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In this paper, we consider an unmanned aerial vehicle (UAV) enabled relayingsystem where multiple UAVs are deployed as aerial relays to supportsimultaneous communications from a set of source nodes to their destinationnodes on the ground. An optimization problem is formulated under practicalchannel models to maximize the minimum achievable expected rate among all pairsof ground nodes by jointly designing UAVs' three-dimensional (3D) placement aswell as the bandwidth-and-power allocation. This problem, however, isnon-convex and thus difficult to solve. As such, we propose a new method,called iterative Gibbs-sampling and block-coordinate-descent (IGS-BCD), toefficiently obtain a high-quality suboptimal solution by synergizing theadvantages of both the deterministic (BCD) and stochastic (GS) optimizationmethods. Specifically, our proposed method alternates between two optimizationphases until convergence is reached, namely, one phase that uses the BCD methodto find locally-optimal UAVs' 3D placement and the other phase that leveragesthe GS method to generate new UAVs' 3D placement for exploration. Moreover, wepresent an efficient method for properly initializing UAVs' placement thatleads to faster convergence of the proposed IGS-BCD algorithm. Numericalresults show that the proposed IGS-BCD and initialization methods outperformthe conventional BCD or GS method alone in terms of convergence-and-performancetrade-off, as well as other benchmark schemes.

3D Placement for Multi-UAV Relaying: An Iterative Gibbs-Sampling and Block Coordinate Descent Optimization Approach