Unmanned Aerial Vehicles (UAVs) are ideal as aerial base stations, mobile relays or data collectors. In this paper, we consider a UAV with a Succesive Interference Cancellation (SIC) radio that visits M collection points to download data from ground devices or sensors. The problem at hand is to determine the links to be scheduled at each data collection point. To this end, we formulate an Integer Linear Program (ILP) to compute the optimal transmission schedule. We also propose a Cross Entropy (CE) approach to select links when there are a large number of ground devices. Our reseults show that SIC helps double the amount of data collected by the UAV. We also find that the average throughput is affected by the number of ground devices and the number of data collection points. Lastly, our CE approach is capable of producing a schedule that is near optimal.