{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T06:12:31Z","timestamp":1762409551891,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,3,26]],"date-time":"2019-03-26T00:00:00Z","timestamp":1553558400000},"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>The Nyquist folding receiver (NYFR) can achieve a high-probability interception of an ultra-wideband (UWB) signal with fewer devices, while the output of the NYFR is converted into a hybrid modulated signal of the local oscillator (LO) and the received signal, which requires the matching parameter estimation methods. The linear frequency modulation (LFM) signal is a typical low probability of intercept (LPI) radar signal. In this paper, an estimation method of both the Nyquist Zone (NZ) index and the chirp rate for the LFM signal intercepted by NYFR was proposed. First, according to the time-frequency characteristics of the LFM signal, the accurate NZ and the rough chirp rate was estimated based on least squares (LS) and random sample consensus (RANSAC). Then, the information of the LO was removed from the hybrid modulated signal by the known NZ, and the precise chirp rate was obtained by using the fractional Fourier transform (FrFT). Moreover, a fast search method of FrFT optimal order was presented, which could obviously reduce the computational complexity. The simulation demonstrated that the proposed method could precisely estimate the parameters of the hybrid modulated output signal of the NYFR.<\/jats:p>","DOI":"10.3390\/s19061477","type":"journal-article","created":{"date-parts":[[2019,3,27]],"date-time":"2019-03-27T05:03:12Z","timestamp":1553662992000},"page":"1477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Nyquist Zone Index and Chirp Rate Estimation of LFM Signal Intercepted by Nyquist Folding Receiver Based on Random Sample Consensus and Fractional Fourier Transform"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0004-4199","authenticated-orcid":false,"given":"Xinqun","family":"Liu","sequence":"first","affiliation":[{"name":"National Key Laboratory of Science and Technology on ATR, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Li","sequence":"additional","affiliation":[{"name":"Artificial Intelligence Research Center (AIRC), National Innovation Institute of Defense Technology (NIIDT), NO.2 Fengtai South Road, Fengtai District, Beijing 100071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolei","family":"Fan","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science and Technology on ATR, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zengping","family":"Chen","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science and Technology on ATR, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,26]]},"reference":[{"key":"ref_1","first-page":"346","article-title":"Low Probability of Intercept Radar","volume":"1","author":"Schleher","year":"1985","journal-title":"Int. Radar Conf."},{"key":"ref_2","unstructured":"Pace, P.E. (2009). To See and Not Be Seen. Detecting and Classifying Low Probability of Intercept Radar, ARTECH HOUSE. [2nd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1109\/49.761034","article-title":"Analog-to-digital converter survey and analysis","volume":"17","author":"Walden","year":"1999","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1364\/OE.15.001955","article-title":"Photonic analog-to-digital converters","volume":"15","author":"Valley","year":"2007","journal-title":"Opt. Express"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Casey, S.D., and Cohl, H.S. (2015, January 25\u201329). UWB signal processing: Projection, B-splines, and modified Gegenbauer bases. Proceedings of the 2015 International Conference on Sampling Theory and Applications (SampTA), Washington, DC, USA.","DOI":"10.1109\/SAMPTA.2015.7148840"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Casey, S.D., and Cohl, H.S. (2017, January 3\u20137). Sampling architectures for ultra-wideband signals. Proceedings of the 2017 International Conference on Sampling Theory and Applications (SampTA), Tallinn, Estonia.","DOI":"10.1109\/SAMPTA.2017.8024452"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4719","DOI":"10.1109\/TSP.2011.2161472","article-title":"Xampling: Signal Acquisition and Processing in Union of Subspaces","volume":"59","author":"Mishali","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1109\/JETCAS.2012.2223611","article-title":"Analog-to-Information and the Nyquist Folding Receiver","volume":"2","author":"Maleh","year":"2012","journal-title":"IEEE J. Emerg. Sel. Top. Circuits Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Fudge, G.L., Bland, R.E., Chivers, M.A., Ravindran, S., Haupt, J., and Pace, P.E. (2008, January 26\u201329). A Nyquist folding analog-to-information receiver. Proceedings of the 2008 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2008.5074464"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/TIT.2009.2034811","article-title":"Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals","volume":"56","author":"Tropp","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Laska, J., Kirolos, S., Wakin, M., Duarte, M., Baron, D., Ragheb, T., Massoud, Y., and Baraniuk, R. (2006, January 29\u201330). Random Sampling for Analog-to-Information Conversion of Wideband Signals. Proceedings of the 2006 IEEE Dallas\/CAS Workshop on Design, Applications, Integration and Software, Richardson, TX, USA.","DOI":"10.1109\/DCAS.2006.321036"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Li, T., Zhu, Q., and Chen, Z. (2018). Parameter Estimation of SAR Signal Based on SVD for the Nyquist Folding Receiver. Sensors, 18.","DOI":"10.3390\/s18061768"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"095057","DOI":"10.1117\/1.JRS.9.095057","article-title":"Detection and parameter estimation for space-borne radar linear frequency modulated pulse signal in low signal-to-noise ratio","volume":"9","author":"Jinzhen","year":"2015","journal-title":"J. Appl. Rem. Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1360\/02yf0456","article-title":"Detection and Parameter Estimation of Multicomponent LFM Signal Based on the Fractional Fourier Transform","volume":"47","author":"Qi","year":"2004","journal-title":"Sci. China Ser. F Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1109\/78.661326","article-title":"Linear frequency-modulated signal detection using Radon-ambiguity transform","volume":"46","author":"Minsheng","year":"1998","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1109\/78.388866","article-title":"Analysis of multicomponent LFM signals by a combined Wigner-Hough transform","volume":"43","author":"Barbarossa","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1109\/TAES.2012.6129644","article-title":"Detection and Estimation of LFMCW Radar Signals","volume":"48","author":"Geroleo","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/j.crma.2008.03.014","article-title":"The restricted isometry property and its implications for compressed sensing","volume":"346","author":"Emmanuel","year":"2008","journal-title":"C. R. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1186\/s13634-016-0392-5","article-title":"The RIP and block-RIP analysis of Nyquist folding receiver for recovering signals","volume":"2016","author":"Jiang","year":"2016","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Jiang, K., Chen, S., Zhu, J., Wang, J., and Tang, B. (2017, January 24\u201327). Fractional Spectral Reconstruction of Signals from Periodic Non-uniformly Sub-sampling based on a Nyquist Folding Scheme. Proceedings of the International Conference on Graphics and Signal Processing (ICGSP\u201917), Singapore.","DOI":"10.1145\/3121360.3121379"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"69","DOI":"10.2528\/PIERC11062801","article-title":"Parameter Estimation of LFM Signal Intercepted by Left Sideband Synchronous Nyquist Folding Receiver","volume":"23","author":"Zeng","year":"2011","journal-title":"Prog. Electromagn. Res. C"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, T., Fan, X., Zhu, Q., and Chen, Z. (2017, January 6\u20139). Parameter estimation of LFM signals intercepted by a composite local oscillation SNYFR. Proceedings of the 2017 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS), Xiamen, China.","DOI":"10.1109\/ISPACS.2017.8266510"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Pace, P.E., Kusmanoff, A., and Fudge, G.L. (2009, January 1\u20134). Nyquist folding analog-to-information receiver: Autonomous information recovery using quadrature mirror filtering. Proceedings of the 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2009.5470156"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1109\/78.740131","article-title":"Multiridge detection and time-frequency reconstruction","volume":"47","author":"Carmona","year":"1999","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1145\/358669.358692","article-title":"Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography","volume":"24","author":"Fischler","year":"1981","journal-title":"Commun. ACM"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1016\/j.imavis.2004.02.009","article-title":"Randomized RANSAC with Td,d test","volume":"22","author":"Matas","year":"2004","journal-title":"Image Vis. Comput."},{"key":"ref_27","first-page":"035018","article-title":"Intra-pulse modulation type recognition for pulse compression radar signal","volume":"11","author":"Xiaolei","year":"2017","journal-title":"J. Appl. Remote Sens."},{"key":"ref_28","first-page":"42","article-title":"Recognition of Intra-pulse Signals Modulation Based on Fractional Fourier Transform","volume":"51","author":"Ning","year":"2011","journal-title":"Telecommun. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2141","DOI":"10.1109\/78.536672","article-title":"Digital computation of the fractional Fourier transform","volume":"44","author":"Ozaktas","year":"1996","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/6\/1477\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:40:46Z","timestamp":1760186446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/6\/1477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,26]]},"references-count":29,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19061477"],"URL":"https:\/\/doi.org\/10.3390\/s19061477","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,3,26]]}}}