Subband Adaptive Filtering with l1-Norm Constraint for Sparse System Identification

Abstract EN

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 weighted l1-norm constraint into the cost function of the NSAF algorithm.

To get the optimum solution of the weighted l1-norm regularized cost function, a subgradient calculus is employed, resulting in a stochastic gradient based update recursion of the weighted l1-norm regularized NSAF.

The choice of distinct weighted l1-norm regularization leads to two versions of the l1-norm regularized NSAF.

Numerical results clearly indicate the superior convergence of the l1-norm regularized NSAFs over the classical NSAF especially when identifying a sparse system.