Meta Distribution of SIR in the Internet of Things Modelled as a Euclidean Matching

TL;DR

This paper models user-base station interactions in dense IoT networks using bipartite Euclidean matching, revealing limitations of traditional bipolar models and proposing improvements for reliability analysis.

Contribution

It introduces the bipartite Euclidean matching framework to better characterize link reliability in dense IoT networks, highlighting the shortcomings of the bipolar model.

Findings

BEM provides detailed SIR distribution insights in dense networks.

Traditional bipolar models underestimate network reliability.

Gamma distribution for link distances improves model accuracy.

Abstract

The Poisson bipolar model considers user-base station pairs distributed at random on a flat domain, similar to matchsticks scattered onto a table. Though this is a simple and tractable setting in which to study dense networks, it doesn't properly characterise the stochastic geometry of user-base station interactions in some dense deployment scenarios, which may involve short and long range links, with some paired very nearby optimally, and others sub-optimally due to local crowding. Since the users will pair one-to-one with base stations, we can consider using the popular bipartite Euclidean matching (BEM) from spatial combinatorics, and study the corresponding (meta) distribution of the signal-to-interference-ratio (SIR). This provides detailed information about the proportion of links in the network meeting a target reliability constraint. We can then observe via comparison the impact of taking into account the variable/correlated short-range distances between the transmitter-receiver pairs on the communication statistics. We illustrate and quantify how the widely-accepted bipolar model fails to capture the network-wide reliability of communication in a typical ultra-dense setting based on a binomial point process. We also show how assuming a Gamma distribution for link distances may be a simple improvement on the bipolar model. Overall, BEMs provide good grounds for understanding more sophisticated pairing features in ultra-dense networks.