On the Mean-Square Performance of the Constrained LMS Algorithm

TL;DR

This paper analyzes the mean-square performance of the constrained LMS algorithm, providing theoretical expressions for its transient and steady-state behavior, supported by simulations.

Contribution

It offers the first detailed theoretical analysis of the mean-square performance of the constrained LMS algorithm, including new formulas for its transient and steady-state behavior.

Findings

Theoretical expressions accurately predict algorithm performance.

Simulation results validate the derived formulas.

Constrained LMS shows reliable mean-square performance.

Abstract

The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical insights into the performance of this algorithm, we examine its mean-square performance and derive theoretical expressions for its transient and steady-state mean-square deviation. Our methodology is inspired by the principle of energy conservation in adaptive filters. Simulation results corroborate the accuracy of the derived formula.