Recently, the use of unmanned aerial vehicles (UAVs) as a relay node has been envisaged as an enabling technology in the upcoming wireless communication era. Thus, in this paper, we consider a full-duplex (FD) cooperative communication system with a source and a destination, where UAV serves as a mobile relay. Here, the transmission power cost is debited to energy harvested using simultaneous wireless information and power transfer (SWIPT) and self-interference energy harvesting (EH) via power-splitting (PS) protocol. In poor channel conditions, UAV uses a soft angular modulation scheme to perceive the soft information. In this proposed system, we present the outage probability over the Nakagami-m fading channels. A closed-form solution for the outage probability is derived. In addition, we formulate an optimization problem to minimize end-to-end outage probability subject of the UAV's power profile. The KKT conditions have been used to obtain a closed-form solution of the proposed optimization problem. Finally, numerical results are provided to evaluate the proposed system under various setups.