Robust Diffusion Recursive Algorithm for Distributed Widely-Linear Exponential Functional Link Network

Distributed adaptive filtering has emerged as a critical methodology across diverse application domains, including wireless sensor networks, distributed signal processing, and intelligent control systems. However, existing diffusion-based adaptive filters suffer performance degradation in non-Gaussian noise and complex network topologies, leading to sub-optimal operation and instability risks. These limitations motivate the development of a robust framework that maintains distributed processing advantages while improving noise robustness. To address this, we propose a distributed widely-linear exponential functional link network (D-WLEFLN) combining wide-linear architecture with exponential expansions for enhanced nonlinear modeling. Furthermore, we develop a kernel risk Blake- Zisserman (KRBZ) based cost function to achieve enhanced outlier resilience. Building upon this foundation, a diffusion recursive kernel risk Blake-Zisserman (D-RKRBZ) algorithm is developed through recursive optimization, alongside a computationally efficient variant specifically designed for the WL architecture to maintain operational efficiency while preserving estimation accuracy. We provide theoretical analysis for the proposed algorithm, encompassing both mean stability and mean square performance. Simulation results validate that the performance of the proposed D-RKRBZ algorithm closely aligns with theoretical analysis. Comparative evaluations against existing diffusion counterparts reveal that D-RKRBZ can achieve lower mean square deviation (MSD) in complex-valued non-Gaussian environments, including contaminated Gaussian (CG) noise and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha $</tex-math></inline-formula> stable noise scenarios.