  This paper considers an unmanned-aerial-vehicle-enabled (UAV-enabled)
wireless network where a relay UAV is used for two-way communications between a
ground base station (BS) and a set of distant user equipment (UE). The UAV
adopts the amplify-and-forward strategy for two-way relaying over orthogonal
frequency bands. The UAV positioning and the transmission powers of all nodes
are jointly designed to maximize the sum rate of both uplink and downlink
subject to transmission power constraints and the signal-to-noise ratio
constraint on the UAV control channel. The formulated joint positioning and
power control (JPPC) problem has an intricate expression of the sum rate due to
two-way transmissions and is difficult to solve in general. We propose a novel
concave surrogate function for the sum rate and employ the successive convex
approximation (SCA) technique for obtaining a high-quality approximate
solution. We show that the proposed surrogate function has a small curvature
and enables a fast convergence of SCA. Furthermore, we develop a
computationally efficient JPPC algorithm by applying the FISTA-type accelerated
gradient projection (AGP) algorithm to solve the SCA problem as well as one of
the projection subproblem, resulting in a double-loop AGP method. Simulation
results show that the proposed JPPC algorithms are not only computationally
efficient but also greatly outperform the heuristic approaches.
