New adaptive algorithms for identification of sparse impulse responses — Analysis and comparisons

The convergence of the classical adaptive filtering algorithms becomes slow when the number of coefficients is very large. However, in many applications, such as digital network and acoustical echo cancelers, the system being modeled presents sparse impulse response, that is, most of its coefficients have small magnitudes. In order to improve the convergence for these applications, several algorithms have been proposed recently, which employ individual step-sizes for the updating of the different coefficients. The adaptation step-sizes are made larger for the coefficients with larger magnitudes, resulting in a faster convergence for the most significant coefficients. In this paper, we give an overview of the most important adaptive algorithms developed for the fast identification of systems with sparse impulse responses. Their convergence rates are compared through computer simulations for the identification of the channel impulse responses in a digital network echo cancellation application. A theoretical analysis of an improved version of the PNLMS algorithm is presented.