# Quantum Calculus-based Volterra LMS for Nonlinear Channel Estimation

## TL;DR

This paper introduces a $q$-calculus based nonlinear adaptive filtering method, $q$-VLMS, which improves convergence speed for nonlinear channel estimation compared to traditional Volterra LMS.

## Contribution

The paper proposes a novel $q$-VLMS algorithm that enhances convergence performance of Volterra LMS using $q$-calculus, verified through analysis and simulations.

## Key findings

- Improved convergence speed over traditional Volterra LMS.
- Effective nonlinear channel estimation demonstrated.
- Theoretical step-size bounds validated by simulations.

## Abstract

A novel adaptive filtering method called $q$-Volterra least mean square ($q$-VLMS) is presented in this paper. The $q$-VLMS is a nonlinear extension of conventional LMS and it is based on Jackson's derivative also known as $q$-calculus. In Volterra LMS, due to large variance of input signal the convergence speed is very low. With proper manipulation we successfully improved the convergence performance of the Volterra LMS. The proposed algorithm is analyzed for the step-size bounds and results of analysis are verified through computer simulations for nonlinear channel estimation problem.