A Stackelberg Game Approach for IRS-Aided WPCN Multicast Systems

This paper investigates an intelligent reflecting surface (IRS) aided wireless powered communication network (WPCN) with a focus on multicast transmissions in a game-theoretic way, where a transmitter first harvests energy from a power station (PS) and then transmits the information to multiple Internet of Things (IoT) devices in a multicast form. An IRS is deployed to assist the wireless energy transfer (WET) and wireless information transfer (WIT) processes. Considering that the PS and the transmitter belong to different service providers, we propose two schemes based on Stackelberg game, namely IRS-aided transmitter dominant energy trading (IRS-TDET) with the transmitter as the leader and IRS-aided PS dominant energy trading (IRS-PDET) with the PS as the leader. To solve the non-convex optimization problem of the leader-level game in the IRS-TDET scheme, we first derive the closed-form optimal phase shifts in the WET stage, and then use the semidefinite relaxation approach to solve the max-min problem about the phase shifts of the WIT stage. Finally, a low-complexity alternating optimization algorithm is developed to solve the simplified non-convex optimization problem with regard to the energy price and WET time. Numerical results show that the performance of proposed IRS-TDET and IRS-PDET is superior to that of the corresponding non-IRS aided schemes, and the deployment of IRS can effectively improve the utilities of both the PS and the transmitter. In addition, it is preferred to deploy the IRS near the transmitter in WPCN, and the transmitter can be deployed near the PS or the IoT devices to obtain higher utility.