Mounting a reconfigurable intelligent surface (RIS) on an unmanned aerial vehicle (UAV) holds promise for improving traditional terrestrial network performance. Unlike conventional methods deploying passive RIS on UAVs, this study delves into the efficacy of an aerial active RIS (AARIS). Specifically, the downlink transmission of an AARIS network is investigated, where the base station (BS) leverages rate-splitting multiple access (RSMA) for effective interference management and benefits from the support of an AARIS for jointly amplifying and reflecting the BS's transmit signals. Considering both the non-trivial energy consumption of the active RIS and the limited energy storage of the UAV, we propose an innovative element selection strategy for optimizing the on/off status of RIS elements, which adaptively and remarkably manages the system's power consumption. To this end, a resource management problem is formulated, aiming to maximize the system energy efficiency (EE) by jointly optimizing the transmit beamforming at the BS, the element activation, the phase shift and the amplification factor at the RIS, the RSMA common data rate at users, as well as the UAV's trajectory. Due to the dynamicity nature of UAV and user mobility, a deep reinforcement learning (DRL) algorithm is designed for resource allocation, utilizing meta-learning to adaptively handle fast time-varying system dynamics. Simulations indicate that incorporating an active RIS at the UAV leads to substantial EE gain, compared to passive RIS-aided UAV. We observe the superiority of the RSMA-based AARIS system in terms of EE, compared to existing approaches adopting non-orthogonal multiple access (NOMA).
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