Stackelberg Game-Based Multiple Access Design for Intelligent Reflecting Surface Assisted Wireless Powered IoT Networks

This paper integrates an intelligent reflecting surface (IRS) into a wireless powered Internet-of-Things (IoT) network, where IoT devices need to harvest energy from an energy station (ES) before transmitting their monitoring data to an access point. An IRS is invoked to improve energy and spectral efficiency by changing propagation environment. Considering that the ES and IoT devices come from different operators, IoT devices need to provide monetary payment in exchange for the ES's charging before implementing nonlinear energy harvesting. We build this energy interaction via Stackelberg game under three multiple access schemes, i.e., IRS-assisted time division multiple access (IRS-TDMA), IRS-assisted non-orthogonal multiple access (IRS-NOMA), and IRS-assisted frequency division multiple access (IRS-FDMA). To solve the common follower game among the three schemes, we first employ an alternating optimization (AO) algorithm with Majorization-Minimization (MM) to alternately optimize the energy beamforming and energy phase shifts, and then derive the optimal ES transmit power. For the leader game of IRS-TDMA, the optimal time allocation and optimal information phase shifts are first derived in closed form through Lagrange dual method and triangular inequality, respectively. On this basis, an AO algorithm is developed to optimize energy price and energy transfer time alternately. Similar procedures are also used to solve the leader games for IRS-NOMA and IRS-FDMA. Simulation results show that IRS-NOMA and IRS-FDMA achieve the same utilities for the ES and IoT devices. Due to IRS time selectivity, IRS-TDMA is more energy and spectral efficient than IRS-NOMA and IRS-FDMA, and this advantage is more pronounced in higher numbers of IRS elements and IoT devices.