Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Joint Distribution of Distance and Angles in Finite Wireless Networks   Directional beamforming will play a paramount role in 5G and beyond networks
in order to combat the higher path losses incurred at millimeter wave bands.
Appropriate modeling and analysis of the angles and distances between
transmitters and receivers in these networks are thus essential to understand
performance and limiting factors. Most existing literature considers either
infinite and uniform networks, where nodes are drawn according to a Poisson
point process, or finite networks with the reference receiver placed at the
origin of a disk. Under either of these assumptions, the distance and azimuth
angle between transmitter and receiver are independent, and the angle follows a
uniform distribution between $0$ and $2\pi$. Here, we consider a more realistic
case of finite networks where the reference node is placed at any arbitrary
location. We obtain the joint distribution between the distance and azimuth
angle and demonstrate that these random variables do exhibit certain
correlation, which depends on the shape of the region and the location of the
reference node. To conduct the analysis, we present a general mathematical
framework which is specialized to exemplify the case of a rectangular region.
We then also derive the statistics for the 3D case where, considering antenna
heights, the joint distribution of distance, azimuth and zenith angles is
obtained. Finally, we describe some immediate applications of the present work,
including the analysis of directional beamforming, the design of analog
codebooks and wireless routing algorithms.

33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat