A Tractable Approach to Coverage and Rate in Cellular Networks

TLDR

Traditional cellular network models place base stations on a grid and assume random or deterministic user locations, but these highly idealized models are not tractable, leading to reliance on complex simulations and a long‑standing need for more tractable models. The study develops general stochastic geometry models for multi‑cell SINR. The authors derive tractable expressions for the downlink SINR CCDF and mean rate under general assumptions, yielding quickly computable integrals or closed‑form results, and analyze coverage gain and rate loss from static frequency reuse. The proposed model predicts coverage that is a lower bound compared to the grid model, yet both models are similarly accurate, and its tractability and ability to capture dense, opportunistic base‑station placement make it advantageous for future networks.

Abstract

Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.