Counter-Interception and Counter-Exploitation Features of Noise Radar Technology
Abstract
:1. Introduction
2. Pseudo-Random Numbers Generators and Cryptography Security
3. Information Content of Radar Signals
3.1. Mutual Information of a Random Process
3.2. On the Significance of MIR and SFM in Radar
- (a)
- Linear Frequency Modulation (LFM) pulse with duration such that .
- (b)
- Noise Radar operation emitting noise waveforms with three cases:
- (b1)
- “natural” Peak-to-Average Power Ratio, (Gaussian process for the components I and Q);
- (b2)
- “low ”, e.g., (non-Gaussian process for I and Q);
- (b3)
- “unimodular” waveform, (non-Gaussian process for I and Q).
4. Estimation of Entropy and Mutual Information by Simulation
4.1. “Natural” PAPR (Gaussian Process)
4.2. Controlled PAPR (Non-Gaussian Process)
5. Conclusions, Recommendations and Perspectives for Future Research
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Appendix A
Appendix A.1. Entropy and Negentropy
Appendix A.2. Self-Information and Mutual-Information
Appendix B
Definition of a Second-Order Stationary (SOS) Process
- (i)
- it is WSS, i.e., is constant and the covariance function only depends on the index difference , i.e.,;
- (i)
- the pseudo covariance function only depends on the index difference , i.e., .
Appendix C
function E = EntropyEstimationHist(X1)
| function E = EntropyEstimationHist2D(X1,X2)
|
h = histogram(X1); | h = histogram2(X,X2); |
x = h.BinEdges; | x = h.XBinEdges; |
BinCount = h.BinCounts; | y = h.YBinEdges; |
zero = find(BinCount == 0); | stepx = x(2) − x(1); |
for k = 1:length(zero)
| stepy = y(2) − y(1); |
BinCount(zero(k)) = 1e − 18; | BinCount = h.BinCounts; |
end
| zero = find(BinCount == 0); |
BinCount = BinCount/sum(BinCount); | for k = 1:length(zero)
|
step = x(2) − x(1); | BinCount(zero(k)) = 1e − 18; |
E = log(step) − sum(BinCount.*log(BinCount)); |
end
|
end
| BinCount = BinCount/sum(sum(BinCount)); |
E = log(stepx*stepy) − sum(sum(BinCount.*log(BinCount))); | |
end
|
References
- Farina, A.; Galati, G. Surveillance radars: State of the art, research and perspectives. In Optimised Radar Processors; IET Press: London, UK, 1987; ISBN 9781849191760. [Google Scholar] [CrossRef]
- Farina, A. Electronic Counter-Counter Measures, Chapter 9. In Radar Handbook, 2nd ed.; Skolnik, M.I., Ed.; Mc. Graw Hill: New York, NY, USA, 1990. [Google Scholar]
- Li, N.-J.; Zhang, Y.-T. A Survey of Radar ECM and ECCM. IEEE Trans. Aerosp. Electron. Syst. 1995, 31, 1110–1120. [Google Scholar] [CrossRef]
- Guerci, J.R. Cognitive radar: A knowledge-aided fully adaptive approach. In Proceedings of the 2010 IEEE Radar Conference, Arlington, VA, USA, 10–14 May 2010; pp. 1365–1370. [Google Scholar] [CrossRef]
- Haykin, S.; Xue, Y.; Setoodeh, P. Cognitive radar: Step toward bridging the gap between neuroscience and engineering. Proc. IEEE 2012, 100, 3102–3130. [Google Scholar] [CrossRef]
- Aberman, K.; Aviv, S.; Eldar, Y.C. Adaptive frequency allocation in radar imaging: Towards cognitive SAR. In Proceedings of the 2010 IEEE Radar Conference, Seattle, WA, USA, 8–12 May 2017; pp. 1348–1351. [Google Scholar] [CrossRef]
- Horne, C.; Ritchie, M.; Griffiths, H. Proposed ontology for cognitive radar systems. IET Radar Sonar Navig. 2018, 12, 1363–1370. [Google Scholar] [CrossRef]
- Mitchell, A.E.; Garry, J.L.; Duly, A.J.; Smith, G.E.; Bell, K.L.; Rangaswamy, M. Fully Adaptive Radar for Variable Resolution Imaging. IEEE Trans. Geosci. Remote Sens. 2019, 57, 9810–9819. [Google Scholar] [CrossRef]
- Lang, Y.-C. Dynamic Spectrum Management—From Cognitive Radio to Blockchain and Artificial Intelligence; Springer: Berlin/Heidelberg, Germany, 2020. [Google Scholar] [CrossRef] [Green Version]
- Sidiropoulos, N.D.; De Lathauwer, L.; Fu, X.; Wang, K.; Papalexakis, E.E. Tensor Decomposition for Signal Processing and Machine Learning. IEEE Trans. Signal Process. 2017, 65, 3551–3582. [Google Scholar] [CrossRef]
- Chiriyath, A.R.; Paul, B.; Bliss, D.W. Radar-Communications Convergence: Coexistence, Cooperation, and Co-Design. IEEE Trans. Cogn. Commun. Netw. 2017, 3. [Google Scholar] [CrossRef]
- Liu, F.; Zhou, L.; Masouros, C.; Li, A.; Luo, W.; Petropulu, A. Toward Dual-functional Radar-Communication Systems: Optimal Waveform Design. IEEE Trans. Signal Process. 2018, 66, 4264–4279. [Google Scholar] [CrossRef] [Green Version]
- Oroian, T.C.; Enache, F.; Ciotirnae, P. Some considerations about third-order statistics for different types of radar signals. In Proceedings of the 10th Intern. Symposium on Advanced Topics in Electrical Engineering (ATEE), Bucharest, Romania, 23–25 March 2017. [Google Scholar] [CrossRef]
- Aly, O.A.M.; Omar, A.S. Detection and localization of RF radar pulses in noise environments using wavelet packet transform and higher order statistics. Prog. Electromagn. Res. PIER 2006, 58, 301–317. [Google Scholar]
- Barbarossa, S. Parameter estimation of undersampled signals by Wigner–Ville analysis. IEEE Conf. Acoust. Speech Signal Process. ICASSP 91 2002, 5, 3944–3947. [Google Scholar]
- Gulum, T.O.; Pace, P.E.; Cristi, R. Extraction of Polyphase Radar Modulation Parameters Using a Wigner-Ville Distribution Radon Transform. In Proceedings of the IEEE International Conf. on Acoustics, Speech and Signal Processing, Las Vegas, NV, USA, 31 March–4 April 2008. [Google Scholar] [CrossRef]
- Copeland, D.B.; Pace, P.E. Detection and analysis of FMCW and P-4 polyphase LPI waveforms using quadrature mirror filter trees. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Orlando, FL, USA, 13–17 May 2002; pp. IV-3960–IV-3963. [Google Scholar] [CrossRef]
- Roberts, R.S.; Brown, W.A.; Loomis, H.H. Computationally efficient algorithms for cyclic spectral analysis. IEEE Signal Process. Mag. 1991, 8, 38–49. [Google Scholar] [CrossRef]
- Hejazi Kookamari, F.; Norouzi, Y.; Nayebi, M.M. Using a moving aerial platform to detect and localise a low probability of intercept radar. IET Radar Sonar Navig. 2017, 11, 1062–1069. [Google Scholar] [CrossRef]
- Hejazi Kookamari, F.; Norouzi, Y.; Kashani, E.S.; Nayebi, M.M. A Novel Method to Detect and Localize LPI Radars. IEEE Trans. Aerosp. Electron. Syst. 2019, 55, 2327–2336. [Google Scholar] [CrossRef]
- Kong, S.H.; Kim, M.; Hoang, L.M.; Kim, E. Automatic LPI radar waveform recognition using CNN. IEEE Access 2018, 6, 4207–4219. [Google Scholar] [CrossRef]
- Liu, G.S.; Gu, H.; Su, W.M.; Sun, H.B. The analysis and design of modern Low Probability of Intercept radar. In Proceedings of the 2001 CIE International Conference on Radar Proceedings (Cat No.01TH8559), Beijing, China, 15–18 October 2001; pp. 120–124. [Google Scholar] [CrossRef]
- Wirth, W.D. Omni directional low probability of intercept radar. In Proceedings of the International Conference on Radar 89, Paris, France, 24–28 April 1989; Volume 1 (A90-40951 18-32), pp. 25–30. [Google Scholar]
- Wirth, W.D. Long term coherent integration for a floodlight radar. In Proceedings of the IEEE 1995 International Radar Conference, Alexandria, VA, USA, 8–11 May 1995; pp. 698–703. [Google Scholar] [CrossRef]
- Schleher, D.C. Low probability of intercept radar. In Proceedings of the International Radar Conference, Arlington, VA, USA, 6–9 May 1985; Record (A86-32576 14-32). Institute of Electrical and Electronics Engineers, Inc.: New York, NY, USA, 1985; pp. 346–349. [Google Scholar]
- Burgos-Garcia, M.; Sanmartin-Jara, J. A LPI tracking radar system based on frequency hopping. In Proceedings of the International Radar Symposium, Munich, Germany, 15–17 September 1998; pp. 151–159. [Google Scholar]
- Gross, F.B.; Chen, K. Comparison of detectability of traditional pulsed and spread spectrum radar waveforms in classic passive receivers. IEEE Trans. Aerosp. Electron. Syst. 2005, 41, 746–751. [Google Scholar] [CrossRef]
- Wang, W. Potential transmit beamforming schemes for active LPI radars. IEEE Aerosp. Electron. Syst. Mag. 2017, 32, 46–52. [Google Scholar] [CrossRef]
- Pace, P.E. Detecting and Classifying Low Probability of Intercept Radar, 2nd ed.; Artech House Remote Sensing Library: Norwood, MA, USA, 2008. [Google Scholar]
- Gao, L.; Liu, L.; Cao, Y.; Wang, S.; You, S. Performance analysis of one-step prediction-based cognitive jamming in jammer-radar countermeasure model. J. Eng.-IET 2019, 21, 7958–7961. [Google Scholar] [CrossRef]
- Bachmann, D.J.; Evans, R.J.; Moran, B. Game theoretic analysis of adaptive radar jamming. IEEE Trans. Aerosp. Electron. Syst. 2011, 47, 1081–1100. [Google Scholar] [CrossRef]
- Zhou, H.; Guo, L. Self-adaptive frequency agility realized with FPGA. In Proceedings of the International Conference on Image Analysis and Signal Processing, Taizhou, China, 11–12 April 2009; pp. 419–422. [Google Scholar] [CrossRef]
- Talbot, K.I.; Duley, P.R.; Hyatt, M.H. Specific Emitter Identification and Verification. Technol. Rev. J. 2003, pp. 113–133. Available online: http://jmfriedt.org/phase_digital/03SS_KTalbot.pdf (accessed on 22 September 2021).
- Anjaneyulu, L.; Sarma, N.V.; Murthy, N.S. Identification of LPI radar signals by higher order spectra and neural network techniques. Int. J. Inf. Commun. Technol. 2009, 2, 142–155. [Google Scholar] [CrossRef]
- Kawalec, A.; Owczarek, R. Specific emitter identification using intrapulse data. In Proceedings of the First European Radar Conference, EURAD, Amsterdam, The Netherlands, 14–15 October 2004; pp. 249–252. [Google Scholar]
- D’Agostino, S.; Foglia, G.; Pistoia, D. Specific Emitter Identification: Analysis on real radar signal data. In Proceedings of the European Radar Conference (EuRAD), Rome, Italy, 30 September–2 October 2009; pp. 242–245. [Google Scholar]
- NEWEG-Electronic Warfare Signal Environment by Naval Air Systems Command (US Navy)–EW Simulation and Stimulation. Available online: https://www.navair.navy.mil/nawctsd/sites/g/files/jejdrs596/files/2019-07/2016-neweg.pdf (accessed on 5 November 2021).
- Vankka, J. Digital frequency synthesizer/modulator for continuous-phase modulation with slow fequency hopping. IEEE Trans. Veh. Technol. 1997, 46, 933–940. [Google Scholar] [CrossRef]
- Modarres-Hashemi, M.; Nayebi, M.M. LPD feature improvement in random PRF radar signals. IEE Proc. Radar Sonar Navig. 2004, 151, 225–230. [Google Scholar] [CrossRef]
- De Martino, A. Introduction to Modern EW Systems, 2nd ed.; Artech House Inc.: Norwood, MA, USA, 2018. [Google Scholar]
- Zhi, Z.M.; Li, H.A.; Huang, G. LPI Radar Waveform Recognition Based on Features from Multiple Images. Sensors 2020, 20, 526. [Google Scholar] [CrossRef] [Green Version]
- Liu, G.; Gu, H.; Su, W. The development of random signal radar. IEEE Trans. Aerosp. Electron. Syst. 1999, 35, 770–777. [Google Scholar]
- Liu, G.; Shi, X.; Lu, J.; Yang, G.; Song, Y. Design of noise FM CW radar and its implementation. IEE Proc. Radar Sonar Navig. 1991, 138, 420–426. [Google Scholar]
- Hong, G.; Guosui, L.; Xiaohua, Z. The study of the random binary phase coded CW radar system. Acta Electron. Sin. 1995, 23, 71–74. [Google Scholar]
- Wasserzier, C.; Worms, J.G.; O’Hagan, D.W. How Noise Radar Technology Brings Together Active Sensing and Modern Electronic Warfare Techniques in a Combined Sensor Concept. In Proceedings of the Sensor Signal Processing for Defence Conference, Brighton, UK, 9–10 May 2019. [Google Scholar] [CrossRef]
- Matsumoto, M.; Nishimura, T. Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator. ACM Trans. Model. Comput. Simul. 1998, 8, 3–30. [Google Scholar] [CrossRef] [Green Version]
- Vigna, S. It is high time we let go of the Mersenne Twister. Comput. Sci. Data Struct. Algorithms 2019, arXiv:1910.06437. Available online: https://arxiv.org/pdf/1910.06437 (accessed on 5 November 2021).
- NIST Special Publication (SP) 800-90B. Recommendation for the Entropy Sources Used for Random Bit Generation; 100 Bureau Drive: Gaithersburg, MD, USA, 2018. [Google Scholar] [CrossRef]
- Park, S.; Choi, B.G.; Kang, T.; Park, K.; Kwon, Y.; Kim, J. Efficient hardware implementation and analysis of true random-number generator based on beta source. ETRI J. Spec. Issue SoC AI Process. 2020, 42, 518–526. [Google Scholar] [CrossRef]
- Park, K.; Park, S.; Choi, B.G.; Kang, T.; Kim, J.; Kim, Y.H.; Jin, H.Z. A lightweight true random number generator using beta radiation for IoT applications. ETRI J. 2020, 42, 951–964. [Google Scholar] [CrossRef]
- Ferguson, N.; Schneier, B. Practical Cryptography; Wiley & Sons, Inc.: Hoboken, NJ, USA, 2003; ISBN 978-0-471-22357-3. [Google Scholar]
- Gopala, P.; Lai, L.; El Gamal, H. On the Secrecy Capacity of Fading Channels. IEEE Trans. Inf. Theory 2008, 54, 4687–4698. [Google Scholar] [CrossRef] [Green Version]
- Negi, R.; Goel, S. Guaranteeing secrecy using artificial noise. IEEE Trans. Wirel. Commun. 2008, 7, 2180–2189. [Google Scholar] [CrossRef]
- Liang, Y.; Poor, V.; Shamai, S. Secure Communication Over Fading Channels. IEEE Trans. Inf. Theory 2008, 54, 2470–2492. [Google Scholar] [CrossRef] [Green Version]
- Atzori, L.; Ferrari, G. Internet of Things: Technologies, Challenges and Impact; CNIT Technical Report-05; Texmat. 2020. ISBN Print Version 9788894982381, Digital Version 9788894982398. Available online: https://www.texmat.it/collana-cnit.html (accessed on 22 September 2021).
- Suo, H.; Wan, J.; Zou, C.; Liu, J. Security in the Internet of Things: A Review. In Proceedings of the 2012 International Conference on Computer Science and Electronics Engineering, Hangzhou, China, 23–25 March 2012; pp. 648–651. [Google Scholar] [CrossRef]
- Available online: http://web.mit.edu/6.933/www/Fall2000/mode-s/sidelobe.html (accessed on 5 November 2021).
- Smoll, A.E. Radar Beacon System with Side Lobe Suppression. U.S. Patent 2,966,675, 23 October 1957. [Google Scholar]
- Cover, T.M.; Thomas, J.A. Elements of Information Theory, 2nd ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2006. [Google Scholar]
- Papoulis, A.; Pillai, S.U. Probability, Random Variables and Stochastic Processes, 4th ed.; McGraw-Hill: New York, NY, USA, 2002; Chapter 14. [Google Scholar]
- Bell, M.R. Information Theory and Radar Waveform Design. IEEE Trans. Inf. Theory 1993, 39, 1578–1597. [Google Scholar] [CrossRef] [Green Version]
- Levanon, N.; Mozeson, E. Radar Signals; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2004. [Google Scholar]
- Neeser, F.D.; Massey, J.L. Proper Complex Random Processes with Applications to Information Theory. IEEE Trans. Inf. Theory 1993, 39, 1293–1302. [Google Scholar] [CrossRef] [Green Version]
- Picinbono, B.; Bondon, P. Second-Order Statistics of Complex Signals. IEEE Trans. Signal Process. 1997, 45, 411–420. [Google Scholar] [CrossRef] [Green Version]
- Xiong, W.; Li, H.; Adali, T.; Li, Y.O.; Calhoun, V.D. On Entropy Rate for the Complex Domain and Its Application to i.i.d. Sampling. IEEE Trans. Signal Process. 2010, 58, 2409–2414. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Dubnov, S. Generalization of Spectral Flatness Measure for Non-Gaussian Linear Processes. IEEE Signal Process. Lett. 2004, 11, 698–701. [Google Scholar] [CrossRef]
- Tohidi, E.; Nazari Majd, M.; Bahadori, M.; Jariani, H.H.; Nayebi, M.M. Periodicity in Contrast with Sidelobe Suppression in Random Signal Radars. In Proceedings of the IEEE CIE International Conference on Radar, Chengdu, China, 24–27 October 2011; pp. 442–445. [Google Scholar]
- De Palo, F.; Galati, G.; Pavan, G.; Wasserzier, C.; Savci, K. Introduction to Noise Radar and its Waveforms. Sensors 2020, 20, 5187. [Google Scholar] [CrossRef] [PubMed]
- Schrödinger, E. What is Life—The Physical Aspect of the Living Cell; Cambridge University Press: Cambridge, UK, 1944. [Google Scholar]
- Hyvarinen, A. New Approximations of Differential Entropy for Independent Component Analysis and Projection Pursuit. In Advances in Neural Information Processing Systems; MIT Press: Cambridge, MA, USA, 1998; pp. 273–279. Available online: http://papers.nips.cc/paper/1408-new-approximations-of-differential-entropy-for-independent-component-analysis-and-projection-pursuit.pdf (accessed on 5 November 2021).
- Bellman, R.E. Adaptive Control Processes; Princeton University Press: Princeton, NJ, USA, 1961. [Google Scholar]
Spectrum | MIR | SFM |
---|---|---|
Uniform | 0.00 | 1.00 |
Hamming | 0.272 | 0.580 |
Black-Nuttall | 1.258 | 0.081 |
Spectrum | by histogram | by histogram | ||||||
Uniform | 0.5 | 1.0724 | 0.5004 | 0.5013 | 1.0727 | 1.0737 | 1.0723 | 1.0732 |
Hamming | 0.5 | 1.0724 | 0.5002 | 0.4994 | 1.0725 | 1.0718 | 1.0722 | 1.0718 |
Black-Nuttall | 0.5 | 1.0724 | 0.4974 | 0.4970 | 1.0697 | 1.0703 | 1.0692 | 1.0697 |
Spectrum | by 2D hist. | by 2D hist. | ||||||
Uniform | 0 | 5.3·10−5 | 2.1447 | 2.1447 | 2.1345 | 0 | 1.4·10−9 | 0.0111 |
Hamming | 0.4258 | 0.4267 | 2.0447 | 2.0443 | 2.0338 | 0.10002 | 0.1005 | 0.1099 |
Black-Nuttall | 0.6727 | 0.6681 | 1.8435 | 1.8491 | 1.8366 | 0.3013 | 0.2956 | 0.3024 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Galati, G.; Pavan, G.; Savci, K.; Wasserzier, C. Counter-Interception and Counter-Exploitation Features of Noise Radar Technology. Remote Sens. 2021, 13, 4509. https://doi.org/10.3390/rs13224509
Galati G, Pavan G, Savci K, Wasserzier C. Counter-Interception and Counter-Exploitation Features of Noise Radar Technology. Remote Sensing. 2021; 13(22):4509. https://doi.org/10.3390/rs13224509
Chicago/Turabian StyleGalati, Gaspare, Gabriele Pavan, Kubilay Savci, and Christoph Wasserzier. 2021. "Counter-Interception and Counter-Exploitation Features of Noise Radar Technology" Remote Sensing 13, no. 22: 4509. https://doi.org/10.3390/rs13224509