Coordinates Distributions in Finite Uniformly Random Networks

This work introduces the concept of angular distance distributions of the nodes in a Binomial point process-based model for wireless networks. The need for the derivation of these distributions is motivated by the use of high-frequency bands in the mmWave or even in the sub-THz bands. These frequencies are closely related to the beamforming capabilities of the transceivers in wireless networks. Therefore, the directional characteristics of the beams utilized by the communicating nodes, along with the random location of the latter, lead to an increasing demand for the distributions derived in this paper. A direct consequence of the Binomial process utilized to model the random location of a fixed number of nodes in a ball, is that the extracted distributions are based on the generalized beta distribution. The presented results are applicable to two- and three-dimensional networks and can be used to study various network characteristics among which are the interference, and the beam management.