Statistics of the uplink co-tier interference in closed access heterogeneous networks

In this paper, we derive a statistical model of the co-tier interference in closed access two tier heterogeneous wireless cellular networks with femtocell deployments. The derived model captures the impact of bounded path loss model, wall penetration loss, user distributions, random locations, and density of the femtocells. Firstly, we derive the analytical expressions for the probability density function (PDF) and moment generating function (MGF) of the co-tier interference considering a single femtocell interferer by exploiting the random disc line picking theory from geometric probability. We then derive the MGF of the cumulative interference from all femtocell interferers considering full spectral reuse in each femtocell. Orthogonal spectrum partitioning is assumed between the macrocell and femtocell networks to avoid any cross-tier interference. Finally, the accuracy of the derived expressions is validated through Monte-Carlo simulations and the expressions are shown to be useful in quantifying important network performance metrics such as ergodic capacity.