A Generalized Proportionate-Type Normalized Subband Adaptive Filter
This work addresses adaptive filtering for system identification, offering incremental improvements in convergence speed for specific signal processing applications.
The authors tackled the system identification problem by proposing a generalized proportionate-type normalized subband adaptive filter (GPtNSAF) that uses a new design criterion with sparsity regularization, showing via simulations that increasing subbands benefits quasi-sparse or dispersive systems while sparsity promotion is key for sparse systems, with both aspects speeding up convergence.
We show that a new design criterion, i.e., the least squares on subband errors regularized by a weighted norm, can be used to generalize the proportionate-type normalized subband adaptive filtering (PtNSAF) framework. The new criterion directly penalizes subband errors and includes a sparsity penalty term which is minimized using the damped regularized Newton's method. The impact of the proposed generalized PtNSAF (GPtNSAF) is studied for the system identification problem via computer simulations. Specifically, we study the effects of using different numbers of subbands and various sparsity penalty terms for quasi-sparse, sparse, and dispersive systems. The results show that the benefit of increasing the number of subbands is larger than promoting sparsity of the estimated filter coefficients when the target system is quasi-sparse or dispersive. On the other hand, for sparse target systems, promoting sparsity becomes more important. More importantly, the two aspects provide complementary and additive benefits to the GPtNSAF for speeding up convergence.