Stochastic Behavior of the Nonnegative Least Mean Fourth Algorithm for Stationary Gaussian Inputs and Slow Learning

TL;DR

This paper provides a theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning, addressing nonnegativity constraints in system identification.

Contribution

It is the first to analyze the stochastic behavior of the NNLMF algorithm under these conditions, enhancing understanding of its performance.

Findings

Simulation results confirm the accuracy of the theoretical analysis.

The analysis improves understanding of NNLMF behavior with Gaussian inputs.

Results demonstrate the effectiveness of the NNLMF algorithm in nonnegativity-constrained identification.

Abstract

Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.