Stochastic Geometry Based Cell Load Analysis in Heterogeneous Networks

In this paper, we propose a mathematical framework for downlink heterogeneous networks (HetNets) involving cell load factors, which measure the average resource consumption. Due to mutual interference, the cell load levels of different tiers are in general coupled with each other in a nonlinear manner. By leveraging tools from stochastic geometry, we compute the average cell load levels across tiers via fixed-point equations that are dependent upon network parameters (e.g., deployment density, transmit power, association bias) and users' data demands. As an exemplary application of the proposed model, the effect of the association bias on achieving balanced network loads is investigated in two-tier networks. The optimum association bias factor, although not expressed in closed form, can be found efficiently through the standard bisection search method. Numerical results show that in the feasible load region, the previous cell load estimation based on worst-case SIR (signal-to-interference ratio) gives an upper bound on the cell load levels derived in this paper. In addition, the effectiveness of the proposed optimum bias adaptation for the purpose of load balancing is demonstrated by simulation.