  Unmanned aerial vehicles (UAVs) as aerial base stations (BSs) are able to
provide not only the communication service to ground users, but also the
sensing functionality to localize targets of interests. In this paper, we
consider an airborne integrated sensing and communications (ISAC) system where
a UAV, which acts both as a communication BS and a mono-static radar, flies
over a given area to transmit downlink signal to a ground communication user.
In the meantime, the same transmitted signal is also exploited for mono-static
radar sensing. We aim to optimize the UAV trajectory, such that the performance
for both communication and sensing (C$\&$S) is explicitly considered. In
particular, we first formulate the trajectory design problem into a weighted
optimization problem, where a flexible performance trade-off between C$\&$S is
achieved. As a step forward, a multi-stage trajectory design approach is
proposed to improve the target estimation accuracy. While the resultant
optimization problem is difficult to solve directly, we develop an iterative
algorithm to obtain a locally optimal solution. Finally, numerical results show
that the target estimation error obtained by the trade-off approach is about an
order of magnitude better than a communication-only approach with a slight
decrease on communication performance.
