Acoustics, Speech, and Signal Processing, IEEE International Conference on (2009)
Apr. 19, 2009 to Apr. 24, 2009
Yilun Chen , Department of EECS, University of Michigan, Ann Arbor, 48109-2122, USA
Yuantao Gu , Department of EE, Tsinghua University, Beijing 100084, China
Alfred O. Hero , Department of EECS, University of Michigan, Ann Arbor, 48109-2122, USA
We propose a new approach to adaptive system identification when the system model is sparse. The approach applies ℓ<inf>1</inf> relaxation, common in compressive sensing, to improve the performance of LMS-type adaptive methods. This results in two new algorithms, the zero-attracting LMS (ZA-LMS) and the reweighted zero-attracting LMS (RZA-LMS). The ZA-LMS is derived via combining a ℓ<inf>1</inf> norm penalty on the coefficients into the quadratic LMS cost function, which generates a zero attractor in the LMS iteration. The zero attractor promotes sparsity in taps during the filtering process, and therefore accelerates convergence when identifying sparse systems. We prove that the ZA-LMS can achieve lower mean square error than the standard LMS. To further improve the filtering performance, the RZA-LMS is developed using a reweighted zero attractor. The performance of the RZA-LMS is superior to that of the ZA-LMS numerically. Experiments demonstrate the advantages of the proposed filters in both convergence rate and steady-state behavior under sparsity assumptions on the true coefficient vector. The RZA-LMS is also shown to be robust when the number of non-zero taps increases.
Yilun Chen, A. O. Hero and Y. Gu, "Sparse LMS for system identification," Acoustics, Speech, and Signal Processing, IEEE International Conference on(ICASSP), Taipei, Taiwan, 2009, pp. 3125-3128.