Transient Performance Analysis of the $\ell_1$-RLS

TL;DR

This paper develops analytical models to describe the transient mean and mean-square behavior of the $ ext{l}_1$-RLS algorithm, enhancing understanding of its stochastic dynamics in sparse system identification.

Contribution

It provides the first analytical models for the transient stochastic behavior of the $ ext{l}_1$-RLS algorithm, validated by simulations.

Findings

Models accurately predict transient behavior

Enhanced understanding of $ ext{l}_1$-RLS dynamics

Potential for improved algorithm tuning

Abstract

The recursive least-squares algorithm with $\ell_1$-norm regularization ($\ell_1$-RLS) exhibits excellent performance in terms of convergence rate and steady-state error in identification of sparse systems. Nevertheless few works have studied its stochastic behavior, in particular its transient performance. In this letter, we derive analytical models of the transient behavior of the $\ell_1$-RLS in the mean and mean-square sense. Simulation results illustrate the accuracy of these models.