  Limited by fixed step-size and sparsity penalty factor, the conventional
sparsity-aware normalized subband adaptive filtering (NSAF) type algorithms
suffer from trade-off requirements of high filtering accurateness and quicker
convergence behavior for sparse system identification. To deal with this
problem, this paper proposes variable step-size L0-norm constraint NSAF
algorithms (VSS-L0-NSAFs). We first analyze mean-square-deviation (MSD)
statistics behavior of the L0-NSAF innovatively in according to novel weight
recursion form and arrive at corresponding expressions for the cases that
background noise variance is available and unavailable, where correlation
degree of system input is indicated by scaling parameter r. Based on
derivations, we develop an effective variable step-size scheme through
minimizing the upper bounds of the MSD under some reasonable assumptions and
lemma. Furthermore, an effective reset strategy is incorporated into presented
algorithms to tackle with non-stationary situations. Finally, numerical
simulations corroborate that the proposed algorithms achieve better performance
in terms of estimation accurateness and tracking capability in comparison with
existing related algorithms in sparse system identification and adaptive echo
cancellation circumstances.
