Multitask diffusion adaptation over asynchronous networks

TL;DR

This paper develops a model for multitask diffusion algorithms operating over asynchronous networks, analyzing their stability and performance despite network uncertainties, and demonstrates their effectiveness through simulations and spectral sensing application.

Contribution

It introduces a novel asynchronous network model for multitask diffusion LMS and provides a comprehensive mean and mean-square error analysis.

Findings

Small step-sizes ensure stability and performance.

Theoretical analysis matches simulation results.

Framework applicable to spectral sensing tasks.

Abstract

The multitask diffusion LMS is an efficient strategy to simultaneously infer, in a collaborative manner, multiple parameter vectors. Existing works on multitask problems assume that all agents respond to data synchronously. In several applications, agents may not be able to act synchronously because networks can be subject to several sources of uncertainties such as changing topology, random link failures, or agents turning on and off for energy conservation. In this work, we describe a model for the solution of multitask problems over asynchronous networks and carry out a detailed mean and mean-square error analysis. Results show that sufficiently small step-sizes can still ensure both stability and performance. Simulations and illustrative examples are provided to verify the theoretical findings. The framework is applied to a particular application involving spectral sensing.