Sparse LMS for system identification

We propose a new approach to adaptive system identification when the system model is sparse. The approach applies the ℓ1 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 ZeroAttracting LMS (RZA-LMS). The ZA-LMS is derived via combining a ℓ1 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...

• Type: Conference
• Year: 2009
• Where: ICASSP
• Authors: Yilun Chen, Yuantao Gu, Alfred O. Hero III
• Keywords: ICASSP 2009, LMS Cost Function, Reweighted Zero Attractor, Reweighted ZeroAttracting LMS, Signal Processing