Placement Learning for Multi-UAV Relaying: A Gibbs Sampling Approach

In this paper, we consider a multi-unmanned aerial vehicle (UAV) relaying system where the UAVs are deployed to assist data relaying from multiple ground source nodes to their corresponding destination nodes. An optimization problem is formulated to maximize the minimum achievable rate among all pairs of nodes, by jointly designing the UAV placement and communication resource allocation. To solve this non-convex problem, we first reformulate it into two sub-problems, corresponding to a slave problem for the resource allocation given fixed UAV placement and a master problem for the UAV placement optimization. Then for the non-convex slave problem, we sub-optimally solve it by using the successive convex approximation method. The master problem, however, is intractable due to the lack of a closed-form expression for the max-min rate with respect to the UAV placement. We thus propose a new solution approach, called Gibbs-sampling-based (GSB) placement learning, to gradually learn a sub-optimal UAV placement by generating a sequence of samples for the UAV placement that constitute a Markov chain, where the transition probabilities are determined by the max-min rates of different configurations of UAV placement. Furthermore, a high-quality UAV-placement initialization scheme is proposed to accelerate the convergence speed of the proposed GSB algorithm. Numerical results are presented to demonstrate the significant rate improvement and fast convergence speed of the proposed scheme as compared to various benchmark schemes.