Abstract
This work presents a new mixed (2,p-like)-norm penalized least mean squares (LMS) algorithm for block-sparse system identifications where the nonzero coefficients in the impulse response vector of unknown systems are structured in a single cluster or multiple clusters. The new algorithm divides the tap-weight vector into groups of equal-sized sub-vectors and then introduces a mixed \(l_{2,p\text {-like}}\)-norm constraint on the filter tap-weight vector in addition to the original mean-square-error cost function. The parameter p in the \(l_{2,p\text {-like}}\)-norm constraint takes any value between zero and two, thus improving the identification performance of the block-sparse systems. The effect of the parameter p and the group size on the performance of the proposed algorithm is studied, and general guidelines for choosing these two parameters are provided to facilitate practical use. The advantage of the proposed scheme is that no comparison operations are required while algebraic operations are of the same order as the block-sparse LMS algorithm. Numerical simulations show that the proposed \((2,p\text {-like})\)-norm penalized LMS algorithm outperforms the existing \(l_{2,0}\)- and \(l_{2,1}\)-norm-based block-sparsity-aware algorithms and single-norm penalized LMS strategies.
Similar content being viewed by others
References
Y. Chen, Y. Gu, A.O. Hero, Sparse LMS for system identification, in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 3125–3128 (2009)
Digital network echo cancellers. International Telecommunication Union (ITUT) Recommendation G.168 (2012)
D. Donoho, Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
Y. Gu, Y. Chen, K. Tang, Network echo canceller with active taps stochastic localization, in Proceedings of the IEEE ISCIT, vol. 1, pp. 556–559 (2005)
Y. Gu, J. Jin, S. Mei, \(l_0\) norm constraint LMS algorithm for sparse system identification. IEEE Signal Process. Lett. 16(9), 774–777 (2009)
S. Jiang, Y. Gu, Block-sparsity-induced adaptive filter for multi-clustering system identification. IEEE Trans. Signal Process. 63(20), 5318–5330 (2015)
J. Liu, S.L. Grant, Block sparse memory improved proportionate affine projection sign algorithm. Electron. Lett. 51(24), 2001–2003 (2015)
J. Liu, S.L. Grant, Proportionate adaptive filtering for block-sparse system identification. IEEE/ACM Trans. Audio Speech Lang. Process. 24(4), 623–630 (2016)
X. Liu, Y. Li, Y. Gu, K. Tang, Enhanced stochastic taps NLMS filter with efficient sparse taps localization, in Proceedings of the IEEE ICSP, vol. 4, pp. 16–20 (2006)
A.H. Sayed, Fundamentals of Adaptive Filtering (Wiley, New York, 2003)
K. Shi, P. Shi, Convergence analysis of sparse LMS algorithms with \(l_1\)-norm penalty based on white input signal. Signal Process. 90(12), 3289–3293 (2010)
N. Simon, J. Friedman, T. Hastie, R. Tibshirani, A sparse-group lasso. J. Comput. Graph. Stat. 22(2), 231–245 (2013)
G. Su, J. Jin, Y. Gu, J. Wang, Performance analysis of \(l_0\) norm constraint least mean square algorithm. IEEE Trans. Signal Process. 60(5), 2223–2235 (2012)
O. Taheri, S.A. Vorobyov, Sparse channel estimation with lp-norm and reweighted \(l_1\)-norm penalized least mean squares, in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 2864–2867 (2011)
C. Wang, Y. Zhang, Y. Wei, N. Li, A new LMS algorithm with adaptive zero attractor. IEEE Commun. Lett. 19(12), 2150–2153 (2015)
C. Wang, Y. Zhang, Y. Wei, N. Li, An effective tap-length NLMS algorithm for network echo cancellers. Circuits Syst. Signal Process. 36(4), 1686–1699 (2017)
Y. Wei, Y. Zhang, C. Wang, N. Li, Z. Shi, An NLMS algorithm with tap-selection matrix for sparse system identification. Circuits Syst. Signal Process. 36(6), 2486–2498 (2017)
F.Y. Wu, F. Tong, Gradient optimization p-norm-like constraint LMS algorithm for sparse system estimation. Signal Process. 93(4), 967–971 (2013)
M. Yuan, Y. Lin, Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. Ser. B (Statistical Methodology) 68(1), 49–67 (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was performed while Y. Wei was a visiting student at Missouri University of Science and Technology. The work of Y. Wei was supported in part by a scholarship under the College of Automation, Harbin Engineering University. The work of Y. Zhang was supported in part by the National Natural Science Foundation of China (61773133) and the Natural Science Foundation of Heilongjiang Province under Grant F2016008. The work of Y. R. Zheng was supported by the Wilkens Endowment Fund of Missouri University of Science and Technology.
Rights and permissions
About this article
Cite this article
Wei, Y., Zhang, Y., Wang, C. et al. A Mixed \((\mathbf 2 ,{\varvec{p}}\)-like)-Norm Penalized Least Mean Squares Algorithm for Block-Sparse System Identification. Circuits Syst Signal Process 37, 4683–4694 (2018). https://doi.org/10.1007/s00034-018-0769-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-018-0769-9