Q Cells in Wireless Networks
Martin Haenggi
TL;DR
This work tackles the analytic characterization of the coverage manifold ${\mathcal C}\subset\mathbb{R}^2$, defined as the region where the probability that the SIR exceeds a threshold ${\theta}$ is at least ${u}$. It introduces Q cells—deterministic regions formed by intersections of a small number of disks—as outer bounds on individual transmitter service regions, with the union of Q cells providing an outer bound on ${\mathcal C}$. By connecting to the SIR meta distribution, the authors show how Q cells can be scaled in infinite networks to yield accurate estimates of the coverage manifold, and they establish both coarse and refined Q-cell bounds (including a universal lower bound on the uncovered fraction and an MD-based upper bound) plus a practical scaling recipe. The approach generalizes Voronoi cells, offers interpretable geometric bounds, and provides a scalable, geometry-based methodology for QoS-constrained coverage estimation in wireless networks.
Abstract
For a given set of transmitters such as cellular base stations or WiFi access points, is it possible to analytically characterize the set of locations that are "covered" in the sense that users at these locations experience a certain minimum quality of service? In this paper, we affirmatively answer this question, by providing explicit simple outer bounds and estimates for the coverage manifold. The key geometric elements of our analytical method are the Q cells, defined as the intersections of a small number of disks. The Q cell of a transmitter is an outer bound to the service region of the transmitter, and, in turn, the union of Q cells is an outer bound to the coverage manifold. In infinite networks, connections to the meta distribution of the signal-to-interference ratio allow for a scaling of the Q cells to obtain accurate estimates of the coverage manifold.