Unique coverage in Boolean models

TL;DR

This paper studies the maximum proportion of users uniquely covered by base stations in wireless networks, providing exact solutions in one dimension and bounds with simulations in two dimensions.

Contribution

It offers a complete solution for the one-dimensional case and new bounds, approximations, and simulations for the more complex two-dimensional case.

Findings

Complete solution for 1D case

Bounds and approximations for 2D case

Simulation results supporting theoretical findings

Abstract

Consider a wireless cellular network consisting of small, densely scattered base stations. A user $u$ is {\em uniquely covered} by a base station $b$ if $u$ is the only user within distance $r$ of $b$. This makes it possible to assign the user $u$ to the base station $b$ without interference from any other user $u'$. We investigate the maximum possible proportion of users who are uniquely covered. We solve this problem completely in one dimension and provide bounds, approximations and simulation results for the two-dimensional case.