  The performance optimization of UAV communication systems requires the joint
design of UAV trajectory and communication efficiently. To tackle the challenge
of infinite design variables arising from the continuous-time UAV trajectory
optimization, a commonly adopted approach is by approximating the UAV
trajectory with piecewise-linear path segments in three-dimensional (3D) space.
However, this approach may still incur prohibitive computational complexity in
practice when the UAV flight period/distance becomes long, as the distance
between consecutive waypoints needs to be kept sufficiently small to retain
high approximation accuracy. To resolve this fundamental issue, we propose in
this paper a new and general framework for UAV trajectory and communication
co-design. First, we propose a flexible path discretization scheme that
optimizes only a number of selected waypoints (designable waypoints) along the
UAV path for complexity reduction, while all the designable and non-designable
waypoints are used in calculating the approximated communication utility along
the UAV trajectory for ensuring high trajectory discretization accuracy. Next,
given any number of designable waypoints, we propose a novel path compression
scheme where the UAV 3D path is first decomposed into three one-dimensional
(1D) sub-paths and each sub-path is then approximated by superimposing a number
of selected basis paths weighted by their corresponding path coefficients, thus
further reducing the path design complexity. Finally, we provide a case study
on UAV trajectory design for aerial data harvesting from distributed ground
sensors, and numerically show that the proposed schemes can significantly
reduce the UAV trajectory design complexity yet achieve favorable rate
performance as compared to conventional path/time discretization schemes.
