Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environments (1503.00802v2)

Abstract: Sparse adaptive channel estimation problem is one of the most important topics in broadband wireless communications systems due to its simplicity and robustness. So far many sparsity-aware channel estimation algorithms have been developed based on the well-known minimum mean square error (MMSE) criterion, such as the zero-attracting least mean square (ZALMS), which are robust under Gaussian assumption. In non-Gaussian environments, however, these methods are often no longer robust especially when systems are disturbed by random impulsive noises. To address this problem, we propose in this work a robust sparse adaptive filtering algorithm using correntropy induced metric (CIM) penalized maximum correntropy criterion (MCC) rather than conventional MMSE criterion for robust channel estimation. Specifically, MCC is utilized to mitigate the impulsive noise while CIM is adopted to exploit the channel sparsity efficiently. Both theoretical analysis and computer simulations are provided to corroborate the proposed methods.

• The paper demonstrates a novel algorithm that integrates maximum correntropy with a CIM penalty to enhance sparse channel estimation in impulsive noise environments.
• The proposed CIMMCC algorithm substantially reduces mean square deviation and improves convergence speed in both mixed Gaussian and alpha-stable noise scenarios.
• The method maintains computational simplicity and robust performance, making it effective for real-time wireless communications in non-Gaussian settings.

Maximum Correntropy Criterion Based Sparse Adaptive Filtering Algorithms for Robust Channel Estimation Under Non-Gaussian Environments

The paper introduces a novel approach to sparse adaptive filtering for channel estimation in wireless communication systems operating under non-Gaussian noise conditions. Traditional methods for sparse channel estimation often rely on the minimum mean square error (MMSE) criterion, which assumes Gaussian noise models and may falter in environments with impulsive, heavy-tailed noise distributions. This paper proposes the application of the maximum correntropy criterion (MCC), augmented by a correntropy induced metric (CIM)-based penalty for improved robustness and efficacy under such challenging conditions.

Sparse channel estimation is crucial in broadband communication, where channels exhibit a sparse structure. Many existing algorithms enhance performance by incorporating sparsity-aware penalties into traditional adaptive filtering methods like the LMS and RLS. These methods, however, are limited by their sensitivity to non-Gaussian noise. To address this, the researchers employ MCC, which benefits from its inherent robustness to outliers and its bounded nature across arbitrary distributions, alongside CIM, which approximates the sparse channel's $\ell_0$-norm representation, thus improving the exploitation of sparsity.

Strong numerical results demonstrate the proposed algorithm's efficacy, known as CIMMCC, in reducing mean square deviation (MSD) under both mixed Gaussian and alpha-stable noise models. The paper documents simulations across various scenarios, validating the enhanced stability and speed of convergence of CIMMCC over traditional approaches. Specific simulation setups, such as alpha-stable noise with different values of characteristic factor and kernel widths, illustrate the algorithm's robustness without compromising convergence rates.

The CIMMCC algorithm's derivation through combining MCC with a CIM penalty offers a balanced and efficient means to handle impulsive noises, as demonstrated in multiple simulations including time-varying and sparse echo cancellation scenarios. The computational simplicity of the new approach is highlighted, maintaining a low complexity akin to conventional algorithms, which is a significant benefit for real-time communication systems.

The implications of this research are substantial. Practically, the robust performance in impulsive environments can lead to more reliable wireless communications, crucial in modern applications subject to diverse and unpredictable noise conditions. Theoretically, the integration of MCC and CIM offers a fresh perspective on adaptive filtering under extreme conditions, potentially informing the development of further noise resistant algorithms across other domains.

Future developments could explore the potential for integrating the proposed approach with other adaptive filtering paradigms or its extension to multi-dimensional signal environments. Additionally, the efficacy of MCC and CIM in various domains beyond wireless communication indicates a rich avenue for exploration into robust signal processing techniques within AI frameworks and beyond.