Abstract
In this paper, we investigate the coverage performance and energy efficiency of multi-tier heterogeneous cellular networks (HetNets) which are composed of macrocells and different types of small cells, i.e., picocells and femtocells. By virtue of stochastic geometry tools, we model the multi-tier HetNets based on a Poisson point process (PPP) and analyze the Signal to Interference Ratio (SIR) via studying the cumulative interference from pico-tier and femto-tier. We then derive the analytical expressions of coverage probabilities in order to evaluate coverage performance in different tiers and investigate how it varies with the small cells' deployment density. By taking the fairness and user experience into consideration, we propose a disjoint channel allocation scheme and derive the system channel throughput for various tiers. Further, we formulate the energy efficiency optimization problem for multi-tier HetNets in terms of throughput performance and resource allocation fairness. To solve this problem, we devise a linear programming based approach to obtain the available area of the feasible solutions. System-level simulations demonstrate that the small cells' deployment density has a significant effect on the coverage performance and energy efficiency. Simulation results also reveal that there exits an optimal small cell base station (SBS) density ratio between pico-tier and femto-tier which can be applied to maximize the energy efficiency and at the same time enhance the system performance. Our findings provide guidance for the design of multi-tier HetNets for improving the coverage performance as well as the energy efficiency.