Modeling Heterogeneous Cellular Networks Interference Using Poisson Cluster Processes

Future mobile networks are converging toward heterogeneous multitier networks, where macro-, pico-, and femto-cells are randomly deployed based on user demand. A popular approach for analyzing heterogeneous networks (HetNets) is to use stochastic geometry and treat the location of BSs as points distributed according to a homogeneous Poisson point process (PPP). However, a PPP model does not provide an accurate model for the interference when nodes are clustered around highly populated areas. This motivates us to find better ways to characterize the aggregate interference when transmitting nodes are clustered following a Poisson cluster process (PCP) while taking into consideration the fact that BSs belonging to different tiers may differ in terms of transmit power, node densities, and link reliabilities. To this end, we consider K-tier HetNets and investigate the outage probability, the coverage probability, and the average achievable rate for such networks. We compare the performance of HetNets when nodes are clustered and otherwise. By comparing these two types of networks, we conclude that the fundamental difference between a PPP and a PCP is that, for a PPP, the number of simultaneously covered mobiles and the network capacity linearly increase with K. However, for a PCP, the improvements in the coverage and the capacity diminish as K grows larger, where the curves saturate at some point. Based on these observations, we determine the scenarios that jointly maximize the average achievable rate and minimize the outage probability.