  In this paper, we consider an unmanned aerial vehicle (UAV) enabled relaying
system where multiple UAVs are deployed as aerial relays to support
simultaneous communications from a set of source nodes to their destination
nodes on the ground. An optimization problem is formulated under practical
channel models to maximize the minimum achievable expected rate among all pairs
of ground nodes by jointly designing UAVs' three-dimensional (3D) placement as
well as the bandwidth-and-power allocation. This problem, however, is
non-convex and thus difficult to solve. As such, we propose a new method,
called iterative Gibbs-sampling and block-coordinate-descent (IGS-BCD), to
efficiently obtain a high-quality suboptimal solution by synergizing the
advantages of both the deterministic (BCD) and stochastic (GS) optimization
methods. Specifically, our proposed method alternates between two optimization
phases until convergence is reached, namely, one phase that uses the BCD method
to find locally-optimal UAVs' 3D placement and the other phase that leverages
the GS method to generate new UAVs' 3D placement for exploration. Moreover, we
present an efficient method for properly initializing UAVs' placement that
leads to faster convergence of the proposed IGS-BCD algorithm. Numerical
results show that the proposed IGS-BCD and initialization methods outperform
the conventional BCD or GS method alone in terms of convergence-and-performance
trade-off, as well as other benchmark schemes.
