A Generalized Proportionate-Type Normalized Subband Adaptive Filter

TL;DR

This paper introduces a generalized subband adaptive filtering framework that optimizes system identification by balancing subband error minimization and sparsity promotion, enhancing convergence speed for different system types.

Contribution

It proposes a new design criterion for subband adaptive filters that integrates regularized least squares with sparsity penalties, extending the PtNSAF framework.

Findings

Increasing subbands benefits quasi-sparse/dispersive systems more than promoting sparsity.

Promoting sparsity is crucial for sparse systems.

Combining subband number and sparsity improves convergence speed.

Abstract

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.