Skip to main content
Log in

Extending HOC-based methods for identifying the diagonal parameters of quadratic systems

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

In this paper, methods developed for the linear case of identifying the diagonal parameters of quadratic systems are extended to nonlinear case. Firstly, nonlinear relationships between model kernels and output cumulants are presented. Secondly, the relationship linking output cumulants and the coefficients of systems presented in the linear case, is extended to the general case of nonlinear quadratic systems identification. According to this concept, two nonlinear approaches are developed, the first use the fourth-order cumulants, and the second combined the third- and fourth-order cumulants. The numerical simulation results, for various signal to noise ratio (SNR) and 200 Monte Carlo runs, show that the proposed approaches achieve better accuracy, as compared with the related algorithm in the literature. Furthermore, the second algorithm is more precise in high noise environment (smallest \(\mathrm{SNR}=0\) dB), but the first algorithm more efficient in the weak noise environment case (highest SNR \(\ge \) 8 dB) comparing to using others methods.

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. Zidane, M., Safi, S., Sabri, M., Boumezzough, A.: Theoretical development for blind identification of non linear communication channels. Int. J. Energy Inf. Commun. 6(6), 1–8 (2015)

    Google Scholar 

  2. Antari, J., Chabaab, S., Iqdour, R., Zeroual, A., Safi, S.: Identification of quadratic systems using higher order cumulants and neural networks: application to model the delay of video-packets transmission. J. Appl. Soft Comput. (ASOC) 11(1), 1–10 (2011)

    Article  Google Scholar 

  3. Tan, H.Z., Chow, T.W.S.: Blind identification of quadratic non linear models using neural networks with higher order cumulants. IEEE Trans. Ind. Electron. 47(3), 687–696 (2000)

    Article  Google Scholar 

  4. Tan, H.Z., Mao, Z.Y.: Blind identifiability of quadratic non linear systems in higher order statistics domain. Int. J. Adapt. Control Signal Process 12(7), 567–577 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Abderrahim, K., Abdennour, R.B., Favier, G., Ksouri, M., Msahli, F.: New results on FIR system identification using cumulants. APII-JESA 35(5), 601–622 (2001)

    Google Scholar 

  6. Zidane, M., Safi, S., Sabri, M.: Extension of linear channels identification algorithms to non linear using selected order cumulants. Indones. J. Electr. Eng. Comput. Sci. 2(2), 334–343 (2016)

    Article  Google Scholar 

  7. Chabaa, S., Zeroual, A., Antari, J.: Identification and prediction of internet traffic using artificial neural networks. J. Intell. Learn. Syst. Appl. 2(3), 147–155 (2010)

    Google Scholar 

  8. Koukoulas, P., Tsoulkas, V., Kalouptsidis, N.: A cumulant based algorithm for identification of input output quadratic systems. Automatica 38(3), 391–407 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Giannakis, G.B.: On the identifiability of non-Gaussian ARMA models using cumulants. IEEE Trans. Autom. Control 35(1), 18–26 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pal, P.S., Kar, R., Mandal, D., Ghoshal, S.P.: A hybrid backtracking search algorithm with wavelet mutation-based nonlinear system identification of Hammerstein models. Signal, Image and Video Processing 11(5), 929–936 (2017)

    Article  Google Scholar 

  11. Tanji, H., Tanaka, R., Murakami, T., Ishida, Y.: FIR system identification based on a non parametric Bayesian model using the Indian buffet process. Signal Image Video Process. 10(6), 1105–1112 (2016)

    Article  Google Scholar 

  12. Aliyu, M.L., Alkassim, M.A., Salman, M.S.: A p-norm variable step-size LMS algorithm for sparse system identification. Signal Image Video Process 9(7), 1559–1565 (2015)

    Article  Google Scholar 

  13. Ma, W., Chen, B., Qu, H., Zhao, J.: Sparse least mean p-power algorithms for channel estimation in the presence of impulsive noise. Signal Image Video Process. 10(3), 503–510 (2016)

    Article  Google Scholar 

  14. Haque, M.A., Al Bashar, M.S., Naylor, P.A., Hirose, K., Hasan, M.K.: Energy constrained frequency-domain normalized LMS algorithm for blind channel identification. Signal Image Video Process. 1(3), 203–213 (2007)

    Article  MATH  Google Scholar 

  15. Zidane, M., Safi, S., Sabri, M., Boumezzough, A.: Blind identification channel using higher order cumulants with application to equalization for MC-CDMA system”. Int. J. Electr. Robot. Electron. Commun. Eng. 8(2), 369–375 (2014)

    Google Scholar 

  16. Zidane, M., Safi, S., Sabri, M., Boumezzough, A.: Higher order statistics for identification of minimum phase channels. Int. J. Math. Comput. Phys. Quantum Eng. 8(5), 831–836 (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohammed Zidane.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zidane, M., Safi, S. & Sabri, M. Extending HOC-based methods for identifying the diagonal parameters of quadratic systems. SIViP 12, 125–132 (2018). https://doi.org/10.1007/s11760-017-1138-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-017-1138-z

Keywords

Navigation