Skip to main content
SpringerLink
Log in

\(\ell _1\)-Norm Iterative Wiener Filter for Sparse Channel Estimation

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

The recursive-least-squares (RLS) algorithm is one of the most representative adaptive filtering algorithms. \(\ell _1\)-norm full-recursive RLS has also been successfully applied to various sparsity-related areas. However, computing the autocorrelation matrix inverse in the \(\ell _1\)-norm full-recursive RLS generates numerical instability that results in divergence. In addition, the regularization coefficient calculation for \(\ell _1\)-norm often requires actual channel information or relies on empirical methods. The iterative Wiener filter (IWF) has a similar performance to the RLS algorithm and does not require the inverse of the autocorrelation matrix. Therefore, IWF can be used as a numerically stable RLS. This paper proposes \(\ell _1\)-norm IWF for sparse channel estimation using the IWF and \(\ell _1\)-norm. The algorithm proposed in this paper includes a realistic regularization coefficient calculation that does not require actual channel information. The simulation shows that the sparse channel estimation performance of the proposed algorithm is similar to the conventional \(\ell _1\)-norm full-recursive RLS using real channel information as well as being superior in terms of numerical stability.

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

Similar content being viewed by others

References

  1. M.S. Ahmad, O. Kukrer, A. Hocanin, Recursive inverse adaptive filtering algorithm. Digital Signal Process. 21(4), 491–496 (2011)

    Article  Google Scholar 

  2. J.W. Choi, T.J. Riedl, K. Kim, A.C. Singer, J.C. Preisig, Adaptive linear turbo equalization over doubly selective channels. IEEE J. Ocean. Eng. 36(4), 473–489 (2011)

    Article  Google Scholar 

  3. B. Das, M. Chakraborty, Improved \(l_{0}\)-RLS adaptive filter algorithms. Electron. Lett. 53(25), 1650–1651 (2017)

    Article  Google Scholar 

  4. E.M. Eksioglu, A.K. Tanc, RLS algorithm with convex regularization. IEEE Signal Process. Lett. 18(8), 470–473 (2011)

    Article  Google Scholar 

  5. S. Haykin, Adaptive Filter Theory 5th (Prentice Hall, Upper Saddle River, USA, 2014)

    MATH  Google Scholar 

  6. S. Khalid, S. Abrar, Blind adaptive algorithm for sparse channel equalization using projections onto lp-ball. Electron. Lett. 51(18), 1422–1424 (2015)

    Article  Google Scholar 

  7. J. Lim, S. Lee, Regularization factor selection method for \(l_{1}\)-regularized RLS and its modification against uncertainty in the regularization factor. Appl. Sci. 9(1), 1–11 (2019)

    Article  Google Scholar 

  8. L. Liu, Y. Zhang, D. Sun, VFF \(l_{1}\)-norm penalised WL-RLS algorithm using DCD iterations for underwater acoustic communication. IET Commun. 11(5), 615–621 (2017)

    Article  Google Scholar 

  9. O.O. Oyeyemi, Reweighted \(l_{1}\)-vff modified RLS-based channel estimator for OFDM-IDMA systems. In: Proceedings of IEEE 89th Vehicular Technology Conference 2019 (2019), pp. 1–7

  10. J. Rudander, T. Husøy, P. Orten, P. Walree, Comparing RLS and LMS adaptive equalizers for large hydrophone arrays in underwater acoustic communication channels. Proc. OCEANS 2019, 1–5 (2019)

    Google Scholar 

  11. M.S. Salman, O. Kukrer, A. Hocanin, Recursive inverse algorithm: mean-square-error analysis. Digital Signal Process. 66, 10–17 (2017)

    Article  MathSciNet  Google Scholar 

  12. A. Sholiyi, T. O’Farrell, O.A. Alzubi, J. Alzubi, Performance evaluation of turbo codes in high speed downlink packet access using EXIT charts. Int. J. Future Gener. Commun. Netw. 10(8), 1–14 (2017)

    Article  Google Scholar 

  13. A. Sholiyi, J.A. Alzubi, O.A. Alzubi, O. Almomani, T. O’Farrell, Near capacity irregular turbo code, Indian. J. Sci. Technol. 8(23), 1–10 (2015)

    Google Scholar 

  14. T. Tian, F.Y. Wu, Y. Kunde, Estimation of underwater acoustic channel via block-sparse recursive least-squares algorithm, In: Proceedings of IEEE International Conference on Signal Processing, Communications and Computing 2019 (2019), pp. 1–6

  15. A. Uncini, Fundamentals of Adaptive Signal Processing (Springer, Berlin, 2015)

    Book  Google Scholar 

  16. B. Widrow, E. Walach, Adaptive Inverse Control: A Signal Processing Approach (Wiley, Piscataway, 2007)

    Book  Google Scholar 

  17. B. Xi, Y. Liu, Iterative wiener filter. Electron. Lett. 49(5), 343–344 (2013)

    Article  Google Scholar 

  18. X. Zhang, K. Li, Z. Wu, Y. Fu, H. Zhao, B. Chen, Convex regularized recursive maximum correntropy algorithm. Signal Process. 129, 12–16 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

This paper was supported by Agency for Defense Development (ADD) in S. Korea (UD190005DD).

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Sejong University, Kunja, Kwangjin, 98, Seoul, 143-747, Korea

    Jun-seok Lim

Authors
  1. Jun-seok Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun-seok Lim.

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

Lim, Js. \(\ell _1\)-Norm Iterative Wiener Filter for Sparse Channel Estimation. Circuits Syst Signal Process 39, 6386–6393 (2020). https://doi.org/10.1007/s00034-020-01467-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-020-01467-x

Keywords

Search

Navigation