We consider unmanned aerial vehicle (UAV)-enabled wireless systems where downlink communications between a multi-antenna UAV and multiple users are assisted by a hybrid active-passive reconfigurable intelligent surface (RIS). We aim at a fairness design of two typical UAV-enabled networks, namely the static-UAV network where the UAV is deployed at a fixed location to serve all users at the same time, and the mobile-UAV network which employs the time division multiple access protocol. In both networks, our goal is to maximize the minimum rate among users through jointly optimizing the UAV’s location/trajectory, transmit beamformer, and RIS coefficients. The resulting problems are highly nonconvex due to a strong coupling between the involved variables. We develop efficient algorithms based on block coordinate ascend and successive convex approximation to effectively solve these problems in an iterative manner. In particular, in the optimization of the mobile-UAV network, closed-form solutions to the transmit beamformer and RIS passive coefficients are derived. Numerical results show that a hybrid RIS equipped with only 4 active elements and a power budget of 0 dBm offers an improvement of 38%-63% in minimum rate, while that achieved by a passive RIS is only about 15%, with the same total number of elements.
