Skip to main content
Log in

Extracting Narrow-Band Signal from a Chaotic Background with LLVCR

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

In this paper, the problem of extracting a narrow-band signal in strong chaotic background is considered. A method which in simulation can extract narrow-band signal well is put forward. The proposed method is a mixed model which combines the local linear (LL) model and varying-coefficient regression model (LLVCR). We first use LL model to predict the short-term chaotic signal. Since the varying-coefficient model can fit the narrow-band signal well. We mix them and establish a mixed model to estimate the narrow-band signal in strong chaotic background. For estimating simply and effectively, we develop an efficient algorithm to select and optimize the parameters of LLVCR model those are hard to be exhaustively searched for. In the proposed algorithm, based on the short-term predictability and sensitivity to initial conditions of chaos motion, the minimum fitting error criterion is used as the objective function to get the estimation of parameters of the presented LLVCR model. In addition, the center frequencies can be detected from the fitting error of LL model by using periodogram at first. The simulation results show that LLVCR model and its estimation algorithm have appreciable flexibility to extract the narrow-band signal in different chaotic background [Lorenz, Henon and Mackey-Glass (M-G) equations].

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Leung, H. (2014). An overview of chaotic signal processing, chaotic signal processing (Vol. 1, pp. 1–26). Beijing: Higher Education Press.

  2. Baptista, M. S. (1998). Cryptography with chaos. Physics Letters A, 240, 50–54.

    Article  MathSciNet  MATH  Google Scholar 

  3. Leung, H., & Lo, T. (1993). Chaotic radar signal processing over sea. IEEE Journal of Oceanic Engineering, 18, 287–295.

    Article  Google Scholar 

  4. Han, X., Li, W., & Zeng, Z. (2002). Acoustic chaos and sonic infrared imaging. Applied Physics Letters, 81, 3188–3190.

    Article  Google Scholar 

  5. Wang, G., Lin, J., & Chen, X. (1999). The application of chaotic oscillators to weak signal detection. IEEE Transactions on Industrial Electronics, 46(2), 440–444.

    Article  Google Scholar 

  6. Wang, G., Zheng, W., & He, S. (2002). Estimation of amplitude and phase of a weak signal by using the property of sensitive dependence on initial conditions of a nonlinear oscillator. Signal Processing, 82(1), 103–115.

    Article  MATH  Google Scholar 

  7. Liu Q. Z. & Song W. Q. (2009) Detection weak period signal using chaotic oscillator. In Computational science and its applications (ICCSA 2009) (pp. 685-692). Berlin: Springer .

  8. Deng X., Liu H., Wang L. & Liu T. (2013) Study on detection of small-sized range-spread target by using chaotic Duffing oscillator. In IEEE Conference anthology, pp. 1–4.

  9. Xue, L., & Xin, Y. (2014). The study for the method to weak signal detection based on the combination of the chaotic ocillator system and stochastic resonance system. Scientific Journal of Information Engineering, 4(3), 44–56.

    Google Scholar 

  10. Stark, J., & Arumugam, B. V. (1992). Extracting slowly varying signals from a chaotic background. International Journal of Bifurcation and Chaos, 2(02), 413–419.

    Article  MATH  Google Scholar 

  11. Haykin, S., & Li, B. X. (1993). Detection of signals in chaos. IEEE Proceedings, 83(1), 95–122.

    Article  Google Scholar 

  12. Leung, H., & Huang, X. P. (1996). Parameter estimation in chaotic noise. IEEE Transactions on Signal Processing, 44(10), 2456–2463.

    Article  Google Scholar 

  13. Short, K. M. (1997). Signal extraction from chaotic communications. International Journal of Bifurcation and Chaos, 7(07), 1579–1597.

    Article  MATH  Google Scholar 

  14. Ma X. Y., Huang X. B., Wang. F. & Xu X. D. (2001) A new method for small target detection over chaotic background. IEEE CIE international conference on radar processing, pp. 341–344.

  15. Zhu, Z. W., & Leung, H. (2002). Identification of linear systems driven by chaotic signals using nonlinear prediction. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49(2–49), 170–180.

    Google Scholar 

  16. Li, Y., & Yang, B. (2003). Chaotic system for the detection of periodic signals under the background of strong noise. Chinese Science Bulletin, 48(5), 508–510.

    Article  Google Scholar 

  17. Wang, E., Liu, Q., Jia, L., & Ding, Q. (2014). A steady-state point capture-based blind harmonic signal extraction algorithm under the chaotic background. International Journal of Sensor Networks, 15(1), 52–61.

    Article  Google Scholar 

  18. Su, L. Y., Ma, Y. J., & Li, J. J. (2012). Application of local polynomial estimation in suppressing strong chaotic noise. Chinese Physics B, 21(2), 020508.

    Article  Google Scholar 

  19. Zheng, H. L., Xing, H. Y., & Xu, W. (2015). Detection of weak signal embedded in chaotic background using echo state network. Journal of Signal Processing (China), 31(3), 336–345.

    Google Scholar 

  20. Farmer J., D., & Sidorowich, J. J. (1987). Predicting chaotic time series. Physical Review Letters, 59(8), 845–848.

    Article  MathSciNet  Google Scholar 

  21. Takens, F. (1981). Dynamical systems and turbulence. Lecture Notes in Mathematics, 898(9), 366–381.

    Article  MathSciNet  Google Scholar 

  22. Cao, L. (1997). Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena, 110(1), 43–50.

    Article  MATH  Google Scholar 

  23. Fan, J. Q., & Cai, Z. W. (2003). Adaptive varying-coefficient linear models. Journal of Royal Statistical Society B, 65(1), 57–80.

    Article  MathSciNet  MATH  Google Scholar 

  24. Lorenz, E. N. (1963). Deterministic non-periodic flow. Journal of Atmospheric Sciences, 20(2), 130–141.

    Article  Google Scholar 

  25. Henon, M., & Pomeau, Y. (1976). Turbulence and Navier Stokes equations. Berlin: Springer.

    Google Scholar 

  26. Mackey, M., & Glass, L. (1977). Oscillation and chaos in physiological control systems. Science, 197(4300), 287–289.

    Article  Google Scholar 

Download references

Acknowledgements

This project was supported by Natural Science Foundation Project of China (Grant no. 11471060), Fundamental and Advanced Research Project of CQ CSTC of China (Grant no. cstc2014jcyjA40003).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Liyun Su.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Su, L., Li, C. Extracting Narrow-Band Signal from a Chaotic Background with LLVCR. Wireless Pers Commun 96, 1907–1927 (2017). https://doi.org/10.1007/s11277-017-4275-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-017-4275-3

Keywords

Navigation