Distance Distributions in Finite Ad Hoc Networks: Approaches, Applications, and Directions

Most performance metrics in wireless ad hoc networks, such as interference, Signal-to-Interference-plus-Noise Ratio, path loss, outage probability, link capacity, node degree, hop count, network coverage, and connectivity, are nonlinear functions of the distances among communicating, relaying, and interfering nodes. A probabilistic distance-based model is definitely needed in quantifying these metrics, which eventually involves the Nodal Distance Distribution (NDD) in a finite network intrinsically depending on the network coverage and nodal spatial distribution. In general, there are two types of NDD, i.e., (1) Ref2Ran: the distribution of the distance between a given reference node and a node uniformly distributed at random, and (2) Ran2Ran: the distribution of the distance between two nodes uniformly distributed at random. Traditionally, ad hoc networks were modeled as rectangles or disks. Recently, both types of NDD have been extended to the networks in the shape of one or multiple arbitrary polygons, such as convex, concave, disjoint, or tiered networks. In this paper, we survey the state-of-the-art approaches to the two types of NDD with uniform or nonuniform node distributions and their applications in wireless ad hoc networks, as well as discussing the open issues, challenges, and future research directions.