Skip to main content
SpringerLink
Log in

Tracking Performance of Robust RLS Algorithm for MIMO Channel Estimation

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

A robust recursive least square (RRLS) algorithm that has been designed for SISO communications by Bhotto and Antoniou (IEEE Signal Process Lett 18(3):185–188, 2011) is unable to work for MIMO system because of single error constraint. In this paper, a modified version of RRLS algorithm with the application of MIMO channel estimation is introduced. An RRLS algorithm is modified in such a way that it can provide much faster convergence rate in MIMO channel estimation than that of RLS and variable forgetting factor RLS (VFF-RLS) algorithms. Moreover, the optimum forgetting factor is derived for MIMO RRLS in order to minimize the error function. Simulation results show that the MIMO RRLS provides fast convergence performance as compared to RLS and VFF-RLS algorithms without additional multiplication complexity, however, an additional linear term of N in the addition complexity of modified MIMO RRLS does not enhance its computational complexity and keeps it almost equivalent to those of RLS and VFF-RLS algorithms. Moreover, it is observed that the optimum forgetting factor is highly dependent on RRLS scaling parameter, \(E_b/N_o\), doppler shift and number of antennas.

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

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

Similar content being viewed by others

References

  1. Bhotto, M. Z. A., & Antoniou, A. (2011). Robust recursive least-squares adaptive-filtering algorithm for impulsive-noise environments. IEEE Signal Processing Letters, 18(3), 185–188.

    Article  Google Scholar 

  2. Pelekanakis, K., & Chitre, M. (2015). Robust equalization of mobile underwater acoustic channels. IEEE Journal of Oceanic Engineering, 40(4), 775–784.

    Article  Google Scholar 

  3. Subudhi, B., & Pradhan, R. (2016). An adaptive predictive error filter based maximum power point tracking algorithm for a photovoltaic system. The Journal of Engineering, 2016(4), 54–61.

    Article  Google Scholar 

  4. Raza, H., & Khan, N. M. (2017). Low complexity linear channel estimation for MIMO communication systems. Wireless Personal Communications, 97(4), 5031–5044.

    Article  Google Scholar 

  5. Foschini, G. J., & Gans, M. J. (1988). On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Communicaitons, 6(3), 311–335.

    Article  Google Scholar 

  6. Pohl, V., Nguyen, P. H., Jungnickel, V., & Von Helmolt, C. (2003). How often channel estimation is needed in MIMO systems. In Proceedings of the IEEE telecommunications conference (pp. 814–818). San Francisco, CA, USA.

  7. Tong, L. (1995). Blind sequence estimation. IEEE Transactions on Communications, 43(12), 2986–2994.

    Article  Google Scholar 

  8. Vosoughi, A., & Scaglione, A. (2003). Channel estimation for precoded MIMO systems. In Proceedings of the IEEE workshop statistical signal process (pp. 442–445). St. Louis, MO, USA.

  9. Bergman, N. (1999). Recursive Bayesian estimation, Department of Electrical Engineering, Linkoping University, Linkoping Studies in Science and Technology. Doctoral dissertation, 579, 11.

  10. Boroujeny, B. F. (2013). Adaptive Filters: Theory and Applications. New York: Wiley.

    Book  Google Scholar 

  11. Haykin, S. (2013). Adaptive filter theory. Pearson: Prentice Hall.

    MATH  Google Scholar 

  12. Sayed, A. H. (2008). Adaptive filters. Hoboken, NJ: Wiley.

    Book  Google Scholar 

  13. Verhaegen, M., & Verdult, V. (2012). Filtering and system identification, a least squares approach. New York: Cambridge University Press.

    MATH  Google Scholar 

  14. Kovacevic, B., Banjac, Z., & Milosavljevic, M. (2013). Adaptive digital filters. Berlin: Springer.

    Book  Google Scholar 

  15. Basseville, M., & Benveniste, A. (1986). Detection of abrupt changes in signals and dynamical systems. Berlin: Springer.

    MATH  Google Scholar 

  16. Arablouei, R., & Dogancay, K. (2011). Modified RLS algorithm with enhanced tracking capability for MIMO channel estimation. Electronics Letters, 47(19), 1101–1103.

    Article  Google Scholar 

  17. Paleologu, C., Benesty, J., & Ciochina, S. (2008). A robust variable forgetting factor recursive least-squares algorithm for system identification. IEEE Signal Process Letters, 15, 597–600.

    Article  Google Scholar 

  18. Akino, T. K. (2008). Optimum-weighted RLS channel estimation for rapid fading MIMO channels. IEEE Transactions on Wireless Communications, 7(11), 4248–4260.

    Article  Google Scholar 

  19. Leung, S. H., & So, C. F. (2005). Gradient-based variable forgetting factor RLS algorithm in time-varying environments. IEEE Transactions on Signal Processing, 53(8), 3141–3150.

    Article  MathSciNet  Google Scholar 

  20. Tylavsky, D. J., & Sohie, G. R. (1986). Generalization of the Matrix Inversion Lemma. In Proceedings of IEEE, San Fransisco, CA USA (Vol. 74, No. 7, pp. 1050–1052).

  21. Komninakis, C., Fragouli, C., Sayed, A. H., & Wesel, R. D. (2002). Multi-input multi-output fading channel tracking and equalization using Kalman estimation. IEEE Transactions on Signal Processing, 50(5), 1065–1076.

    Article  Google Scholar 

  22. Anderson, T. W. (2007). An introduction to multivariate statistical analysis. Hoboken: Wiley.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Department, Hamdard Institute of Engineering and Technology, Islamabad, 44000, Pakistan

    Hasan Raza

  2. Electrical Engineering Department, Capital University of Science and Technology, Islamabad, 44000, Pakistan

    Noor M. Khan

Authors
  1. Hasan Raza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Noor M. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hasan Raza.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raza, H., Khan, N.M. Tracking Performance of Robust RLS Algorithm for MIMO Channel Estimation. Wireless Pers Commun 111, 395–409 (2020). https://doi.org/10.1007/s11277-019-06865-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-019-06865-2

Keywords

Search

Navigation