Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels: A Stochastic Geometry Approach

In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other—cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path—loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long—term averaged maximum biased—received—power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small— and mid—scale fluctuations. In addition, our method can efficiently handle correlated Log—Normal shadowing with little increase of the computational complexity. The proposed MGF—based approach needs the computation of either a single or a two—fold numerical integral, thus reducing the complexity of Pcov—based frameworks, which require, for general fading distributions, the computation of a four—fold integral.