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New Trends in Chaos-Based Communications and Signal Processing

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A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 22))

Abstract

In the last decades many possible applications of nonlinear dynamics in communication systems and signal processing have been reported. Conversely, techniques usually employed by the signal processing and communication systems communities, as correlation, power spectral density analysis, and linear filters, among others have been used to characterize chaotic dynamical systems. This chapter presents four works that aim to use tools from both fields to generate new and interesting results: (1) a message authentication system based on chaotic fingerprint; (2) a study of the spectral characteristics of the chaotic orbits of the Hénon map; (3) an investigation of the chaotic nature of the signals generated by a filtered Hènon map, and (4) a communication system that presents equalization and a switching scheme between chaos-based and conventional modulations.

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References

  1. Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64, 821–824.

    Article  MathSciNet  Google Scholar 

  2. Ott, E., Grebogi, C., & Yorke, J. A. (1990) Controlling chaos. Physical Review Letters, 64, 1196–1199.

    Article  MathSciNet  Google Scholar 

  3. Lau, F. C. M., & Tse, C. K. (2003) Chaos-based digital communication systems. Berlin: Springer.

    Book  Google Scholar 

  4. Kennedy, M. P., Setti, G., & Rovatti, R. (Eds.). (2000). Chaotic electronics in telecommunications. Boca Raton, FL: CRC Press.

    Google Scholar 

  5. Eisencraft, M., Attux, R. R. F., & Suyama, R. (Eds.). (2013). Chaotic signals in digital communications (electrical engineering & applied signal processing series). Boca Raton, FL: CRC Press.

    Google Scholar 

  6. Fontes, R. T., & Eisencraft, M. (2016). A digital bandlimited chaos-based communication system. Communications in Nonlinear Science and Numerical Simulation, 37, 374–385.

    Article  MathSciNet  Google Scholar 

  7. Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fischer, I., García-Ojalvo, J., Mirasso, C. R., Pesquera, L., & Shore, K. A. (2005). Chaos-based communications at high bit rates using commercial fibre-optic links. Nature, 438, 343–346.

    Article  Google Scholar 

  8. Ren, H.-P., Baptista, M. S., & Grebogi, C. (2013). Wireless communication with chaos. Physical Review Letters, 110, 184101.

    Article  Google Scholar 

  9. Michaels, A. J., & Lau, C. (2014). Generalized multi-carrier chaotic shift keying. In 2014 IEEE Military Communications Conference (pp. 657–662). .

    Google Scholar 

  10. Kaddoum, G. (2016). Wireless chaos-based communication systems: A comprehensive survey. IEEE Access, 4, 2621–2648

    Article  Google Scholar 

  11. Hénon, M. (1976). A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics, 50, 94–102.

    Article  MathSciNet  Google Scholar 

  12. Eisencraft, M., Fanganiello, R. D., & Baccalá, L. A. (2009). Synchronization of discrete-time chaotic systems in bandlimited channels. Mathematical Problems in Engineering, 2009, 1–12.

    Article  Google Scholar 

  13. Paar, C., & Pelzl, J. (2011). Understanding cryptography. Berlin: Springer.

    MATH  Google Scholar 

  14. Jorswieck, E., Tomasin, S., & Sezgin, A. (2015). Broadcasting into the uncertainty: Authentication and confidentiality by physical-layer processing. Proceedings of the IEEE, 103, 1702–1724.

    Article  Google Scholar 

  15. Yu, P. L., Baras, J. S., & Sadler, B. M. (2008). Physical-layer authentication. IEEE Transactions on Information Forensics and Security, 3, 38–51.

    Article  Google Scholar 

  16. Verma, G., Yu, P., & Sadler, B. M. (2015). Physical layer authentication via fingerprint embedding using software-defined radios. IEEE Access, 3, 81–88.

    Article  Google Scholar 

  17. Goergen, N. S., Lin, W. S., Liu, K. J. R., & Clancy, T. C. (2011). Extrinsic channel-like fingerprinting overlays using subspace embedding. IEEE Transactions on Information Forensics and Security, 6, 1355–1369.

    Article  Google Scholar 

  18. Alligood, K. T., Sauer, T. D., & Yorke, J. A. (2000). Chaos. Textbooks in mathematical sciences. New York: Springer.

    Google Scholar 

  19. Strogatz, S. H. (2001) Nonlinear dynamics and chaos. Boulder, CO: The Perseus Books Group.

    Google Scholar 

  20. Maurer, U. M. (2000). Authentication theory and hypothesis testing. IEEE Transactions on Information Theory, 46, 1350–1356.

    Article  MathSciNet  Google Scholar 

  21. Lathi, B. P., & Ding, Z. (2009). Modern digital and analog communication systems. The Oxford series in electrical and computer engineering. Oxford: Oxford University Press.

    Google Scholar 

  22. Sakai, H., & Tokumaru, H. (1980). Autocorrelations of a certain chaos. IEEE Transactions on Acoustics, Speech, and Signal Processing, 28, 588–590.

    Article  MathSciNet  Google Scholar 

  23. Eisencraft, M., Kato, D. M., & Monteiro, L. H. A. (2010). Spectral properties of chaotic signals generated by the skew tent map. Signal Processing, 90, 385–390.

    Article  Google Scholar 

  24. Feltekh, K., Fournier-Prunaret, D., & Belghith, S. (2014). Analytical expressions for power spectral density issued from one-dimensional continuous piecewise linear maps with three slopes. Signal Processing, 94, 149–157.

    Article  Google Scholar 

  25. Costa, R. A., Loiola, M. B., & Eisencraft, M. (2015). Spectral properties of chaotic signals generated by the Bernoulli map. Journal of Engineering Science and Technology Review, 8(2), 12–16.

    Google Scholar 

  26. Costa, R. A., Loiola, M. B., & Eisencraft, M. (2017) Correlation and spectral properties of chaotic signals generated by a piecewise-linear map with multiple segments. Signal Processing, 133, 187–191.

    Article  Google Scholar 

  27. Lasota, A., & Mackey, M. C. (1985). Probabilistic properties of deterministic systems. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  28. Proakis, J. G., & Manolakis, D. K. (2006) Digital Signal Processing (4th ed.). London: Pearson.

    Google Scholar 

  29. Baptista, M. S., Macau, E. E., Grebogi, C., Lai, Y.-C., & Rosa, E. (2000). Integrated chaotic communication scheme. Physical Review E, 62, 4835–4845.

    Article  Google Scholar 

  30. Wu, C. W., & Chua, L. O. (1993). A simple way to synchronize chaotic systems with applications to secure communication systems. International Journal of Bifurcation and Chaos, 03, 1619–1627.

    Article  Google Scholar 

  31. Oppenheim, A. V., & Schafer, R. W. (2009) Discrete-time signal processing (3rd ed.). Upper Saddle River, NJ: Addison Wesley.

    MATH  Google Scholar 

  32. Eisencraft, M., Fanganiello, R. D., & Monteiro, L. H. A. (2011). Chaotic synchronization in discrete-time systems connected by bandlimited channels. IEEE Communications Letters, 15, 671–673.

    Article  Google Scholar 

  33. Fontes, R. T. (2017). Sistema de comunicação digital em banda limitada baseado em sincronismo caótico (PhD thesis). Universidade de São Paulo.

    Google Scholar 

  34. Candido, R., Eisencraft, M., & Silva, M. T. M. (2014) Channel equalization for synchronization of chaotic maps. Digital Signal Processing, 33, 42–49.

    Article  Google Scholar 

  35. Holland, G., Vaidya, N., & Bahl, P. (2001). A rate-adaptive mac protocol for multi-hop wireless networks. In Proceedings of the 7th annual international conference on mobile computing and networking, MobiCom’01, New York, NY, USA (pp. 236–251). New York: ACM.

    Google Scholar 

  36. Candido, R., Eisencraft, M., & Silva, M. T. M. (2013). Channel equalization for chaotic communications systems. In M. Eisencraft, R. Attux, & R. Suyama (Eds.), Chaotic signals in digital communications. Boca Raton, FL: CRC Press.

    Google Scholar 

  37. Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., & Heagy, J. F. (1997). Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos: An Interdisciplinary Journal of Nonlinear Science, 7(4), 520–543.

    Article  MathSciNet  Google Scholar 

  38. Haykin, S., & Moher, M. (2009) Communication systems (5th ed.). New York: Wiley

    Google Scholar 

  39. Sayed, A. H. (2008). Adaptive filters. New York: IEEE Computer Society.

    Book  Google Scholar 

  40. Haykin, S. O. (2013). Adaptive filter theory. Englewood Cliffs, NJ: Prentice Hall.

    MATH  Google Scholar 

  41. Picchi, G., & Prati, G. (1987). Blind equalization and carrier recovery using a “stop-and-go” decision-directed algorithm. IEEE Transactions on Communications, 35, 877–887.

    Article  Google Scholar 

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Acknowledgements

M.E. was partially supported by the National Council for Scientific and Technological Development (CNPq) under Grant 309275/2016-4. M. T. M. S. was partially supported by the São Paulo Research Foundation (FAPESP) under Grant 2017/20378-9 and CNPq under grant 304715/2017-4. C.P. was partially supported by the State of Pernambuco Research Foundation (FACEPE) under Grants APQ-0291-3.04/14 and APQ-0203-3.04/15 and CNPq under grant 303884/2013-4.

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Authors and Affiliations

  1. Escola Politécnica, University of São Paulo, São Paulo, Brazil

    Marcio Eisencraft, Rafael A. Costa, Rodrigo T. Fontes, Renato Candido & Magno T. M. Silva

  2. École de Technologie Supérieure, Montreal, QC, Canada

    João V. C. Evangelista

  3. Federal University of Pernambuco, Recife, Brazil

    Daniel P. B. Chaves & Cecilio Pimentel

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  1. Marcio Eisencraft
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  2. João V. C. Evangelista
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  3. Rafael A. Costa
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  4. Rodrigo T. Fontes
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  5. Renato Candido
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  6. Daniel P. B. Chaves
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  7. Cecilio Pimentel
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  8. Magno T. M. Silva
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Correspondence to Marcio Eisencraft .

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Editors and Affiliations

  1. Instituto Nacional de Pesquisas Espaciais – INPE, São José dos Campos, Brazil

    Elbert E. N. Macau

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Eisencraft, M. et al. (2019). New Trends in Chaos-Based Communications and Signal Processing. In: Macau, E. (eds) A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems . Nonlinear Systems and Complexity, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-78512-7_7

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  • DOI: https://doi.org/10.1007/978-3-319-78512-7_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78511-0

  • Online ISBN: 978-3-319-78512-7

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