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On the Mean Interference-to-Signal Ratio in Spatially Correlated Cellular Networks

The Inhomogeneous Double Thinning (IDT) approach is a tractable and general approximation for analyzing cellular networks in which the locations of the base stations are spatially correlated. Usually, however, the parameters of the approximation depend on the intensity and the specific parameters of the point process. Therefore, it is often difficult to unveil the impact of the system parameters from the resulting analytical framework. In this letter, we focus our attention on spatially repulsive cellular networks, and introduce a new parameterization for the IDT approach that is suitable for analysis. By assuming a bounded path-loss model, we prove the following trends for the Mean Interference-to-Signal Ratio (MISR): (i) the MISR monotonically decreases as the path-loss exponent increases and the deployment density of the base stations decreases; and (ii) the difference between the MISRs of Poisson and non-Poisson cellular networks monotonically decreases as the path-loss exponent increases and the density of the base stations decreases. As case studies, we specialize the proposed parametrization to the $\beta $ -Ginibre and square lattice point processes. We prove, in particular, that the MISR monotonically decreases as $\beta $ increases. These findings are shown to be in agreement with Monte Carlo simulations, and with numerical and analytical studies reported in prior works, thus substantiating the validity of the proposed parametrization.