The Optimal and the Greedy: Drone Association and Positioning Schemes for Internet of UAVs

This work considers the deployment of unmanned aerial vehicles (UAVs) over a predefined area to serve a number of ground users. Due to the heterogeneous nature of the network, the UAVs may cause severe interference to the transmissions of each other. Hence, a judicious design of the user-UAV association and UAV locations is desired. A potential game is defined where the players are the UAVs. The potential function is the total sum rate of the users. The agents' utility in the potential game is their marginal contribution to the global welfare or their so-called wonderful life utility. A game-theoretic learning algorithm, binary log-linear learning (BLLL), is then applied to the problem. Given the potential game structure, a consequence of our utility design, the stochastically stable states using BLLL are guaranteed to be the potential maximizers. Hence, we optimally solve the joint user-UAV association and 3-D-location problem. Next, we exploit the submodular features of the sum rate function for a given configuration of UAVs to design an efficient greedy algorithm. Despite the simplicity of the greedy algorithm, it comes with a performance guarantee of $1-1/e$ of the optimal solution. To further reduce the number of iterations, we propose another heuristic greedy algorithm that provides very good results. Our simulations show that, in practice, the proposed greedy approaches achieve significant performance in a few iterations.