Skip to main content
SpringerLink
Log in

Spread-spectrum signals and the chaotic logistic map

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

Chaotic systems provide a simple means of generating deterministic signals that resemble white noise. It is this noise-like property that provides the potential for applying chaotic systems in communications. In this work, we report a detailed study of the logistic map for use as direct-sequence spread-spectrum (DS/SS) codes. The advantages of the chaotic DS/SS codes are the almost unlimited number of distinct sequences of arbitrary lengths, the ease of generating these sequences, and the increased privacy afforded by the noise-like appearance of these sequences. Some design criteria are provided from the correlation properties of these sequences, and bit-error rate (BER) results are generated by Monte Carlo simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. A. Bernhardt, Chaotic frequency modulation,Proc. SPIE Chaos in Communications, vol. 2038, 162–181, 1993.

    Google Scholar 

  2. T. L. Carroll and L. M. Pecora, Synchronizing chaotic circuits,IEEE Trans. Circuits and Systems, vol. 38, no. 4, 453–456, 1991.

    Article  Google Scholar 

  3. K. M. Cuomo and A. V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications,Phys. Rev. Lett., vol. 71, no. 1, 65–68, 1993.

    Article  Google Scholar 

  4. K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, Synchronization of Lorenz-based chaotic circuits with applications to communications,IEEE Trans. Circuits and Systems, vol. 40, no. 10, 626–632, 1993.

    Article  Google Scholar 

  5. H. Dedieu, M. P. Kennedy, and M. Hasler, Chaos shift keying: Modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits,IEEE Trans. Circuits and Systems, vol. 40, no. 10, 634–642, 1993.

    Google Scholar 

  6. R. C. Dixon,Spread Spectrum Systems, Wiley, New York, 1976.

    Google Scholar 

  7. E. Geraniotis and B. Ghaffari, Performance of binary and quaternary direct-sequence spread-spectrum multiple-access systems with random signature sequences.IEEE Trans. Commun., vol. 39, no. 5, 713–724, 1991.

    Article  Google Scholar 

  8. E. A. Geraniotis and M. B. Pursley, Error probability for direct-sequence spread-spectrum multiple-access communications — Part II: Approximations,IEEE Trans. Commun., vol. COM-30, no. 5, 985–995, 1982.

    Article  Google Scholar 

  9. S. Hayes and C. Grebogi, Coding information in the natural complexity of chaos,Proc. SPIE Chaos in Communications, vol. 2038, 153–161, 1993.

    Google Scholar 

  10. S. Hayes, C. Grebogi, and E. Ott, Communicating with chaos,Phys. Rev. Lett., vol. 70, no. 20, 3031–3034, 1993.

    Article  Google Scholar 

  11. G. Heidari-Bateni and C. D. McGillem, Chaotic sequences for spread spectrum: An alternative to PN-sequences,Proc. IEEE ICWC-92, 437–440, 1992.

    Google Scholar 

  12. G. Heidari-Bateni and C. D. McGillem, A chaotic direct-sequence spread-spectrum communications system,IEEE Trans. Commun., vol. 42, nos. 2/3/4, 1524–1527, 1994.

    Article  Google Scholar 

  13. G. Heidari-Bateni, C. D. McGillem, and M. F. Tenorio, A novel multiple-address digital communication system using chaotic signals,Proc. IEEE ICC-92, 1232–1236, 1992.

    Google Scholar 

  14. Lj. Kocarev, K. S. Halle, K. Eckert, L. O. Chau, and U. Parlitz, Experimental demonstration of secure communication via chaotic synchronization,Int. J. Bifurcation and Chaos, vol. 2, no. 3, 709–713, 1992.

    Article  MATH  Google Scholar 

  15. A. W. Lam and F.M. Ozluturk, Performance bounds for DS/SSMA communications with complex signature sequences,IEEE Trans. Commun., vol. 40, no. 10, 1607–1614, 1992.

    Article  MATH  Google Scholar 

  16. J. S. Lehnert and M. B. Pursley, Error probabilities for binary direct-sequence spread-spectrum communications with random signature sequences,IEEE Trans. Commun., vol. COM-35, no. 1, 87–98, 1987.

    Article  Google Scholar 

  17. A. V. Oppenheim, G. W. Wornell, S. H. Isabelle, and K. M. Cuomo, Signal processing in the context of chaotic signals,Proc. ICASSP-92, vol. IV, 117–120, 1992.

    Google Scholar 

  18. L. M. Pecora, Overview of chaos and communications research,Proc. SPIE, Chaos in Communications, vol. 2038, 2–25, 1993.

    Google Scholar 

  19. L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems,Phys. Rev. Lett., vol. 64, no. 8, 821–824, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  20. L. M. Pecora and T. L. Carroll, Driving systems with chaotic signals,Phys. Rev. Lett., vol. 44, no. 4, 2374–2383, 1991.

    MathSciNet  Google Scholar 

  21. M. B. Pursley, Performance evaluation for phase-coded spread-spectrum multiple-access communication — Part I: System analysis,IEEE Trans. Commun., vol. COM-25, no. 8, 795–799, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  22. M. B. Pursley, D. V. Sarwate, and W. E. Stark, Error probability for direct-sequence spread-spectrum multiple-access communications — Part I: Upper and lower bounds,IEEE Trans. Commun., vol. COM-30, no. 5, 975–984, 1982.

    Article  Google Scholar 

  23. B. Sklar,Digital Communications: Fundamentals and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1988.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Xerox Corporation, 701 South Aviation Blvd./ESAE-225, 90245, El Segundo, CA

    J. Tou

  2. Communcations Research Laboratory, McMaster University, L8S-4K1, Hamilton, Ontario, Canada

    P. Yip

  3. Department of Electrical and Computer Engineering, University of Calgary, T2N-1N4, Calgary, Alberta, Canada

    H. Leung

Authors
  1. J. Tou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Yip
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Leung
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tou, J., Yip, P. & Leung, H. Spread-spectrum signals and the chaotic logistic map. Circuits Systems and Signal Process 18, 59–73 (1999). https://doi.org/10.1007/BF01206545

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01206545

Keywords

Search

Navigation