Density Estimation in Randomly Distributed Wireless Networks

Networks of randomly distributed nodes appear in various fields, including forestry and wireless communications, and can often be modeled, using stochastic geometry theory, as Poisson point processs (PPPs). In these contexts, estimation of nodes density is important for monitoring and optimizing the network. Originally, this problem has been addressed in forestry where the trees are the nodes and, assuming these are distributed according to an infinite two-dimensional homogeneous PPP, the spatial density can be estimated by measuring the distances from one reference tree to its neighbors. However, in many other scenarios, nodes could result invisible with some probability, for example depending on distance. In this paper, we derive the Cramer-Rao bounds and new estimators for the node spatial density, taking into account a limited capability in sensing neighbors. As an example, we provide estimators of the spatial density of transmitting devices in wireless networks with links affected by thermal noise, path loss, and shadowing.