Skip to main content
SpringerLink
Log in

Assessment and improvement of autocorrelation performance of chaotic sequences using a phase space method

  • Research Papers
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

Chaotic sequences have been widely used as pseudorandom sequences. However, how to judge whether their autocorrelation performance is good remains a problem because we have no simple method for assessing and improving the autocorrelation performance. Using a phase space method, we have discovered that the autocorrelation performance of a chaotic sequence is determined by whether its phase space trajectory is axis symmetrical, and have deduced theorems to describe and solve these problems. This paper presents a simple yet effective method to assess and improve the autocorrelation performance of chaotic sequences. Several simulations are presented to validate the theorems and method.

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. Gambi E, Chiaraluce F, Spinsante S. Chaos-based radars for automotive applications: theoretical issues and numerical simulation. IEEE Trans Veh Technol, 2008, 57: 3858–3863

    Article  Google Scholar 

  2. Sune R J. Noise radar using random phase and frequency modulation. IEEE Trans Geosci Remote Sens, 2004, 42: 2370–2384

    Article  Google Scholar 

  3. Flores B C, Solis E A, Thomas G. Assessment of chaos-based FM signals for range-Doppler imaging. IEE Proc Radar Sonar Navig, 2003, 150: 313–322

    Article  Google Scholar 

  4. Flores B C, Solis E A, Thomas G. Chaotic signals for wideband radar imaging. Proc SPIE Int Soc Opt Eng, 2002, 4727: 100–111

    Google Scholar 

  5. Chen B, Zhou Z O, Liu G H, et al. Application of chaos series as noise source in noise radar. Modern Radar, 2008, 305: 24–28

    Google Scholar 

  6. Chen B, Tang J, Zhang Y, et al. Chaotic signals with weak-structure used for high resolution radar imaging. In: Proceedings of 2009 International Conference on Communications and Mobile Computing, Kunming, Yunnan, China, 2009. 1: 325–330

  7. Myers J, Flores B C. Radar imaging via random FM correlations. Proc SPIE Int Soc Opt Eng, 1999, 3721: 130–139

    Google Scholar 

  8. Vijayaraghavan V, Henry L. A novel chaos-based high-resolution imaging technique and its application to through-thewall imaging. IEEE Signal Process Lett, 2005, 12: 528–531

    Article  Google Scholar 

  9. Xu Y, Narayanan R M, Xu X, et al. Polarimetric processing of coherent random noise radar data for buried object detection. IEEE Trans Geosci Remote Sens, 2001, 39: 467–478

    Article  Google Scholar 

  10. Gu H, Liu G, Zhu X, et al. A new kind of noise-radar random binary phase coded CW radar. In: Proceedings of IEEE National Radar Conference, Syracuse, NY, USA, 1997. 202–206

  11. Wu X, Liu W, Zhao L, et al. Chaotic phase code for radar pulse compression. In: Proceedings of IEEE National Radar Conference, Atlanta, GA, USA, 2001. 279–283

  12. Dawood M, Narayanan R M. Ambiguity function of an ultrawideband random noise radar. In: Proceedings of IEEE Antennas and Propagation Society International Symposium, Salt Lake City, UT, USA, 2000. 4: 2142–2145

  13. Yang Y T, Wang M Z, Zhang Z M. Research on digital sound spreading-frequency modulation based on hyperchaos sequence. J UESTC, 2007, 9: 699–702

    Google Scholar 

  14. Zhong Q C, Zhu Q X, Zhang P L. Multiple chaotic maps encryption system. J UESTC, 2009, 4: 274–277

    MathSciNet  Google Scholar 

  15. Chon K H, Kanters J K, Iyengar N, et al. Detection of chaotic determinism in stochastic short time series. In: Proceedings of the 19th International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, USA, 1997. 10: 275–277

  16. Bucolo M, Caponetto R, Fortuna L, et al. Does chaos work better than noise. IEEE Circuits Syst Mag, 2002, 2: 4–19

    Article  Google Scholar 

  17. Jose A R, Eduardo R, Juan C E, et al. Correlation analysis of chaotic trajectories from Chua’s system. Chaos Soliton Fract, 2008, 36: 1157–1169

    Article  Google Scholar 

  18. Liu Z, Zhu X H, Hu W, et al. Principles of chaotic signal radar. Int J Bifurcat Chaos Appl Sci Eng, 2007, 17: 1735–1739

    Article  MATH  Google Scholar 

  19. Setti G, Mazzini G, Rovatti R, et al. Statistical modeling of discrete-time chaotic processes: basic finite-dimensional tools and applications. Proc IEEE, 2002, 90: 662–690

    Article  Google Scholar 

  20. Rovatti R, Mazzini G, Setti G, et al. Statistical modeling and design of discrete-time chaotic processes: advanced finite-dimensional tools and applications. Proc IEEE, 2002, 90: 820–841

    Article  Google Scholar 

  21. Kohda T, Tsuneda A. Statistics of chaotic binary sequences. IEEE Trans Inf Theory, 1997, 43: 104–112

    Article  MATH  MathSciNet  Google Scholar 

  22. Kohda T. Information sources using chaotic dynamics. Proc IEEE, 2002, 90: 641–661

    Article  Google Scholar 

  23. Jose A R, Eduardo R, Juan C E, et al. Correlation analysis of chaotic trajectories from Chua’s system. Chaos Soliton Fract, 2008, 36: 1157–1169

    Article  Google Scholar 

  24. Syuji M, Miki U K, Kei E, et al. New developments in large deviation statistics and time correlation calculations in chaotic dynamics and stochastic processes. IEICE Tech Report, 2008, 3: 37–42

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Software and Communication Engineering, JiangXi University of Finance and Economy, Nanchang, 330032, China

    Bin Chen

Authors
  1. Bin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, B. Assessment and improvement of autocorrelation performance of chaotic sequences using a phase space method. Sci. China Inf. Sci. 54, 2647–2659 (2011). https://doi.org/10.1007/s11432-011-4445-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-011-4445-y

Keywords

Search

Navigation