  In this paper, we propose a novel normalized subband adaptive filter
algorithm suited for sparse scenarios, which combines the proportionate and
sparsity-aware mechanisms. The proposed algorithm is derived based on the
proximal forward-backward splitting and the soft-thresholding methods. We
analyze the mean and mean square behaviors of the algorithm, which is supported
by simulations. In addition, an adaptive approach for the choice of the
thresholding parameter in the proximal step is also proposed based on the
minimization of the mean square deviation. Simulations in the contexts of
system identification and acoustic echo cancellation verify the superiority of
the proposed algorithm over its counterparts.
