Robust Consensus in the Presence of Impulsive Channel Noise

TL;DR

This paper introduces a novel distributed consensus algorithm that remains effective despite impulsive channel noise, relaxing traditional noise moment constraints and ensuring convergence to the true average with quantifiable variance.

Contribution

It is the first to develop a consensus algorithm tolerant to impulsive noise without requiring finite moments, expanding robustness in distributed networks.

Findings

Nodes reach consensus asymptotically to a finite random variable.

The expectation of the consensus equals the initial sample average.

Simulation results confirm the theoretical robustness and performance.

Abstract

A distributed average consensus algorithm robust to a wide range of impulsive channel noise distributions is proposed. This work is the first of its kind in the literature to propose a consensus algorithm which relaxes the requirement of finite moments on the communication noise. It is shown that the nodes reach consensus asymptotically to a finite random variable whose expectation is the desired sample average of the initial observations with a variance that depends on the step size of the algorithm and the receiver nonlinear function. The asymptotic performance is characterized by deriving the asymptotic covariance matrix using results from stochastic approximation theory. Simulations corroborate our analytical findings and highlight the robustness of the proposed algorithm.