Analysis of Dense Cellular Networks with Stretched Exponential Path Loss

Distance-based attenuation is a critical aspect of wireless communications. As opposed to the ubiquitous power-law path loss model, this paper proposes a stretched exponential path loss model that is suitable for short-range communication. In this model, the signal power attenuates over a distance r as e(-alpha r beta), where alpha, beta are tunable parameters. We integrate this path loss model into a downlink cellular network with base stations modeled by a Poisson point process, and derive expressions for the coverage probability and area spectral efficiency. Although the most general result for coverage probability has a double integral, several special cases are given where the coverage probability has a compact or even closed form. We show that coverage probability collapses to zero for high base station densities. We next prove that the area spectral efficiency is non-decreasing with the base station density and converges to a constant for high densities.