Locally Estimating Log-normal Shadowing Parameters with Applications in Graph Planarization

We consider wireless networks with homogeneously Poisson distributed node positions and node connections based on the log-normal shadowing model. We describe a local method for estimating the log-normal shadowing parameters and the intensity of the underlying Poisson point process which are both global network parameters. We then apply the locally found parameters in a local method to planarize wireless network graphs which so far was depending on knowledge of these global parameters. Thereby, we present with this paper a fully local planarization strategy for wireless communication networks well beyond simplified wireless network models. Here, planarization means constructing a subgraph of a graph with nodes on the plane, such that the subgraph has no intersecting edges. At the same time, edges are to be removed in such a way that the subgraph remains connected. Local estimation of the log-normal shadowing parameters as well as local planarization based on these estimated parameters are then investigated by simulation. The simulation results show that local estimation of the parameters in combination with local planarization almost achieves the performance of the so far known method based on global knowledge.