Stochastic Geometry Modeling and Analysis of Finite Millimeter Wave Wireless Networks

TL;DR

This paper presents a stochastic geometry framework for analyzing finite mmWave wireless networks, accounting for directional beams, LOS/NLOS channels, and random node placement, providing insights into coverage and rate performance.

Contribution

It introduces a novel stochastic geometry model for finite mmWave networks considering directional beams and blockage effects, deriving key performance metrics.

Findings

Coverage probability bounds depend on receiver location and beamwidth.

LOS and NLOS association probabilities are explicitly derived.

System performance is significantly affected by blockage and beam parameters.

Abstract

This paper develops a stochastic geometry-based approach for the modeling and analysis of finite millimeter wave (mmWave) wireless networks where a random number of transmitters and receivers are randomly located inside a finite region. We consider a selection strategy to serve a reference receiver by the transmitter providing the maximum average received power among all transmitters. Considering the unique features of mmWave communications such as directional transmit and receive beamforming and having different channels for line-of-sight (LOS) and non-line-of-sight (NLOS) links according to the blockage process, we study the coverage probability and the ergodic rate for the reference receiver that can be located everywhere inside the network region. As key steps for the analyses, the distribution of the distance from the reference receiver to its serving LOS or NLOS transmitter and LOS and NLOS association probabilities are derived. We also derive the Laplace transform of the interferences from LOS and NLOS transmitters. Finally, we propose upper and lower bounds on the coverage probability that can be evaluated easier than the exact results, and investigate the impact of different parameters including the receiver location, the beamwidth, and the blockage process exponent on the system performance.