A tractable framework for the analysis of dense heterogeneous cellular networks

This paper investigates the downlink performance of dense K -tier heterogeneous cellular networks (HCNs) under general settings. First, Gaussian approximation bounds for the standardized aggregate wireless interference (AWI) in dense K -tier HCNs are obtained for when base stations (BSs) in each tier are distributed over the plane according to a spatial and general Poisson point process. The Kolmogorov-Smirnov (KS) distance is used to measure deviations of the distribution of the standardized AWI from the standard normal distribution. An explicit and analytical expression bounding the KS distance between these two distributions is obtained as a function of a broad range of network parameters, such as per-tier transmission power levels, per-tier BS intensity, BS locations, general fading statistics, and general bounded path-loss models. Bounds achieve a good statistical match between the standardized AWI distribution and its normal approximation even for moderately dense HCNs. Second, various spatial performance metrics of interest, such as outage capacity, ergodic capacity, and area spectral efficiency in the downlink of K-tier HCNs for general signal propagation models are investigated by making use of the derived distribution approximation results. Considering two specific BS association policies, it is shown that the derived performance bounds track the actual performance metrics reasonably well for a wide range of BS intensities, with the gap among them becoming negligibly small for denser HCN deployments. Finally, both analytical and numerical results on the area spectral efficiency reveal a non-linear growth trend with diminishing returns of HCN performance. Hence, the SIR invariance property does not hold under bounded path-loss models, which is a critical finding from the HCN design perspective. In particular, it points out a critical BS density beyond which the HCN performance starts to decline due to excessive wireless interference.