Advertisement

Investigations on Sparse System Identification with \(l_0\)-LMS, Zero-Attracting LMS and Linearized Bregman Iterations

  • Andreas GebhardEmail author
  • Michael Lunglmayr
  • Mario Huemer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10672)

Abstract

Identifying a sparse system impulse response is often performed with the \(l_0\)-least-mean-squares (LMS)-, or the zero-attracting LMS algorithm. Recently, a linearized Bregman (LB) iteration based sparse LMS algorithm has been proposed for this task. In this contribution, the mentioned algorithms are compared with respect to their parameter dependency, convergence speed, mean-square-error (MSE), and sparsity of the estimate. The performance of the LB iteration based sparse LMS algorithm only slightly depends on its parameters. In our opinion it is the favorable choice in terms of achieving sparse impulse response estimates and low MSE. Especially when using an extension called micro-kicking the LB based algorithms converge much faster than the \(l_0\)-LMS.

Keywords

Sparse System identification Adaptive filter LMS 

References

  1. 1.
    Chen, Y., Gu, Y., Hero, A.O.: Sparse LMS for system identification. In: 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3125–3128, April 2009Google Scholar
  2. 2.
    Gu, Y., Jin, J., Mei, S.: \(l_{0}\) norm constraint LMS algorithm for sparse system identification. IEEE Sig. Process. Lett. 16(9), 774–777 (2009)CrossRefGoogle Scholar
  3. 3.
    Lunglmayr, M., Huemer, M.: Efficient linearized Bregman iteration for sparse adaptive filters and Kaczmarz solvers. In: 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM), pp. 1–5, July 2016Google Scholar
  4. 4.
    Hu, T., Chklovskii, D.B.: Sparse LMS via online linearized Bregman iteration. In: 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 7213–7217, May 2014Google Scholar
  5. 5.
    Chen, J., Richard, C., Song, Y., Brie, D.: Transient performance analysis of zero-attracting LMS. IEEE Sig. Process. Lett. 23(12), 1786–1790 (2016)CrossRefGoogle Scholar
  6. 6.
    Salman, M.S., Jahromi, M.N.S., Hocanin, A., Kukrer, O.: A zero-attracting variable step-size LMS algorithm for sparse system identification. In: 2012 IX International Symposium on Telecommunications (BIHTEL), pp. 1–4, October 2012Google Scholar
  7. 7.
    Su, G., Jin, J., Gu, Y.: Performance analysis of \(\text{L}_{0}\text{-LMS }\) with Gaussian input signal. In: IEEE 10th International Conference on Signal Processing, pp. 235–238, October 2010Google Scholar
  8. 8.
    Wang, C., Zhang, Y., Wei, Y., Li, N.: A new \(l_0\)-LMS algorithm with adaptive zero attractor. IEEE Commun. Lett. 19(12), 2150–2153 (2015)CrossRefGoogle Scholar
  9. 9.
    Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for total variation-based image restoration. Multiscale Model. Simul. 4(2), 460–489 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Cai, J.F., Osher, S., Shen, Z.: Convergence of the linearized Bregman iteration for \(\ell _{1}\)-norm minimization. AMS Math. Comput. 78(268), 2127–2136 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Yin, W.: SIAM J. Imaging Sci. 3(4), 856–877 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lunglmayr, M., Huemer, M.: Microkicking for fast convergence of sparse Kaczmarz and sparse LMS. In: 25th European Signal Processing Conference (EUSIPCO) 2017 (2017)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Christian Doppler Laboratory for Digitally Assisted RF Transceivers for Future Mobile Communications, Institute of Signal ProcessingJohannes Kepler University LinzLinzAustria

Personalised recommendations