Robust Active and Passive Beamformer Design for IRS-Aided Downlink MISO PS-SWIPT With a Nonlinear Energy Harvesting Model

Abstract

This paper optimizes the energy consumption of the downlink of a multiple-antenna base station (BS) transmitting to several single-antenna users. The BS utilizes simultaneous wireless information and power transfer (SWIPT) while receivers apply power-splitting (PS) with a nonlinear energy harvesting model leading to PS-SWIPT. We use an intelligent reflecting surface (IRS) and propose a joint design to optimize the active data and the BS’s energy beamformers, IRS’s passive beamformers, and the receivers’ PS ratios under perfect and imperfect CSI availability. In particular, the total BS transmit power is minimized while guaranteeing a minimum rate and harvested energy for each receiver. We apply the block coordinate descent (BCD) method to optimize active and passive beamformers iteratively. We enforce the rank-one constraint and solve the corresponding optimization problem via successive convex approximation (SCA) for accurate semidefinite relaxations. Furthermore, we propose a worst-case robust design for the imperfect CSI case and reformulate this problem with infinitely many constraints. With the BCD method, the problem is iteratively solved via semidefinite programming (SDP) and a second sub-problem with a linear objective and quadratic matrix inequalities, which is also solved via SCA. Numerical results show significant improvements (e.g., 30% decrease in transmit power) than those of no-IRS and IRS with random phase shifts.