Advertisement

Spread Spectrum Communication with Chaotic Frequency Modulation

  • Alexander R. Volkovskii
  • Lev S. Tsimring
  • Nikolai F. Rulkov
  • Ian Langmore
  • Stephen C. Young
Part of the Institute for Nonlinear Science book series (INLS)

Summary

We describe two different approaches to employ chaotic signals in spread-spectrum (SS) communication systems with phase and frequency modulation. In the first one a chaotic signal is used as a carrier. We demonstrate that using a feedback loop controller, the local chaotic oscillator in the receiver can be synchronized to the transmitter. The information can be transmitted using phase or frequency modulation of the chaotic carrier signal. In the second system the chaotic signal is used for frequency modulation of a voltage controlled oscillator (VCO) to provide a SS signal similar to frequency hopping systems. We show that in a certain parameter range the receiver VCO can be synchronized to the transmitter VCO using a relatively simple phase lock loop (PLL) circuit. The same PLL is used for synchronization of the chaotic oscillators. The information signal can be transmitted using a binary phase shift key (BPSK) or frequency shift key (BFSK) modulation of the frequency modulated carrier signal. Using an experimental circuit operating at radio frequency band and a computer modeling we study the bit error rate (BER) performance in a noisy channel as well as multiuser capability of the system.

Keywords

Chaotic System Phase Lock Loop Chaotic Oscillator Voltage Control Oscillator Chaotic Signal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. A. Scholtz. The Origins of Spread-Spectrum Communications. IEEE Trans. Commun., COM-30(5), pp. 822–854, 1982. R. L. Pickholtz, D. L. Schilling, and L. B. Milstein. Theory of Spread-Spectrum Communications-A Tutorial IEEE Trans. Commun., com-30 (5), pp. 855–884, 1982.MathSciNetCrossRefADSGoogle Scholar
  2. 2.
    M. K. Simon, J. K. Omura, R. A. Scholtz, and B. K. Levitt. Spread Spectrum Communications, Computer Science Press, Rockville, MD, 1985. M. K. Simon, J. K. Omura, R. A. Scholtz, and B. K. Levitt. Spread Spectrum Communication Handbook (McGraw-Hill, New York, 1994).Google Scholar
  3. 3.
    J. Karaoguz. High-rate wireless personal area networks, IEEE Commun. Mag vol. 39(12), pp. 96–102, 2001. 39:96–102.CrossRefGoogle Scholar
  4. 4.
    M. P. Kennedy and G. Kolumban (Eds.) IEEE Trans. Circuit. Syst. I, vol. 47(12), pp. 1661–1732, 2000.Google Scholar
  5. 5.
    L. Kocarev, G. M. Maggio, M. Ogarzalek, L. Pecora, and K. Yao (Eds.) IEEE Trans. Circuit. Syst. I vol. 48(12), pp. 1385–1527, 2001.Google Scholar
  6. 6.
    L. Pecora and T. Carroll. Synchronization in chaotic systems, Phys. Rev. Lett. vol. 64(8), pp. 821–824, 1990.zbMATHMathSciNetCrossRefADSGoogle Scholar
  7. 7.
    M. P. Kennedy, G. Kolumban, G. Kis, and Z. Jako, Performance evaluation of FM-DCSK modulation in multipath environments IEEE Trans. Circuit Syst. I, vol. 47(12), pp. 1702–1711, 2000. M. P. Kennedy, G. Kolumban, G. Kis, Simulation of the multipath performance of FM-DCSK digital communications using chaos, in Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI, ISCAS’99 (Cat. No.99CH36349), vol. 4, pp. 568–571, 1999.CrossRefGoogle Scholar
  8. 8.
    L. Kocarev, K, S. Halle, K. Eckert, L. O. Chua, and U. Parlitz, Experimental Demonstration of Secure Communications via Chaotic Synchronization Int. J. Bifurc. Chaos vol. 2(3), pp. 709–713, 1992. L. Kocarev, U. Parlitz, General Approach for Chaotic Synchronization with Applications to Communication Phys. Rev. Lett. vol. 74(25), pp. 5028–5031, 1995. K. Cuomo and A. V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications, Phys. Rev. Lett. vol. 71 (1) pp. 65–68, 1993. T. Carrol and L. Pecora, Cascading synchronized chaotic systems, Physica D vol. 67 (2), pp. 126–140, 1993. A. R. Volkovskii, N. F. Rul’kov, Synchronous chaotic response of a nonlinear oscillator system as a principal for detection of the information component of chaos, Sov. Tech. Phys. Lett., vol. 19, p. 97, 1993.zbMATHCrossRefGoogle Scholar
  9. 9.
    U. Feldmann, M. Hasler, W. Schwarz, Communication by chaotic signals: The inverse system approach, Int. J. Circuit Theory and Applications vol. 24(5), pp. 551–579, 1996.zbMATHCrossRefGoogle Scholar
  10. 10.
    U. Parlitz and L. Kocarev, Multichannel communication using auto-synchronization, Int. J. Bifurcation and Chaos, vol. 6(3), pp. 581–588, 1996.zbMATHCrossRefGoogle Scholar
  11. 11.
    W. P. Torres, A. V. Oppenheim, and R. R. Rosales, Generalized frequency modulation, IEEE Trans. Circuit. Syst. I, vol. 48(12), pp. 1405–1412, 2001.zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    C. C. Chen and K. Yao, Numerical evaluation of error probabilities of self-synchronizing chaotic communications, IEEE Comm. Lett., vol. 4(2), pp. 37–39. C. C. Chen and K. Yao, Stochastic-calculus-based numerical evaluation and performance analysis of chaotic communication systems, Trans. Circuit. Syst. I, vol. 47 (12), pp. 1663–1672, 2000.Google Scholar
  13. 13.
    G. M. Maggio and Z. Galias, Applications of symbolic dynamics to differential chaos shift keying, IEEE Trans. Circuit. Syst. I, vol. 49(12), pp. 1729–1735, 2002.CrossRefGoogle Scholar
  14. 14.
    N. F. Rulkov and L. S. Tsimring, Synchronization methods for communication with chaos over band-limited channels, Int. J. Circuit Theory Appl., vol. 27(6), pp. 555–567, 1999.zbMATHCrossRefGoogle Scholar
  15. 15.
    M. M. Sushchik et al., Chaotic pulse position modulation: a robust method of communicating with chaos IEEE Comm. Lett., vol. 4(4), pp. 128–130, 2000.CrossRefGoogle Scholar
  16. 16.
    G. Heidari-Bateni and C. D. McGillem, A chaotic direct-sequence spread-spectrum communication system, IEEE Trans. Commun., vol. 42(3), pp. 1524–1527, 1994. G. Heidari-Bateni, C. D. McGillem, and M. F. Tenorio, A novel multiple address digital communication. In: IEEE Int. Conf. Communications ICC’92 pp. 1232–1236, 1992. T. Kohda and A. Tsuneda, Statistics of chaotic binary sequences, IEEE Trans. Information Technology, vol. 43, (1), pp. 104–112, 1997. R. Hegger, H. Kantz, L. Matassini, Chaos-based asynchronous DS-CDMA systems and enhanced rake receivers: measuring the improvements, IEEE Trans. Circuit. Syst. I vol. 48 (12), pp. 1445–1453, 2001.CrossRefGoogle Scholar
  17. 17.
    C. C. Chen, K. Yao K, K. Umeno, and E. Biglieri Design of spread-spectrum sequences using chaotic dynamical systems and ergodic theory, IEEE Trans. Circuit. Syst. I vol. 48(9) pp. 1110–1114, 2001.zbMATHCrossRefGoogle Scholar
  18. 18.
    L. Cong and L. Shaoqian, Chaotic spreading sequences with multiple access performance better than random sequences, IEEE Trans. Circuit. Syst. I, vol. 47(3), pp. 394–397, 2000.CrossRefGoogle Scholar
  19. 19.
    L. Cong and S. Songgeng, Chaotic frequency hopping sequences, IEEE Trans. Commun. vol. 46(11), pp. 1433–1437, 1998. L. Cong; W. Xiaofu, Design and realization of an FPGA-based generator for chaotic frequency hopping sequences, IEEE Trans. Circuit. Syst. I, vol. 48 (5), pp. 521–532, 2001.CrossRefGoogle Scholar
  20. 20.
    P. A. Bernhardt, Chaotic frequency modulation, in Proceedings of SPIE-the International Society for Optical Engineering, vol. 2038 pp. 162–181, 1993. P. A. Bernhardt, Communications using chaotic frequency modulation, Int. J. Bifurc. Chaos in Appl. Sci. Eng., vol. 4 (2), pp. 427–40, 1994.ADSGoogle Scholar
  21. 21.
    A. Volkovskii, Synchronization of chaotic systems using phase control IEEE Trans. Circuit. Syst. I vol. 44(10), pp. 913–917, 1997.MathSciNetCrossRefGoogle Scholar
  22. 22.
    F. M. Gardner, Phaselock Techniques (Wiley, New York, 1979).Google Scholar
  23. 23.
    E. Ott, C. Grebogi, and J. A. Yorke, Controlling chaos, Phys. Rev. Lett, vol. 64(11), pp. 1196–1199, 1990.zbMATHMathSciNetCrossRefADSGoogle Scholar
  24. 24.
    Y. C. Lai and C. Grebogi, Synchronization of chaotic trajectories using control, Phys. Rev. E, vol. 47(4), pp. 2357–2359, 1993.MathSciNetCrossRefADSGoogle Scholar
  25. 25.
    D. Vassiliadis, Parametric adaptive control and parameter identification of low-dimensional chaotic systems, Physica D, vol. 71(3), pp. 319–341, 1994.zbMATHCrossRefADSGoogle Scholar
  26. 26.
    A. S. Dmitriev, Y V. Kislov, and S O. Starkov, Experimental study of appearance and interaction of strange attractors in the circle type self-oscillator, Sov. Phys. Tech. Lett. vol. 30, pp. 1439–1441, 1985.Google Scholar
  27. 27.
    N. F. Rulkov, A. R. Volkovskii, A. Rodriguez-Lozano, E. Del Rio, and M. G. Velarde, Mutual synchronization of chaotic self-oscillators with dissipative coupling, Int. J. Bif. Chaos vol. 2, pp. 669–676, 1992.zbMATHCrossRefGoogle Scholar
  28. 28.
    N. M. Filiol, C. Plett, T. Riley, and M. A. Copeland, An interpolated frequency-hopping spread-spectrum transceiver, IEEE Trans. Circuits Syst vol. 45, pp. 3–12, 1998.Google Scholar
  29. 29.
    A. J. Viterbi, Principles of Coherent Communication (McGraw-Hill, New York, 1966).Google Scholar
  30. 30.
    A. R. Volkovskii and L. S. Tsimring, Synchronization and communication using chaotic frequency modulation Int. J. Circ. Theor. Appl., vol. 27 pp. 569–576, 1999.zbMATHCrossRefGoogle Scholar
  31. 31.
    H. Fujisaka and T. Yamada, Stability Theory of Synchronized Motion in Coupled-Oscillator Systems, Progress of Theoretical Physics (Japan), vol. 69(1), pp. 32–47, 1983.zbMATHMathSciNetCrossRefADSGoogle Scholar
  32. 32.
    V.S. Afraimovich, N.N. Verichev, and M.I. Rabinovich, Stochastic Synchronization of Oscillations in Dissipative Systems, Radio Phys. and Quantum Electron., vol. 29, pp. 747–751, 1986.MathSciNetCrossRefGoogle Scholar
  33. 33.
    N. F. Rulkov, A. R. Volkovskii, A. Rodriguez-Lozano, E. Del Rio and M. G. Velarde, Mutual synchronization of chaotic self-oscillators with dissipative coupling, Int. J. Bif. and Chaos, vol. 2 pp. 669–676, 1992zbMATHCrossRefGoogle Scholar
  34. 34.
    L. Pecora, T. Carrol, G. Johnson, and D. Mar, Fundamentals of synchronization in chaotic systems, concepts and applications, Chaos, vol. 7(4) pp. 520–543, 1997.zbMATHMathSciNetCrossRefADSGoogle Scholar
  35. 35.
    J. C. Sprott, Some simple chaotic flows, Phys. Rev. E, vol. 50 pp. 647–650, 1994.MathSciNetCrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Alexander R. Volkovskii
    • 1
  • Lev S. Tsimring
    • 1
  • Nikolai F. Rulkov
    • 1
  • Ian Langmore
    • 2
  • Stephen C. Young
    • 3
  1. 1.Institute for Nonlinear ScienceUniversity of CaliforniaSan Diego, La Jolla
  2. 2.Dept. of Electrical and Computer EngineeringUniversity of CaliforniaSan Diego
  3. 3.Dept. of PhysicsUniversity of Southern CaliforniaLos Angeles

Personalised recommendations