE.2007.4302289"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/1\/75\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:45:10Z","timestamp":1760190310000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/1\/75"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,24]]},"references-count":29,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["rs12010075"],"URL":"https:\/\/doi.org\/10.3390\/rs12010075","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,24]]}}}