SINR and Throughput Scaling in Ultradense Urban Cellular Networks

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. We use a dual-slope path loss model that is well supported empirically, wherein a “close-in” pathloss exponent $\alpha_0$ is used for distances less than a corner distance $R_c$ , and then changes to $\alpha_1 > \alpha_0$ outside $R_c$ . We extend recent 2D coverage probability and potential throughput results to $d$ dimensions, and prove that if the close-in path loss exponent $\alpha_0 , then the SINR eventually decays to zero. For example, $\alpha_0 \le 3$ results in an eventual SINR of 0 for all users in a 3D network, which is a troubling fact. We also show that the potential (i.e. best case) aggregate throughput decays to zero for $\alpha_0 . Both of these scaling results also hold for the more realistic case that we term 3D+, where there are no BSs below the user, as in a dense urban network with the user on or near the ground.