Stochastic Geometry for Wireless Networks
Abstract
Random geometric graphs have provided an excellent framework for
modeling in wireless networks. Vertices of the graphs form the
communicating entities and an edge between two nodes in the graph
indicates the ability of the two nodes to communicate. In the simplest
model, two edges are connected if the distance between the two nodes is
less than a cutoff radius. Our interest is in the behavior of the system
when the number of nodes is large. First we will discuss some point
process models for describing the distribution of the nodes, and derive
some properties of the Poisson point process. Then the problems of
coverage, percolation and connectivity will be discussed. These include
the radius required to cover an arbitrary fraction of the space, existence
of a phase transition or the emergence of a giant component and the
critical radius required for the graph to be connected with high
probability.