Connectivity Scaling Laws in Wireless Networks

TL;DR

This paper derives scaling laws for local and global connectivity in bounded wireless networks, linking key parameters like transmit power and antennas to network connectivity properties, aiding in boundary effect mitigation and topology control.

Contribution

It introduces new scaling laws that relate network parameters to connectivity probabilities, providing insights for network design and boundary effect mitigation.

Findings

Local connectivity probability scales as $ ext{O}(z^ ext{C})$ with system parameters.

Connectivity scaling depends on the ratio of network dimension to path loss exponent.

Results enable improved boundary effect mitigation and network topology control.

Abstract

We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas exploited for diversity coding and/or beamforming at each node. We demonstrate that the local probability of connectivity scales like $\mathcal{O}(z^\mathcal C)$ in these parameters, where $\mathcal C$ is the ratio of the dimension of the network domain to the path loss exponent, thus enabling efficient boundary effect mitigation and network topology control.