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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64, 821–824.
Ott, E., Grebogi, C., & Yorke, J. A. (1990) Controlling chaos. Physical Review Letters, 64, 1196–1199.
Lau, F. C. M., & Tse, C. K. (2003) Chaos-based digital communication systems. Berlin: Springer.
Kennedy, M. P., Setti, G., & Rovatti, R. (Eds.). (2000). Chaotic electronics in telecommunications. Boca Raton, FL: CRC Press.
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.
Fontes, R. T., & Eisencraft, M. (2016). A digital bandlimited chaos-based communication system. Communications in Nonlinear Science and Numerical Simulation, 37, 374–385.
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.
Ren, H.-P., Baptista, M. S., & Grebogi, C. (2013). Wireless communication with chaos. Physical Review Letters, 110, 184101.
Michaels, A. J., & Lau, C. (2014). Generalized multi-carrier chaotic shift keying. In 2014 IEEE Military Communications Conference (pp. 657–662). .
Kaddoum, G. (2016). Wireless chaos-based communication systems: A comprehensive survey. IEEE Access, 4, 2621–2648
Hénon, M. (1976). A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics, 50, 94–102.
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.
Paar, C., & Pelzl, J. (2011). Understanding cryptography. Berlin: Springer.
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.
Yu, P. L., Baras, J. S., & Sadler, B. M. (2008). Physical-layer authentication. IEEE Transactions on Information Forensics and Security, 3, 38–51.
Verma, G., Yu, P., & Sadler, B. M. (2015). Physical layer authentication via fingerprint embedding using software-defined radios. IEEE Access, 3, 81–88.
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.
Alligood, K. T., Sauer, T. D., & Yorke, J. A. (2000). Chaos. Textbooks in mathematical sciences. New York: Springer.
Strogatz, S. H. (2001) Nonlinear dynamics and chaos. Boulder, CO: The Perseus Books Group.
Maurer, U. M. (2000). Authentication theory and hypothesis testing. IEEE Transactions on Information Theory, 46, 1350–1356.
Lathi, B. P., & Ding, Z. (2009). Modern digital and analog communication systems. The Oxford series in electrical and computer engineering. Oxford: Oxford University Press.
Sakai, H., & Tokumaru, H. (1980). Autocorrelations of a certain chaos. IEEE Transactions on Acoustics, Speech, and Signal Processing, 28, 588–590.
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.
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.
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.
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.
Lasota, A., & Mackey, M. C. (1985). Probabilistic properties of deterministic systems. Cambridge: Cambridge University Press.
Proakis, J. G., & Manolakis, D. K. (2006) Digital Signal Processing (4th ed.). London: Pearson.
Baptista, M. S., Macau, E. E., Grebogi, C., Lai, Y.-C., & Rosa, E. (2000). Integrated chaotic communication scheme. Physical Review E, 62, 4835–4845.
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.
Oppenheim, A. V., & Schafer, R. W. (2009) Discrete-time signal processing (3rd ed.). Upper Saddle River, NJ: Addison Wesley.
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.
Fontes, R. T. (2017). Sistema de comunicação digital em banda limitada baseado em sincronismo caótico (PhD thesis). Universidade de São Paulo.
Candido, R., Eisencraft, M., & Silva, M. T. M. (2014) Channel equalization for synchronization of chaotic maps. Digital Signal Processing, 33, 42–49.
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.
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.
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.
Haykin, S., & Moher, M. (2009) Communication systems (5th ed.). New York: Wiley
Sayed, A. H. (2008). Adaptive filters. New York: IEEE Computer Society.
Haykin, S. O. (2013). Adaptive filter theory. Englewood Cliffs, NJ: Prentice Hall.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-78512-7_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78511-0
Online ISBN: 978-3-319-78512-7
eBook Packages: EngineeringEngineering (R0)