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Subband Adaptive Filter Exploiting Sparsity of System

Authors: Young-Seok Choi


This paper presents a normalized subband adaptive filtering (NSAF) algorithm to cope with the sparsity condition of an underlying system in the context of compressive sensing. By regularizing a weighted l1-norm of the filter taps estimate onto the cost function of the NSAF and utilizing a subgradient analysis, the update recursion of the l1-norm constraint NSAF is derived. Considering two distinct weighted l1-norm regularization cases, two versions of the l1-norm constraint NSAF are presented. Simulation results clearly indicate the superior performance of the proposed l1-norm constraint NSAFs comparing with the classical NSAF.

Keywords: Subband adaptive filtering, sparsity constraint, weighted l1-norm.

Digital Object Identifier (DOI):

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[1] S. Haykin, Adaptive Filter Theory, 4th edition, Upper Saddle River, NJ: Prentice Hall, 2002.
[2] A. H. Sayed, Fundamentals of Adaptive Filtering, New York: Wiley, 2003.
[3] A. Gilloire and M. Vetterli, “Adaptive filtering in subbands with critical sampling: analysis, experiments, and application to acoustic echo cancellation,” IEEE Trans. Signal Process., vol. 40, no. 8, pp. 1862–875, Aug. 1992.
[4] M. D. Couriville and P. Duhamel, “Adaptive filtering in subbands using a weighted criterion,” IEEE Trans. Signal Processing, vol. 46, no. 9, pp. 2359–2371, Sept. 1998.
[5] S. S. Pradhan and V. U. Reddy, “A new approach to subband adaptive filtering,” IEEE Trans. Signal Processing, vol. 47, no. 3, pp. 655–664, Mar. 1999.
[6] K. A. Lee and W. S. Gan, “Improving convergence of the NLMS algorithm using constrained subband updates,” IEEE Signal Processing Lett., vol. 11, no. 9, pp. 736–739, Sept. 2004.
[7] Y. Chen, Y. Gu, and A. O. Hero, “Sparse LMS for system identification,” in Proc. Int. Conf. on Acoustics, Speech, and Signal Process. (ICASSP 2009), pp. 3125–3128, 2009.
[8] Y. Gu, J. Jin, and S. Mei, “l0 norm constraint LMS algorithm for sparse system identification,” IEEE Signal Process. Lett., vol. 16, no. 9, pp. 774–777, Sep. 2009.
[9] E. M. Eksioglu and A. K. Tanc, “RLS Algorithm with convex regularization,” IEEE Signal Process. Lett., vol. 18, no. 8, pp. 470–473, Aug. 2011.
[10] R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag., vol. 24, no. 4, pp. 118–121, July 2007.
[11] D. Bertsekas, A. Nedic, and A. Ozdaglar, Convex analysis and optimization, Athena Scientific, Cambridge, MA USA, 2003.
[12] E. J. Cand`es, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted l1 minimization,” J. Fourier Anal. Appl., vol. 14, pp. 877–905, 2008.
[13] P. P. Vaidyanathan, Multirate Systems and Filterbanks, Englewood Cliffs, NJ: Prentice-Hall, 1993.