In this paper, we consider unmanned aerial vehicles (UAVs) assisted cellular communication system, where UAVs can be used as amplify-and-forward (AF) relays. The effective channel with UAV assisted communication can be modeled as a Rayleigh product-channel, and we derive a tight lower-bound of the ergodic capacity in closed-form. With the obtained lower-bound, trade-offs between the transmit power and the equipped number of antennas of the UAVs can be analyzed. Alternatively, for a giving setting of users and the base-transceiver station (BTS), the needed transmit power and number of antennas for the UAVs can be derived in order to have a higher ergodic capacity with the UAV assisted communication than that without it.