Robust Transmission Design for RIS-Assisted Multi-Cluster Wireless Powered Communications With Hardware Impairments

This paper focuses on a reconfigurable intelligent surface (RIS) assisted multi-cluster wireless powered communication network (WPCN) in the presence of hardware impairments (HIs). With the aid of an RIS, passive devices (PDs) grouped into multiple clusters first jointly collect the energy radiated by an energy source (ES), and then transmit useful information to an access point through a hybrid time- and frequency- division multiple access (HTF) scheme. Specifically, the PDs from different clusters occupy different transmission time to avoid inter-cluster interference, while the PDs within the same cluster occupy different bandwidth to avoid intra-cluster interference. Due to non-ideal hardware, the impact of the phase shift (PS) error at the RIS and the HIs at the transceivers are revealed. Then, the closed-form expression for average system sum rate (ASSR) is derived. Assuming that the ES and the PDs are deployed by different service providers, a Stackelberg game (SG) is utilized to model energy trading based on price incentive. In the established SG, the PDs act as a leader to maximize the difference between the ASSR benefit and energy payment by optimizing energy price, RIS PSs in the information tansfer stage, as well as time and bandwidth allocation. Meanwhile, the ES acts as a follower to maximize the difference between energy payment and energy cost by optimizing transmit power, energy beamforming, and RIS PSs in the energy transfer stage. The follower and leader level problems are solved through algorithms such as majorization-minimization, alternating optimization, Lagrange dual approach, Karush-Kuhn-Tucker condition, block coordinate descent, and one-dimensional search. Simulation results verify that compared to the benchmark schemes, the proposed HTF scheme achieves higher PDs’ utility value and lower ES’s energy consumption, and strikes a balance between utility and overhead.