Subband Adaptive Filtering with -Norm Constraint for Sparse System Identification

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 -norm constraint into the cost function of the NSAF algorithm. To get the optimum solution of the weighted -norm regularized cost function, a subgradient calculus is employed, resulting in a stochastic gradient based update recursion of the weighted -norm regularized NSAF. The choice of distinct weighted -norm regularization leads to two versions of the -norm regularized NSAF. Numerical results clearly indicate the superior convergence of the -norm regularized NSAFs over the classical NSAF especially when identifying a sparse system.