Constrained Maximum Correntropy Adaptive Filtering

TL;DR

This paper introduces a constrained maximum correntropy criterion (CMCC) adaptive filtering algorithm that outperforms traditional MSE-based methods in non-Gaussian impulsive noise environments, offering robustness, simplicity, and low complexity.

Contribution

The paper proposes a novel constrained adaptive filtering algorithm based on MCC, explicitly incorporating linear constraints, and demonstrates its superior performance and convergence properties in impulsive noise scenarios.

Findings

CMCC outperforms MSE-based algorithms in impulsive noise environments.

The algorithm has low computational complexity and easy implementation.

Theoretical analysis confirms convergence and steady-state performance.

Abstract

Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (MSE) criterion, which is an ideal optimality criterion under Gaussian noises. This assumption however fails to model the behavior of non-Gaussian noises found in practice. Motivated by the robustness and simplicity of maximum correntropy criterion (MCC) in non-Gaussian impulsive noises, this paper proposes a new adaptive filtering algorithm called constrained maximum correntropy criterion (CMCC). Specifically, CMCC incorporates a linear constraint into a MCC filter to solve a constrained optimization problem explicitly. The proposed adaptive filtering algorithm is easy to implement and has low computational complexity, and in terms of convergence accuracy (say lower mean square deviation) and stability, can significantly outperform those MSE based constrained adaptive algorithms in presence of heavy-tailed impulsive noises. Additionally, the mean square convergence behaviors are studied under energy conservation relation, and a sufficient condition to ensure the mean square convergence and the steady-state mean square deviation (MSD) of the proposed algorithm are obtained. Simulation results confirm the theoretical predictions under both Gaussian and non- Gaussian noises, and demonstrate the excellent performance of the novel algorithm by comparing it with other conventional methods.