Three dimensional (3D) radiation pattern of an antenna mounted at a drone can significantly influence the air-to-ground (A2G) link quality. Even when a drone transmitter is very close to a ground receiver, if the antenna orientations are not aligned properly, a significant degradation can be observed in the received signal power at the receiver. To characterize such effects for a doughnut-shaped antenna radiation pattern, using an ultra-wideband (UWB) transmitter at the drone and a UWB receiver at the ground, we carry out A2G channel measurements to capture the link quality at the ground receiver for various link distances, drone heights, and antenna orientations. We develop a simple analytical model to approximate the influence of 3D antenna patterns on the received signal strength (RSS), which show reasonable agreement with measurements despite the simplicity of the model and the complicated 3D radiation from the UWB antennas. We also explore how the signal strength can be improved when multiple antennas with different orientations are utilized at transmitter/receiver.