Abstract: This paper presents a normalized subband adaptive
filtering (NSAF) algorithm to cope with the sparsity condition of
an underlying system in the context of compressive sensing. By
regularizing a weighted l1-norm of the filter taps estimate onto the
cost function of the NSAF and utilizing a subgradient analysis,
the update recursion of the l1-norm constraint NSAF is derived.
Considering two distinct weighted l1-norm regularization cases, two
versions of the l1-norm constraint NSAF are presented. Simulation
results clearly indicate the superior performance of the proposed
l1-norm constraint NSAFs comparing with the classical NSAF.