Robust transmission design for active IRS-aided multiuser MIMO cognitive radio systems with non-linear energy harvesting models

This paper studies a multiuser multiple-input multiple-output simultaneous wireless information and power transfer cognitive radio system with the aid of an active intelligent reflecting surface (IRS). Considering the scenario that nonlinear energy harvesting models and power splitting (PS) protocols are adopted at energy receivers and that channel state information (CSI) imperfections of the channels to the primary users (PUs) are taken into consideration, we aim at designing the secondary base station (SBS) transmit precoding matrices, the IRS reflection coefficient matrix, and the secondary user (SU) PS ratios. The design objective is to maximize the system sum-rate (SR) under the transmit power constraints at the SBS, amplification power constraints at the IRS, amplitude constraints on IRS reflection elements, robust interference power (IP) constraints at the PUs, and minimum harvested energy constraints at the SUs. The formulated optimization problem is intractable to directly solve since the design variables are nonlinearly coupled, the objective function and constraints are highly nonconvex, and robust IP constraints are semi-infinite. To tackle the mathematical challenges, we derive the amenable surrogate functions and constraints while to handle the semi-infinite robust IP constraints, we transform them into linear matrix inequalities. Then, to find optimized solutions to the considered design problem, we exploit alternating optimization frames to derive an efficient iterative algorithm (IA). The convergence and computational complexity of the developed IA are shown. Simulation results illustrate the performance gains of the designed problem and robustness of IP constraints against CSI imperfections. Additionally, the numerical results show that the active IRS-aided systems exhibit superior SR performance over the passive IRS-aided systems.