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 α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is used for distances less than a corner distance R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , and then changes to α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> > α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> outside R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . We extend recent 2D coverage probability and potential throughput results to d dimensions, and prove that if the close-in path loss exponent α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <; d, then the SINR eventually decays to zero. For example, α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ≤ 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 α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <; d/2. Both of these scaling results also hold for the more realistic case that we term 3D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> , where there are no BSs below the user, as in a dense urban network with the user on or near the ground.