Tractable Framework for the Analysis of General Multi-Tier Heterogeneous Cellular Networks

This paper investigates the downlink performance of K-tier heteregeneous 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 KolmogorovSmirnov (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 pertier 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 propogation 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. S. Ak is with the Department of Electrical and Electronics Engineering, Antalya International University 07190, Antalya, Turkey (e-mail: [email protected]). H. Inaltekin and H. V. Poor are with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA (e-mail: {hinaltek, poor}@princeton.edu). This research was supported in part by the European Union Research Executive Agency Marie Curie FP7-Reintegration-Grants under Grant PCIG10-GA-2011-303713, in part by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant 115E162, and in part by the U.S. National Science Foundation under Grant ECCS-1343210. This work was presented in part at the IEEE International Symposium on Information Theory (ISIT), in Barcelona, Spain, July 2016 [1], [2].