Derivative Based Proportionate Approach for Sparse Impulse Response Identification

TL;DR

This paper introduces a novel proportionate algorithm for sparse impulse response identification that dynamically adjusts step-sizes based on the derivatives of filter coefficients, improving convergence rates.

Contribution

It presents a new proportionate approach utilizing the time derivatives of coefficients, enhancing convergence without increasing computational complexity.

Findings

Improved convergence rate demonstrated in simulations

Computational complexity remains similar to existing methods

Effective step-size assignment based on coefficient derivatives

Abstract

Proportionate type algorithms were developed and excessively used in the echo cancellation problems due to sparse characteristics of the echo channels. In the past, most of the attention was paid to a particular type of proportionate approach, which assigns step-sizes to filter coefficients proportional to the magnitude of the corresponding coefficient. In this letter, we propose a new proportionate type algorithm, which takes dynamic behavior of the estimated filter coefficient into account while assigning individual step-sizes to each coefficient. Proposed algorithm introduces an effective way to assign individual step-sizes using the time derivatives of the filter coefficients. Computational complexity of the proposed algorithm is similar to those of previously proposed algorithms. Simulation results have shown the improvements in the convergence rate achieved by the proposed algorithm.