3-D Spatial Modeling of Network Interference in Two-Tier Heterogeneous Networks

The multi-tier heterogeneous network (HetNet) architecture can potentially address the massive connectivity and high throughput demands of the emerging fifth generation (5G) of wireless networks. However, the inter-tier interference in HetNets is considered to be a major performance bottleneck. This paper proposes a geometry-based three-dimensional (3-D) stochastic channel model for the spatial characterization of the sum interference in a two-tier HetNet with small cells in tier-1 overlaid with massive multiple-input-multiple-output equipped macro-cell base stations in tier-2. The angular spreads of the interference and the desired signals are analyzed by using the theory of 3-D multipath shape-factors and analytical expressions are derived for their second-order fading statistics, viz: level-crossing-rate (LCR), average-fade-duration (AFD), spatial autocovariance, and the coherence distance. Further, analytical expressions to investigate the second-order fading statistics against signal-to-interference ratio are also derived. The validation of the derived analytical expressions is established through a comparison with computer-based simulations. To provide insights into the network sum interference mechanism, the LCR and AFD expressions are derived for the special case when the rate of fluctuation of the desired signal is much higher than that of the interference signal and vice versa. Furthermore, the impact of the model’s physical parameters, such as the link distance and the receiver’s direction of motion as well as the fading distribution parameters such as its intensity and shape factors on the fading statistics of the interference are evaluated. These results demonstrate that the elevation angle has a significant impact on the interference characterization in HetNet architectures such that it cannot be ignored in modeling emerging 5G communication scenarios.