Fundamentals of Modeling Finite Wireless Networks using Binomial Point Process

TL;DR

This paper develops a mathematical framework for modeling finite wireless networks using binomial point processes, analyzing coverage, diversity, spectral efficiency, and caching strategies with new distance distributions.

Contribution

It introduces a novel set of distance distributions for finite networks, enabling comprehensive analysis of coverage, diversity, and caching policies under different transmitter selection methods.

Findings

Derived new distance distributions for finite networks.

Analyzed diversity loss due to SIR correlation.

Optimized the number of active links and caching probabilities.

Abstract

Modeling the locations of nodes as a uniform binomial point process (BPP), we present a generic mathematical framework to characterize the performance of an arbitrarily-located reference receiver in a finite wireless network. Different from most of the prior works where the serving transmitter (TX) node is located at the fixed distance from the reference receiver, we consider two general TX-selection policies: i) uniform TX-selection: the serving node is chosen uniformly at random amongst transmitting nodes, and ii) k-closest TX-selection: the serving node is the k-th closest node out of transmitting nodes to the reference receiver. The key intermediate step in our analysis is the derivation of a new set of distance distributions that lead not only to the tractable analysis of coverage probability but also enable the analyses of wide range of classical and currently trending problems in wireless networks. Using this new set of distance distributions, we first investigate the diversity loss due to SIR correlation in a finite network. We then obtain the optimal number of links that can be simultaneously activated to maximize network spectral efficiency. Finally, we evaluate optimal caching probability to maximize the total hit probability in cache-enabled finite networks.