  In this paper, we propose and analyze the sparsity-aware sign subband
adaptive filtering with individual weighting factors (S-IWF-SSAF) algorithm,
and consider its application in acoustic echo cancellation (AEC). Furthermore,
we design a joint optimization scheme of the step-size and the sparsity penalty
parameter to enhance the S-IWF-SSAF performance in terms of convergence rate
and steady-state error. A theoretical analysis shows that the S-IWF-SSAF
algorithm outperforms the previous sign subband adaptive filtering with
individual weighting factors (IWF-SSAF) algorithm in sparse scenarios. In
particular, compared with the existing analysis on the IWF-SSAF algorithm, the
proposed analysis does not require the assumptions of large number of subbands,
long adaptive filter, and paraunitary analysis filter bank, and matches well
the simulated results. Simulations in both system identification and AEC
situations have demonstrated our theoretical analysis and the effectiveness of
the proposed algorithms.
