{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T17:52:41Z","timestamp":1767981161176,"version":"3.49.0"},"reference-count":50,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T00:00:00Z","timestamp":1713139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Brazilian Navy, the Brazilian Army, the National Council for Scientific and Technological Development\u2014CNPq, the Brazilian Development Bank (BNDES)","award":["001"],"award-info":[{"award-number":["001"]}]},{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior\u2013Brazil (CAPES)","award":["001"],"award-info":[{"award-number":["001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The prevalence of Low Probability of Interception (LPI) and Low Probability of Exploitation (LPE) radars in contemporary Electronic Warfare (EW) presents an ongoing challenge to defense mechanisms, compelling constant advances in protective strategies. Noise radars are examples of LPI and LPE systems that gained substantial prominence in the past decade despite exhibiting a common drawback of limited Doppler tolerance. The Advanced Pulse Compression Noise (APCN) waveform is a stochastic radar signal proposed to amalgamate the LPI and LPE attributes of a random waveform with the Doppler tolerance feature inherent to a linear frequency modulation. In the present work, we derive closed-form expressions describing the APCN signal\u2019s ambiguity function and spectral containment that allow for a proper analysis of its detection performance and ability to remove range ambiguities as a function of its stochastic parameters. This paper also presents a more detailed address of the LPI\/LPE characteristic of APCN signals claimed in previous works. We show that sophisticated Electronic Intelligence (ELINT) systems that employ Time Frequency Analysis (TFA) and image processing methods may intercept APCN and estimate important parameters of APCN waveforms, such as bandwidth, operating frequency, time duration, and pulse repetition interval. We also present a method designed to intercept and exploit the unique characteristics of the APCN waveform. Its performance is evaluated based on the probability of such an ELINT system detecting an APCN radar signal as a function of the Signal-to-Noise Ratio (SNR) in the ELINT system. We evaluated the accuracy and precision of the random variables characterizing the proposed estimators as a function of the SNR. Results indicate a probability of detection close to 1 and show good performance, even for scenarios with a SNR slightly less than \u221210 dB. The contributions in this work offer enhancements to noise radar capabilities while facilitating improvements in ESM systems.<\/jats:p>","DOI":"10.3390\/s24082532","type":"journal-article","created":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T10:24:26Z","timestamp":1713176666000},"page":"2532","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On a Closer Look of a Doppler Tolerant Noise Radar Waveform in Surveillance Applications"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8953-4935","authenticated-orcid":false,"given":"Maximiliano","family":"Barbosa","sequence":"first","affiliation":[{"name":"Brazilian Navy Weapons Systems Directorate, Rio de Janeiro 20010-000, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3153-8757","authenticated-orcid":false,"given":"Leandro","family":"Pralon","sequence":"additional","affiliation":[{"name":"Brazilian Army Technological Center, Rio de Janeiro 23020-470, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3584-8701","authenticated-orcid":false,"given":"Antonio L. L.","family":"Ramos","sequence":"additional","affiliation":[{"name":"Department of Science and Industry Systems, University of South-Eastern Norway (USN), 3616 Kongsberg, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1426-9636","authenticated-orcid":false,"suffix":"Jr.","given":"Jos\u00e9 Antonio","family":"Apolin\u00e1rio","sequence":"additional","affiliation":[{"name":"Military Institute of Engineering, Rio de Janeiro 22290-270, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,15]]},"reference":[{"key":"ref_1","unstructured":"Neri, F. (2018). Introduction to Electronic Defense Systems, Artech House. [3rd ed.]."},{"key":"ref_2","unstructured":"Kulpa, K. (2013). Signal Processing in Noise Waveform Radar, Artech House."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1109\/TAES.2013.6404130","article-title":"Range-Doppler resolution of the linear-FM noise radar waveform","volume":"49","author":"Govoni","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Galati, G., Pavan, G., and De Palo, F. (2014, January 16\u201318). Noise radar technology: Pseudorandom waveforms and their information rate. Proceedings of the 15th International Radar Symposium (IRS), Gdansk, Poland.","DOI":"10.1109\/IRS.2014.6869191"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Pralon, L., Beltr\u00e3o, G., Barreto, A., and Cosenza, B. (2021). On the analysis of PM\/FM noise radar waveforms considering modulating signals with varied stochastic properties. Sensors, 21.","DOI":"10.3390\/s21051727"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Savci, K., Galati, G., and Pavan, G. (2021). Low-PAPR waveforms with shaped spectrum for enhanced low probability of intercept noise radars. Remote Sens., 13.","DOI":"10.3390\/rs13122372"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Palo, F.D., Galati, G., Pavan, G., Wasserzier, C., and Savci, K. (2020). Introduction to noise radar and its waveforms. Sensors, 20.","DOI":"10.3390\/s20185187"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/MAES.2020.2990591","article-title":"Noise Radar\u2014Overview and Recent Developments","volume":"35","author":"Savci","year":"2020","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Stove, A.G., Lukin, K.A., and Orlenko, V.M. (2022, January 12\u201314). Analysis of Partially Deterministic Waveforms in Noise Radar Applications. Proceedings of the 23rd International Radar Symposium (IRS), Gdansk, Poland.","DOI":"10.23919\/IRS54158.2022.9904992"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Galati, G., Pavan, G., and Wasserzier, C. (2022, January 12\u201314). Interception of Continuous-Emission Noise Radars Transmitting Different Waveform Configurations. Proceedings of the 23rd International Radar Symposium (IRS), Gdansk, Poland.","DOI":"10.23919\/IRS54158.2022.9904981"},{"key":"ref_11","unstructured":"Martino, A.D. (2018). Introduction to Modern EW Systems, Artech House. [2nd ed.]."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Galati, G., Pavan, G., De Palo, F., and Stove, A. (2016, January 10\u201312). Potential applications of noise radar technology and related waveform diversity. Proceedings of the 2016 17th International Radar Symposium (IRS), Krakow, Poland.","DOI":"10.1109\/IRS.2016.7497329"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Galati, G., Pavan, G., Savci, K., and Wasserzier, C. (2021). Counter-interception and counter-exploitation features of noise radar technology. Remote Sens., 13.","DOI":"10.3390\/rs13224509"},{"key":"ref_14","unstructured":"Lukin, K., Kulyk, V., and Zemlyaniy, O. (2002, January 18\u201320). Application of dynamical chaos for design of random waveform generators. Proceedings of the Noise Radar Technology Workshop, Yalta, Ukraine."},{"key":"ref_15","unstructured":"Thayaparan, T., and Wernik, C. (2006). Noise Radar Technology Basics, Defense Research and Development. Technical Report."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2370","DOI":"10.1109\/TGRS.2004.834589","article-title":"Noise radar using random phase and frequency modulation","volume":"42","author":"Axelsson","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1049\/ip-rsn:20030702","article-title":"Generalised wideband ambiguity function of a coherent ultrawideband random noise radar","volume":"150","author":"Dawood","year":"2003","journal-title":"IEE Proc.-Radar Sonar Navig."},{"key":"ref_18","unstructured":"Pralon, L., Pompeo, B., Beltr\u00e3o, G., Cioqueta, H., Cosenza, B., and Fortes, J.M. (November, January 31). Random phase\/frequency modulated waveforms for noise radar systems considering phase shift. Proceedings of the 2012 9th European Radar Conference, Amsterdam, The Netherlands."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Pralon, L., Beltr\u00e3o, G., Pompeo, B., Pralon, M., and Fortes, J.M. (2017, January 8\u201312). Near-thumbtack ambiguity function of random frequency modulated signals. Proceedings of the 2017 IEEE Radar Conference (RadarConf), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944226"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1109\/TAES.2013.6494419","article-title":"Low Probability of Interception of an Advanced Noise Radar Waveform with Linear-FM","volume":"49","author":"Govoni","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Govoni, M.A., and Elwell, R.A. (2014, January 19\u201323). Radar spectrum spreading using Advanced Pulse Compression Noise (APCN). Proceedings of the IEEE Radar Conference, Cincinnati, OH, USA.","DOI":"10.1117\/12.2051347"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Barbosa, M., Pralon, L., and Apolin\u00e1rio, J. (2022, January 12\u201314). Slow-Moving Target Detection Performance of an LPI APCN Waveform in Surveillance Applications. Proceedings of the 23rd International Radar Symposium (IRS), Gdansk, Poland.","DOI":"10.23919\/IRS54158.2022.9905033"},{"key":"ref_23","unstructured":"Pace, P. (2009). Detecting and Classifying Low Probability of Intercept Radar, Arthech House. [2nd ed.]."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Gupta, A., and Bazil Rai, A.A. (2019, January 17\u201318). Feature Extraction of Intra-Pulse Modulated LPI Waveforms Using STFT. Proceedings of the 4th International Conference on Recent Trends on Electronics, Information, Communication Technology (RTEICT), Bangalore, India.","DOI":"10.1109\/RTEICT46194.2019.9016799"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Shyamsunder, M., Subbarao, K., Regimanu, B., and Teja, C.K. (2016, January 9\u201311). Estimation of modulation parameters for LPI radar using Quadrature Mirror Filter Bank. Proceedings of the IEEE Uttar Pradesh Section International Conference on Electrical, Computer and Electronics Engineering (UPCON), Varanasi, India.","DOI":"10.1109\/UPCON.2016.7894659"},{"key":"ref_26","first-page":"9","article-title":"Detection and Parameter Extraction of Low Probability of Intercept Radar Signals using the Hough Transform","volume":"15","author":"Stevens","year":"2016","journal-title":"Glob. J. Res. Eng."},{"key":"ref_27","unstructured":"Yu Gau, J. (2002). Analysis of Low Probability of Intercept (LPI) Radar Signals Using the Wigner Distribution. [Master\u2019s Thesis, Naval Postgraduate School]."},{"key":"ref_28","unstructured":"Jarpa, P. (2002). Quantifying the Differences in Low Probability of Intercept Radar Waveforms Using Quadrature Mirror Filtering. [Master\u2019s Thesis, Naval Postgraduate School]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2003515","DOI":"10.1109\/TIM.2021.3060584","article-title":"FPGA-Based Wigner\u2013Hough Transform System for Detection and Parameter Extraction of LPI Radar LFMCW Signals","volume":"70","author":"Guner","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1109\/TAES.2017.2650518","article-title":"FMCW Signal Detection and Parameter Extraction by Cross Wigner\u2013Hough Transform","volume":"53","author":"Erdogan","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_31","unstructured":"Gulum, T.O., Pace, P.E., and Cristi, R. (April, January 31). Extraction of polyphase radar modulation parameters using a Wigner-Ville distribution\u2014Radon transform. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Las Vegas, NV, USA."},{"key":"ref_32","unstructured":"Boashash, B. (2016). Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Elsevier. [2nd ed.]."},{"key":"ref_33","unstructured":"Popoulis, A., and Pillai, S.U. (1991). Probability, Random Variables, and Stochastic Processes, McGraw-Hill."},{"key":"ref_34","unstructured":"Richards, M.A. (2022). Fundamentals of Radar Signal Processing, McGraw-Hill. [3rd ed.]."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Galati, G., Pavan, G., Savci, K., and Wasserzier, C. (2021). Noise radar technology: Waveforms design and field trials. Sensors, 21.","DOI":"10.3390\/s21093216"},{"key":"ref_36","unstructured":"Oppenheim, A.V., and Schafer, W.R. (2014). Discrete-Time Signal Processing, Pearson. [3rd ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1109\/LSP.2004.831663","article-title":"Generalization of spectral flatness measure for non-Gaussian linear processes","volume":"11","author":"Dubnov","year":"2004","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3813","DOI":"10.1109\/TAES.2021.3088501","article-title":"Subpulse Processing for Unambiguous Doppler Estimation in Pulse-Doppler Noise Radars","volume":"57","author":"Pralon","year":"2021","journal-title":"IEEE TRansactions Aerosp. Electron. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1109\/TAES.2014.140072","article-title":"Stochastic analysis of random frequency modulated waveforms for noise radar systems","volume":"51","author":"Pralon","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_40","unstructured":"Robertson, S. (2019). Practical ESM Analysis, Artech House."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Tsui, J.B. (2015). Digital Techniques for Wideband Receivers, SciTech Publishing.","DOI":"10.1049\/SBRA511E"},{"key":"ref_42","unstructured":"Cohen, L. (1995). Time-Frequency Analysis, Prentice Hall."},{"key":"ref_43","unstructured":"Smith, J.O. (2011). Spectral Audio Signal Processing, W3K."},{"key":"ref_44","unstructured":"Gonzalez, R.C., and Woods, R.E. (2008). Digital Image Processing, Pearson Prentice Hall. [2nd ed.]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1145\/361237.361242","article-title":"Use of the Hough transformation to detect lines and curves in pictures","volume":"15","author":"Duda","year":"1972","journal-title":"Commun. ACM"},{"key":"ref_46","unstructured":"Parker, J.R. (2010). Algorithms for Image Processing and Computer Vision, John Wiley & Sons."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1109\/TSMC.1979.4310076","article-title":"A Threshold Selection Method from Gray-Level Histograms","volume":"9","author":"Otsu","year":"1979","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_48","first-page":"46","article-title":"Performance standards for wideband EW receivers","volume":"32","author":"Tsui","year":"1989","journal-title":"Microw. J."},{"key":"ref_49","first-page":"99","article-title":"Receiver dynamic range. II\u2014Use one figure of merit to compare all receivers","volume":"26","author":"Watson","year":"1987","journal-title":"Microwaves"},{"key":"ref_50","unstructured":"Figueir\u00eado, R. (2019). Approaches for Analysis and Extraction of LPI Radar Features. [Master\u2019s Thesis, Postgraduate Program in Electrical Engineering, COPPE, UFRJ]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/8\/2532\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:28:15Z","timestamp":1760106495000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/8\/2532"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,15]]},"references-count":50,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["s24082532"],"URL":"https:\/\/doi.org\/10.3390\/s24082532","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,15]]}}}