Computing the kk-coverage of a wireless network

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.Comment: Valuetools 2019, Mar 2019, Palma de Mallorca, Spain. 2019. arXiv admin note: text overlap with arXiv:1802.0844

Homology-based Distributed Coverage Hole Detection in Wireless Sensor Networks

Homology theory provides new and powerful solutions to address the coverage problems in wireless sensor networks (WSNs). They are based on algebraic objects, such as Cech complex and Rips complex. Cech complex gives accurate information about coverage quality but requires a precise knowledge of the relative locations of nodes. This assumption is rather strong and hard to implement in practical deployments. Rips complex provides an approximation of Cech complex. It is easier to build and does not require any knowledge of nodes location. This simplicity is at the expense of accuracy. Rips complex can not always detect all coverage holes. It is then necessary to evaluate its accuracy. This work proposes to use the proportion of the area of undiscovered coverage holes as performance criteria. Investigations show that it depends on the ratio between communication and sensing radii of a sensor. Closed-form expressions for lower and upper bounds of the accuracy are also derived. For those coverage holes which can be discovered by Rips complex, a homology-based distributed algorithm is proposed to detect them. Simulation results are consistent with the proposed analytical lower bound, with a maximum difference of 0.5%. Upper bound performance depends on the ratio of communication and sensing radii. Simulations also show that the algorithm can localize about 99% coverage holes in about 99% cases

Simplicial Homology for Future Cellular Networks

Simplicial homology is a tool that provides a mathematical way to compute the connectivity and the coverage of a cellular network without any node location information. In this article, we use simplicial homology in order to not only compute the topology of a cellular network, but also to discover the clusters of nodes still with no location information. We propose three algorithms for the management of future cellular networks. The first one is a frequency auto-planning algorithm for the self-configuration of future cellular networks. It aims at minimizing the number of planned frequencies while maximizing the usage of each one. Then, our energy conservation algorithm falls into the self-optimization feature of future cellular networks. It optimizes the energy consumption of the cellular network during off-peak hours while taking into account both coverage and user traffic. Finally, we present and discuss the performance of a disaster recovery algorithm using determinantal point processes to patch coverage holes