# Study of Robust Distributed Diffusion RLS Algorithms with Side Information for Adaptive Networks

## TL;DR

This paper introduces robust diffusion RLS algorithms for adaptive networks that effectively handle impulsive noise by incorporating side information and reducing computational complexity, with proven convergence and superior performance.

## Contribution

The paper presents novel diffusion RLS algorithms with side information and reduced complexity, enhancing robustness against impulsive noise in adaptive networks.

## Key findings

- Algorithms outperform existing methods in impulsive noise scenarios.
- Proposed methods demonstrate mean-square convergence.
- Reduced complexity makes the algorithms practical for real-world applications.

## Abstract

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate update at each node. A recursive strategy for computing the constraint is proposed using side information from the neighboring nodes to further improve the robustness. We also analyze the mean-square convergence behavior of the proposed algorithm. The second proposed algorithm is a modification of the first one based on the dichotomous coordinate descent iterations. It has a performance similar to that of the former, however its complexity is significantly lower especially when input regressors of agents have a shift structure and it is well suited to practical implementation. Simulations show the superiority of the proposed algorithms over previously reported techniques in various impulsive noise scenarios.