Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks

TL;DR

This paper analyzes a cone-based distributed topology control algorithm for wireless multi-hop networks that preserves connectivity without GPS, using directional information and optimizing power consumption, with theoretical guarantees and simulation validation.

Contribution

It provides a detailed analysis of a GPS-free, cone-based topology control algorithm, establishing optimal cone angle for connectivity and proposing power-saving optimizations.

Findings

Connectivity is guaranteed for cone angle <= 5π/6.

Power consumption can be reduced while maintaining network connectivity.

Simulation results validate the effectiveness of the algorithm and optimizations.

Abstract

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology control algorithm. This algorithm, introduced in [16], does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node $u$ transmits with the minimum power $p_{u,\alpha}$ required to ensure that in every cone of degree $\alpha$ around $u$, there is some node that $u$ can reach with power $p_{u,\alpha}$. We show that taking $\alpha = 5\pi/6$ is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from $s$ to $t$ when every node communicates at maximum power, then, if $\alpha <= 5\pi/6$, there is still a path in the smallest symmetric graph $G_\alpha$ containing all edges $(u,v)$ such that $u$ can communicate with $v$ using power $p_{u,\alpha}$. On the other hand, if $\alpha > 5\pi/6$, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations.