Subband Adaptive Filtering withl1-Norm Constraint for Sparse System Identification

Young-Seok Choi

doi:10.1155/2013/601623

Abstract

This paper presents a new approach of the normalized subband adaptive filter (NSAF) which directly exploits the sparsity condition of an underlying system for sparse system identification. The proposed NSAF integrates a weightedl1-norm constraint into the cost function of the NSAF algorithm. To get the optimum solution of the weightedl1-norm regularized cost function, a subgradient calculus is employed, resulting in a stochastic gradient based update recursion of the weightedl1-norm regularized NSAF. The choice of distinct weightedl1-norm regularization leads to two versions of thel1-norm regularized NSAF. Numerical results clearly indicate the superior convergence of thel1-norm regularized NSAFs over the classical NSAF especially when identifying a sparse system.

Highlights

Over the past few decades, the relative simplicity and good performance of the normalized least mean square (NLMS) algorithm have made it a popular tool for adaptive filtering applications
This paper presents a new approach of the normalized subband adaptive filter (NSAF) which directly exploits the sparsity condition of an underlying system for sparse system identification
The use of multiple-constraint optimization criteria into formulation of a cost function has resulted in the normalized SAF (NSAF) with its computational complexity close to that of the NLMS algorithm [6, 7]

Summary

Introduction

Over the past few decades, the relative simplicity and good performance of the normalized least mean square (NLMS) algorithm have made it a popular tool for adaptive filtering applications. The capability of the NSAF is faded in a sparse system identification scenario To deal with this issue, a variety of proportionate adaptive algorithms have been presented for NSAF, which utilize proportionate step sizes to distinct filter taps [10,11,12]. This paper presents a novel approach of the sparsity-regularized NSAFs, which incorporates the sparsity condition of the system directly into the cost function via a sparsity-inducing constraint term. This is carried out by regularizing a weighted l1-norm of the filter weights estimate.

Conventional NSAF

Weighted l1-Norm Regularized NSAF

Numerical Results

Conclusion