  This work studies the joint problem of power and trajectory optimization in
an unmanned aerial vehicle (UAV)-enabled mobile relaying system. In the
considered system, in order to provide convenient and sustainable energy supply
to the UAV relay, we consider the deployment of a power beacon (PB) which can
wirelessly charge the UAV and it is realized by a properly designed laser
charging system. To this end, we propose an efficiency (the weighted sum of the
energy efficiency during information transmission and wireless power
transmission efficiency) maximization problem by optimizing the source/UAV/PB
transmit powers along with the UAV's trajectory. This optimization problem is
also subject to practical mobility constraints, as well as the
information-causality constraint and energy-causality constraint at the UAV.
Different from the commonly used alternating optimization (AO) algorithm, two
joint design algorithms, namely: the concave-convex procedure (CCCP) and
penalty dual decomposition (PDD)-based algorithms, are presented to address the
resulting non-convex problem, which features complex objective function with
multiple-ratio terms and coupling constraints. These two very different
algorithms are both able to achieve a stationary solution of the original
efficiency maximization problem. Simulation results validate the effectiveness
of the proposed algorithms.
