On The Distance Distributions of The Wireless Ad Hoc Networks

Separation distance between nodes is an important index in characterizing the optimum transmission range, the most probable Euclidean distance between two random selected nodes, the node degree and the network connectivity of wireless ad hoc networks. However, because nodes are randomly deployed, the separation distances between nodes in the wireless ad hoc networks are also random. Thus, in this paper, we present methodologies to analyze three distance-related probability distributions: the distribution of the distance to the k-th nearest neighbor, the distribution of the distance between two random selected nodes and the joint distribution of the distances between nodes and a common reference node