Analysis of Sum-Weight-like algorithms for averaging in Wireless Sensor Networks

TL;DR

This paper analyzes Sum-Weight-like algorithms for distributed averaging in wireless sensor networks, demonstrating exponential error decay and proposing an improved algorithm that leverages broadcast communication without feedback.

Contribution

It provides a detailed convergence analysis of Sum-Weight algorithms and introduces a new algorithm optimized for broadcast channels in sensor networks.

Findings

Squared error decreases exponentially over time.

Sum-Weight algorithms converge to the average value.

Proposed algorithm improves efficiency by exploiting broadcast nature.

Abstract

Distributed estimation of the average value over a Wireless Sensor Network has recently received a lot of attention. Most papers consider single variable sensors and communications with feedback (e.g. peer-to-peer communications). However, in order to use efficiently the broadcast nature of the wireless channel, communications without feedback are advocated. To ensure the convergence in this feedback-free case, the recently-introduced Sum-Weight-like algorithms which rely on two variables at each sensor are a promising solution. In this paper, the convergence towards the consensus over the average of the initial values is analyzed in depth. Furthermore, it is shown that the squared error decreases exponentially with the time. In addition, a powerful algorithm relying on the Sum-Weight structure and taking into account the broadcast nature of the channel is proposed.