Skip to main content
Log in

Design of an Intelligent q-LMS Algorithm for Tracking a Non-stationary Channel

  • Research Article - Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Tracking of a time-varying channel is a challenging task, especially when channel is non-stationary. In this work, we propose a time-varying q-LMS algorithm to efficiently track a random-walk channel. To do so, we first perform tracking analysis of the q-LMS algorithm in a non-stationary environment and then derive the expressions for the transient and steady-state tracking excess mean-square-error (EMSE). Thus, we evaluate an optimum value of q parameter which minimizes the tracking EMSE. Next, by utilizing the derived optimum q, we design a time-varying mechanism to vary the parameter q according to the estimation of instantaneous error energy which provides faster convergence in the initial phase while attain a lower EMSE near final stages of adaptation.

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.

Similar content being viewed by others

References

  1. Haykin, S.: Adaptive Filter Theory. Prentice Hall, Englewood Cliffs (1996)

    MATH  Google Scholar 

  2. Cowan, C.; Grant, P.: Adaptive Filters. Prentice Hall, Englewood Cliffs (1985)

    MATH  Google Scholar 

  3. Sayed, A.H.: Fundamentals of Adaptive Filtering. Wiley, New York (2003)

    Google Scholar 

  4. Widrow, B.; Stearns, S.D.: Adaptive Signal Processing. Prentice Hall, Englewood Cliffs (1985)

    MATH  Google Scholar 

  5. Slock, D.T.M.: On the convergence behavior of the LMS and the normalized LMS algorithms. IEEE Trans. Signal Process. 41(9), 2811–2825 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chan, S.C.; Zhou, Y.: On the performance analysis of the least mean m-estimate and normalized least mean m-estimate algorithms with Gaussian inputs and additive Gaussian and contaminated Gaussian noises. J. Signal Process. Syst. 60(1), 81–103 (2010)

    Article  Google Scholar 

  7. Al-Naffouri, T.Y.; Moinuddin, M.: Exact performance analysis of the \(\epsilon \)-NLMS algorithm for colored circular gaussian inputs. IEEE Trans. Signal Process. 58(10), 5080–5090 (2010)

    Article  MathSciNet  Google Scholar 

  8. Moinuddin, M.; Al-Naffouri, T.Y.; Sohail, M.S.: Exact tracking analysis of the \(\epsilon \)-NLMS algorithm for circular complex correlated Gaussian input. In: 2010 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), pp. 225–230 (2010)

  9. Al-Naffouri, T.Y.; Moinuddin, M.; Sohail, M.S.: Mean behavior of the NLMS algorithm for correlated Gaussian inputs. IEEE Signal Process. Lett. 18(1), 7–10 (2011)

    Article  Google Scholar 

  10. Mai, J.; Sayed, A.H.: A feedback approach to the steady-state performance of fractionally-spaced blind adaptive equalizers. IEEE Trans. Signal Process. 48, 80–91 (2000)

    Article  Google Scholar 

  11. Sayed, A.H.; Rupp, M.: A time-domain feedback analysis of adaptive algorithms via the small gain theorem. In: Proceedings of the SPIE, vol. 2563, pp. 458–469, San Diego, CA (1995)

  12. Rupp, M.; Sayed, A.H.: On the convergence of blind adaptive equalizers for constant modulus signals. IEEE Trans. Signal Process. 48, 80–91 (2000)

    Article  Google Scholar 

  13. Al-Naffouri, T.Y.; Sayed, A.H.: Transient analysis of adaptive filters with error nonlinearities. IEEE Trans. Signal Process. 51(3), 653–663 (2003)

    Article  Google Scholar 

  14. Al-Naffouri, T.Y.; Sayed, A.H.: Transient analysis of data normalized adaptive filters. IEEE Trans. Signal Process. 51(3), 639–652 (2003)

    Article  Google Scholar 

  15. Al-Saggaf, U.M.; Moinuddin, M.; Arif, M.; Zerguine, A.: The \(q\)-least mean squares algorithm. Signal Process. 111, 50–60 (2015)

    Article  Google Scholar 

  16. Ernst, T.: The History of q-Calculus and a New-Method. U. U. D. M. Report 2000:16, Department of Mathematics, Uppsala University, Sweden (2000)

  17. Jackson, F.H.: On \(q\)-functions and a certain difference operator. Trans. R. Soc. Edinb. 46, 253–281 (1908)

    Article  Google Scholar 

  18. Jackson, F.H.: On \(q\)-definite integrals. Q. J. Pure Appl. Math. 41, 193–203 (1910)

    MATH  Google Scholar 

  19. Koekoev, J.: A note on the \(q\)-derivative operator. J. Math. Anal. Appl. 176, 627–634 (1993)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Moinuddin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arif, M., Naseem, I., Moinuddin, M. et al. Design of an Intelligent q-LMS Algorithm for Tracking a Non-stationary Channel. Arab J Sci Eng 43, 2793–2803 (2018). https://doi.org/10.1007/s13369-017-2883-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-017-2883-6

Keywords

Navigation