Ergodic Throughput Maximization for RIS-Equipped-UAV-Enabled Wireless Powered Communications With Outdated CSI

This paper investigates a reconfigurable intelligent surface equipped unmanned aerial vehicle (RISeUAV)-enabled wireless powered communication network (WPCN) consisting of a ground hybrid access point (GHAP), a RISeUAV, and a ground wireless device (GWD). Specifically, the passive GWD first harvests energy through the downlink (DL) wireless power transfer (WPT) assisted by the RISeUAV, and then wireless information transfer (WIT) takes place in the RISeUAV-aided uplink (UL) communications. Due to the partial reciprocity of wireless channels, the unavailable DL channel state information (CSI) can be estimated by an outdated version of the UL CSI. Considering the negative effect of this outdated CSI and a non-linear energy-harvester (NLEH), we formulate a two-timescale active and passive beamforming (TTAPB) framework for maximizing the ergodic throughput (ET) and derive a closed-form expression of the ET, based on which the joint optimization of time allocation for WPT/WIT and UAV placement with two-timescale active and passive beamforming (JOTAUP-TTAPB) scheme is proposed. As for the solution of the JOTAUP-TTAPB scheme, although the objective function is non-convex with respect to the hovering altitude of the RISeUAV, it can be transformed into an equivalent exponential function of fractional forms that facilitates the utilization of a golden-section-search-aided Dinkelbach (GSS-D) algorithm to obtain a jointly optimal solution. Simulation results demonstrate the effectiveness of the TTAPB framework by validating our ET analysis. Furthermore, the JOTAUP-TTAPB scheme outperforms several benchmark schemes in spite of performance degradations of all schemes due to imperfect channel reciprocity, exhibiting remarkable robustness against outdated DL CSI. Moreover, the proposed JOTAUP-TTAPB scheme improves the performance bounds limited by NLEHs. Additionally, not only the GSS-D algorithm for the JOTAUP-TTAPB scheme shows a faster convergence than the golden-section-search-aided alternating optimization, but also the low-complexity joint optimization avoids optimality loss by exploiting semi-closed-form solutions.