SINR and Throughput Scaling in Ultradense Urban Cellular Networks

TL;DR

This paper extends 2D cellular network analysis to 3D, revealing how SINR and throughput scale in dense urban environments with vertical base station stacking, using a dual-slope path loss model.

Contribution

It provides the first 3D coverage and throughput scaling laws for urban cellular networks with dual-slope path loss, including realistic scenarios with no base stations below users.

Findings

Critical path loss exponent equals network dimension (3) for SINR decay.

Potential throughput decays to zero when the path loss exponent is less than half the dimension.

Results hold for realistic 3D+ models with no base stations below the user.

Abstract

We consider a dense urban cellular network where the base stations (BSs) are stacked vertically as well as extending infinitely in the horizontal plane, resulting in a greater than two dimensional (2D) deployment. Using a dual-slope path loss model that is well supported empirically, we extend recent 2D coverage probability and potential throughput results to 3 dimensions. We prove that the "critical close-in path loss exponent" $\alpha_0$ where SINR eventually decays to zero is equal to the dimensionality $d$, i.e. $\alpha_0 \leq 3$ results in an eventual SINR of 0 in a 3D network. We also show that the potential (i.e. best case) aggregate throughput decays to zero for $\alpha_0 < d/2$. Both of these scaling results also hold for the more realistic case that we term ${3\rm{D}^{+}}$, where there are no BSs below the user, as in a dense urban network with the user on or near the ground.