Downlink Interference Management in Dense Drone Small Cells Networks Using Mean-Field Game Theory

The use of drone small cells (DSCs) has recently drawn significant attentions as one key enabler for providing air-to-ground communication services in various situations. This paper investigates the co-channel deployment of dense DSCs, which are mounted on captive unmanned aerial vehicles (UAVs). As the altitude of a DSC has a huge impact on the performance of downlink, the downlink interference control problem is mapped to an altitude control problem in this paper. All DSCs adjust their altitude to improve the available signal-to-interference-plus-noise ratio (SINR). The control problem is modeled as a mean-field game (MFG), where the cost function is designed to combine the available SINR with the cost of altitude controlling. The interference introduced from a big amount of DSCs is derived through a mean-field approximation approach. Within the proposed MFG framework, the related Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov equations are deduced to describe and explain the control policy. The optimal altitude control policy is obtained by solving the partial differential equations with a proposed finite difference algorithm based on the upwind scheme. The simulations illustrate the optimal power controls and corresponding mean field distribution of DSCs. The numerical results also validate that the proposed control policy achieves better SINR performance of DSCs compared to the uniform control scheme.