{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:25:40Z","timestamp":1760235940831,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T00:00:00Z","timestamp":1633651200000},"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>Stepped-frequency waveform may be used to synthesize a wideband signal with several narrow-band pulses and achieve a high-resolution range profile without increasing the instantaneous bandwidth. Nevertheless, the conventional stepped-frequency waveform is Doppler sensitive, which greatly limits its application to moving targets. For this reason, this paper proposes a waveform design method using a staggered pulse repetition frequency to improve the Doppler tolerance effectively. First, a generalized echo model of the stepped-frequency waveform is constructed in order to analyze the Doppler sensitivity. Then, waveform design is carried out in the stepped-frequency waveform by using a staggered pulse repetition frequency so as to eliminate the high-order phase component that is caused by the target\u2019s velocity. Further, the waveform design method is extended to the sparse stepped-frequency waveform, and we also propose corresponding methods for high-resolution range profile synthesis and motion compensation. Finally, experiments with electromagnetic data verify the high Doppler tolerance of the proposed waveform.<\/jats:p>","DOI":"10.3390\/s21196673","type":"journal-article","created":{"date-parts":[[2021,10,10]],"date-time":"2021-10-10T21:37:49Z","timestamp":1633901869000},"page":"6673","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Design and Processing Method for Doppler-Tolerant Stepped-Frequency Waveform Using Staggered PRF"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2543-8143","authenticated-orcid":false,"given":"Yan","family":"Zhang","sequence":"first","affiliation":[{"name":"Beijing Institute of Radio Measurement, Beijing 100854, China"}]},{"given":"Chunmao","family":"Yeh","sequence":"additional","affiliation":[{"name":"Beijing Institute of Radio Measurement, Beijing 100854, China"}]},{"given":"Zhangfeng","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Institute of Radio Measurement, Beijing 100854, China"}]},{"given":"Yaobing","family":"Lu","sequence":"additional","affiliation":[{"name":"Beijing Institute of Radio Measurement, Beijing 100854, China"}]},{"given":"Xuebin","family":"Chen","sequence":"additional","affiliation":[{"name":"Beijing Institute of Radio Measurement, Beijing 100854, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"182839","DOI":"10.1109\/ACCESS.2019.2960260","article-title":"A Novel Echo-Based Error Estimation and Ripple Elimination Method for Stepped Frequency Chirp SAR Signal","volume":"7","author":"Yang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4435","DOI":"10.1109\/JSEN.2017.2707340","article-title":"Design of ultrawideband stepped-frequency radar for imaging of obscured targets","volume":"17","author":"Phelan","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1109\/TMTT.2017.2751463","article-title":"Stepped-carrier OFDM-radar processing scheme to retrieve high-resolution range-velocity profile at low sampling rate","volume":"66","author":"Schweizer","year":"2017","journal-title":"IEEE Trans. Microl. Theory Tech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1530","DOI":"10.1049\/iet-rsn.2017.0204","article-title":"Interpulse-frequency-agile and intrapulse-phase-coded waveform optimization for extend-range correlation sidelobe suppression","volume":"11","author":"Mao","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11391","DOI":"10.1109\/ACCESS.2017.2700994","article-title":"Phase coded stepped frequency linear frequency modulated waveform synthesis technique for low altitude ultra-wideband synthetic aperture radar","volume":"5","author":"Chua","year":"2017","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1109\/TGRS.2006.888865","article-title":"Analysis of Random Step Frequency Radar and Comparison with Experiments","volume":"45","author":"Axelsson","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liao, Z., Lu, D., Hu, J., and Zhang, J. (2016, January 16\u201318). A novel range profile synthesis method for random hopping frequency radar. Proceedings of the IEEE International Conference Digital Signal Processing, Beijing, China.","DOI":"10.1109\/ICDSP.2016.7868520"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4252","DOI":"10.1109\/TGRS.2017.2688728","article-title":"Precise calibration of channel imbalance for very high-resolution SAR with stepped frequency","volume":"55","author":"Wang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1109\/LGRS.2014.2352676","article-title":"A Novel Range Grating Lobe Suppression Method Based on the Stepped-Frequency SAR Image","volume":"12","author":"Ding","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1109\/TAES.2018.2880024","article-title":"High range resolution profile estimation via a cognitive stepped frequency technique","volume":"55","author":"Aubry","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1109\/LGRS.2016.2635154","article-title":"Low Sidelobe Range Profile Synthesis for Sonar Imaging Using Stepped-Frequency Pulses","volume":"14","author":"Liu","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3784","DOI":"10.1109\/JSEN.2019.2897014","article-title":"Phase Compensation and Image Autofocusing for Randomized Stepped Frequency ISAR","volume":"19","author":"Wang","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1109\/LGRS.2018.2870869","article-title":"A Coherent Integration Method for Moving Target Detection Using Frequency Agile Radar","volume":"16","author":"Huang","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4490","DOI":"10.1109\/TSP.2014.2337279","article-title":"Fundamental Limits of HRR Profiling and Velocity Compensation for Stepped-Frequency Waveforms","volume":"62","author":"Liu","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4630","DOI":"10.1109\/TGRS.2011.2151865","article-title":"High-Resolution ISAR Imaging with Sparse Stepped-Frequency Waveforms","volume":"49","author":"Zhang","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1109\/TGRS.2012.2204891","article-title":"Random-Frequency SAR Imaging Based on Compressed Sensing","volume":"51","author":"Yang","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1109\/TGRS.2019.2937965","article-title":"Sparse Frequency Waveform Optimization for High-Resolution ISAR Imaging","volume":"58","author":"Wei","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","unstructured":"Huang, L., Zong, Z., Huang, L., and Shu, Z. (August, January 28). Off-grid sparse stepped-frequency SAR imaging with adaptive basis. Proceedings of the IEEE International Geoscience Remote Sensing Symposium, Yokohama, Japan."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2327","DOI":"10.1109\/JSEN.2011.2136375","article-title":"Reconstruction of Moving Target\u2019s HRRP Using Sparse Frequency-Stepped Chirp Signal","volume":"11","author":"Zhu","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"746","DOI":"10.3969\/j.issn.1004-4132.2010.05.005","article-title":"Velocity compensation methods for LPRF modulated frequency stepped-frequency (MFSF) radar","volume":"21","author":"Xia","year":"2010","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1109\/LGRS.2010.2047492","article-title":"Velocity Estimation and Range Shift Compensation for High Range Resolution Profiling in Stepped-Frequency Radar","volume":"7","author":"Liu","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5043","DOI":"10.1109\/TIP.2017.2728182","article-title":"ISAR imaging of high-speed maneuvering target using gapped stepped-frequency waveform and compressive sensing","volume":"26","author":"Kang","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6791","DOI":"10.1109\/TGRS.2020.2974550","article-title":"High-Resolution ISAR Imaging and Motion Compensation With 2-D Joint Sparse Reconstruction","volume":"58","author":"Shao","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","first-page":"5553","article-title":"Range migration compensation for moving targets in chirp radars with stepped frequency","volume":"19","author":"Wang","year":"2019","journal-title":"J. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"57643","DOI":"10.1109\/ACCESS.2018.2873784","article-title":"Motion Analysis and Compensation Method for Random Stepped Frequency Radar Using the Pseudorandom Code","volume":"6","author":"Liao","year":"2018","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1109\/LGRS.2006.873874","article-title":"A New Approach for Synthesizing the Range Profile of Moving Targets via Stepped-Frequency Waveforms","volume":"3","author":"Chen","year":"2006","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"129018","DOI":"10.1109\/ACCESS.2019.2939789","article-title":"A Novel Scheme for Detection and Estimation of Unresolved Targets With Stepped-Frequency Waveform","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1109\/LSP.2019.2949686","article-title":"Designing Constant Modulus Complete Complementary Sequence with High Doppler Tolerance for Simultaneous Polarimetric Radar","volume":"26","author":"Wang","year":"2019","journal-title":"IEEE Signal. Process. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1109\/TAES.2014.130815","article-title":"Doppler tolerant and detection capable polyphase code sets","volume":"51","author":"Qazi","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Gao, C., Teh, K.C., and Liu, A. (2015, January 2). Frequency coding waveform with segment LFM. Proceedings of the IEEE 5th Asia-Pacific Conference on Synthetic Apperture Radar (APSAR), Singapore.","DOI":"10.1109\/APSAR.2015.7306260"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"23188","DOI":"10.3390\/s150923188","article-title":"ISAR Imaging Based on the Wideband Hyperbolic Frequency-ModulationWaveform","volume":"15","author":"Zhou","year":"2015","journal-title":"Sensors"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2462","DOI":"10.1109\/TAES.2019.2958191","article-title":"A Frequency Diversity Algorithm for Extending the Radar Doppler Velocity Nyquist Interval","volume":"56","author":"Venkatesh","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Tien, V.V., Hop, T.V., Nhu, N., Hoang, D.X., and Van Loi, N. (2019, January 26\u201328). A staggered PRF coherent integration for resolving range-Doppler ambiguity in pulse-Doppler radar. Proceedings of the International Radar Symposium, Ulm, Germany.","DOI":"10.23919\/IRS.2019.8768110"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1109\/TAES.2020.3016851","article-title":"Ambiguity Function Analysis of Random Frequency and PRI Agile Signals","volume":"57","author":"Long","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2020.3039534","article-title":"Joint Frequency and PRF Agility Waveform Optimization for High-Resolution ISAR Imaging","volume":"1","author":"Wei","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7982","DOI":"10.1109\/TGRS.2020.2985768","article-title":"Estimation of PRI Stagger in Case of Missing Observations","volume":"58","author":"Tao","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1049\/iet-rsn.2018.5181","article-title":"High resolution ISAR imaging via MMV based block sparse signal recovery","volume":"13","author":"He","year":"2019","journal-title":"IET Radar Sonar Navig."},{"key":"ref_38","first-page":"5985","article-title":"MIMO radar imaging with non-orthogonal waveforms based on joint-block sparse recovery","volume":"56","author":"Hu","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"10136","DOI":"10.1109\/TGRS.2019.2931626","article-title":"Sparse Scene Recovery for High-Resolution Automobile FMCW SAR via Scaled Compressed Sensing","volume":"57","author":"Jung","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"157019","DOI":"10.1109\/ACCESS.2019.2949756","article-title":"A Fast and Accurate Compressed Sensing Reconstruction Algorithm for ISAR Imaging","volume":"7","author":"Cheng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"6228","DOI":"10.1109\/TSP.2018.2876301","article-title":"Analysis of Frequency Agile Radar via Compressed Sensing","volume":"66","author":"Huang","year":"2018","journal-title":"IEEE Trans. Signal. Process."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Jamil, S., Rahman, M., Ullah, A., Badnava, S., Forsat, M., and Mirjavadi, S.S. (2020). Malicious UAV detection using integrated audio and visual features for public safety applications. Sensors, 20.","DOI":"10.3390\/s20143923"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"15372","DOI":"10.1109\/JIOT.2021.3064376","article-title":"An Efficient Strategy for Accurate Detection and Localization of UAV Swarms","volume":"8","author":"Zheng","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5059","DOI":"10.1109\/TII.2020.3015730","article-title":"Accurate Detection and Localization of Unmanned Aerial Vehicle Swarms-Enabled Mobile Edge Computing System","volume":"17","author":"Zheng","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/7.532282","article-title":"Autofocusing of inverse synthetic aperture radar images using contrast optimization","volume":"32","author":"Berizzi","year":"1996","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/19\/6673\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:10:29Z","timestamp":1760166629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/19\/6673"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,8]]},"references-count":45,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["s21196673"],"URL":"https:\/\/doi.org\/10.3390\/s21196673","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,10,8]]}}}