Wirelessly Powered Data Aggregation via Intelligent Reflecting Surface Assisted Over-the-Air Computation

Fast wireless data aggregation and efficient battery recharging are two critical design challenges of Internet of Things (IoT) networks. Over-the-air computation (AirComp) and energy beamforming (EB) are two promising techniques that can tackle these two challenges. In this paper, we propose to leverage the intelligent reflecting surface (IRS) to drastically enhance the efficiency of both downlink EB and uplink AirComp in IoT networks by exploiting the passive beamforming gains at the IRS. Due to the coupled downlink EB and uplink AirComp, we propose the joint design of energy and aggregation beamformers at the access point, downlink/uplink phase-shift matrices at the IRS, and transmit power at the IoT devices to minimize the mean-squared-error (MSE), which quantifies the AirComp distortion. However, the formulated problem is a highly intractable nonconvex quadratic programming problem. To this end, we first obtain the closed-form expressions of the energy beamformer and the transmit power, and then propose an efficient algorithm that alternatively updates other variables using semidefinite relaxation (SDR) to solve the problem. Simulation results demonstrate the performance gains of the proposed algorithm over the baseline methods and show that deploying an IRS can significantly reduce the MSE of AirComp.