Joint Distribution of Distance and Angle in Rectangular Finite Wireless Networks

In this paper, we investigate the distribution of the distance and azimuth angle between a reference node and a node randomly placed within a rectangular finite wireless network. As a result, we prove that there exists a non-negligible correlation between both random variables, that depends on the shape of the rectangle and on the location of the reference node. To characterize this dependence, we derive the joint distribution of distance and azimuth angle, which is expressed as the sum of a small number of closed-form terms. This expression has applications on the analysis of directional beamforming.