# Computing the $k$-coverage of a wireless network

## TL;DR

This paper presents a novel algorithm that uses simplicial homology to efficiently compute the $k$-coverage in wireless networks, enhancing understanding of network reliability and supporting applications like MIMO and handovers.

## Contribution

The paper introduces a new topological algorithm leveraging simplicial homology to compute $k$-coverage, providing a more effective method than previous approaches.

## Key findings

- Algorithm accurately computes $k$-coverage in simulations.
- Uses topological methods to interpret coverage layers.
- Demonstrates applicability to real-world wireless networks.

## Abstract

Coverage is one of the main quality of service of a wirelessnetwork. $k$-coverage, that is to be covered simultaneously by $k$network nodes, is synonym of reliability and numerous applicationssuch as multiple site MIMO features, or handovers. We introduce here anew algorithm for computing the $k$-coverage of a wirelessnetwork. Our method is based on the observation that $k$-coverage canbe interpreted as $k$ layers of $1$-coverage, or simply coverage. Weuse simplicial homology to compute the network's topology and areduction algorithm to indentify the layers of $1$-coverage. Weprovide figures and simulation results to illustrate our algorithm.