Stochastic Geometry Modeling and Analysis of Single- and Multi-Cluster Wireless Networks

TL;DR

This paper introduces a stochastic geometry framework for modeling and analyzing both single- and multi-cluster wireless networks, deriving coverage probabilities, interference distributions, and bounds, with insights into parameter impacts.

Contribution

It extends existing models by incorporating finite Poisson processes and Matern cluster processes for multi-cluster networks, providing new analytical tools and bounds.

Findings

Coverage probability formulas for different selection strategies.

Derived interference Laplace transforms and bounds.

Insights into parameter effects on network performance.

Abstract

This paper develops a stochastic geometry-based approach for the modeling and analysis of single- and multi-cluster wireless networks. We first define finite homogeneous Poisson point processes to model the number and locations of the transmitters in a confined region as a single-cluster wireless network. We study the coverage probability for a reference receiver for two strategies; closest-selection, where the receiver is served by the closest transmitter among all transmitters, and uniform-selection, where the serving transmitter is selected randomly with uniform distribution. Second, using Matern cluster processes, we extend our model and analysis to multi-cluster wireless networks. Here, the receivers are modeled in two types, namely, closed- and open-access. Closed-access receivers are distributed around the cluster centers of the transmitters according to a symmetric normal distribution and can be served only by the transmitters of their corresponding clusters. Open-access receivers, on the other hand, are placed independently of the transmitters and can be served by all transmitters. In all cases, the link distance distribution and the Laplace transform (LT) of the interference are derived. We also derive closed-form lower bounds on the LT of the interference for single-cluster wireless networks. The impact of different parameters on the performance is also investigated.