Distributed Consensus over Wireless Sensor Networks Affected by Multipath Fading

TL;DR

This paper proposes a consensus algorithm for wireless sensor networks affected by multipath fading, providing conditions for exponential convergence to a global decision despite propagation delays and complex channel effects.

Contribution

It introduces a novel consensus algorithm for wideband wireless sensor networks with multipath channels, deriving necessary and sufficient conditions for convergence.

Findings

Convergence conditions depend on network topology and channel transfer functions.

The algorithm guarantees exponential convergence under bounded delay conditions.

Applicable to networks with multipath, frequency-selective channels.

Abstract

The design of sensor networks capable of reaching a consensus on a globally optimal decision test, without the need for a fusion center, is a problem that has received considerable attention in the last years. Many consensus algorithms have been proposed, with convergence conditions depending on the graph describing the interaction among the nodes. In most works, the graph is undirected and there are no propagation delays. Only recently, the analysis has been extended to consensus algorithms incorporating propagation delays. In this work, we propose a consensus algorithm able to converge to a globally optimal decision statistic, using a wideband wireless network, governed by a fairly simple MAC mechanism, where each link is a multipath, frequency-selective, channel. The main contribution of the paper is to derive necessary and sufficient conditions on the network topology and sufficient conditions on the channel transfer functions guaranteeing the exponential convergence of the consensus algorithm to a globally optimal decision value, for any bounded delay condition.