On the Deployment of Small Cells in 3D HetNets With Multi-Antenna Base Stations

With the dense deployment of small cells, the impact of height difference between base stations (BSs) and user equipment (UE) on the performance of heterogeneous networks (HetNets) becomes significant. The traditional two-dimensional models are no longer sufficient to capture the three-dimensional (3D) features of dense HetNets. On the other hand, deploying multiple antennas on BSs is a promising approach to improve network capacity. In this paper, we propose a 3D model for a
$K$
-tier HetNet with multi-antenna BSs, where different tiers share the same frequency band but may differ in BS height, BS density, number of antennas per BS, BS transmit power, association bias, and path loss exponent. We analytically derive the per-tier association probability under both the strongest received signal and the closest BS cell-association strategies. Based on that, we derive the expressions for the downlink ergodic rate, area spectral efficiency (ASE) and energy efficiency. The numerical results reveal that in the presence of macrocell BSs, for low to medium small-cell BS (SBS) densities, the closest BS cell-association strategy leads to low ergodic rate, ASE and energy efficiency regardless of the SBS height; while at very high SBS densities, under both cell-association strategies, SBSs should be deployed at the same height as UE to achieve high ergodic rate, ASE and energy efficiency. Moreover, we find that for a given SBS height, there exists an optimal combination of SBS density and number of antennas per SBS that maximizes the system energy efficiency.