A Stochastic Geometry Approach to the Rate of Downlink Cellular Networks over Correlated Log-Normal Shadowing

In this paper, an analytical framework to compute the average rate of downlink heterogeneous cellular networks is introduced. The framework exploits the so-called Poisson Point Process (PPP-) based abstraction model for the positions of the Base Stations (BSs), and results from stochastic geometry for other-cell interference modeling and performance analysis are used. The contribution of the present paper is twofold. 1) A simplified framework is proposed, which avoids the computation of the Meijer G-function and is applicable to arbitrary path-loss exponents. The new mathematical approach relies upon the Anderssen et al. sum of exponentials approximation for the Kohlrausch function. 2) The framework is applicable to correlated log-normal shadowing. The new mathematical approach relies upon the Owen and Steck method for the generation of equi-correlated multivariate normal distributions. The frameworks are substantiated through extensive Monte Carlo simulations, and numerical examples show that: i) for low Signal-to-Noise-Ratios (SNRs), the average rate slightly decreases if shadowing correlation increases; and ii) for high-SNRs, the average rate increases if shadowing correlation increases.