Energy Efficiency Optimization for IRS-Aided Multiuser MIMO SWIPT Cognitive Radio Systems with Imperfect CSI

Cognitive radio (CR) techniques have been widely recognized as an effective solution to utilize the radio spectrum resource. An integration of intelligent reflecting surfaces (IRSs) into the CR systems is expected to yield further enhancements in spectral efficiency (SE) and energy efficiency (EE). This paper explores the achievable EE performance of multiuser multiple-input multiple-output (MU-MIMO) simultaneous wireless information and power transfer (SWIPT) systems under the scenario of nonlinear energy harvesting model and imperfection of channel state information (CSI). The optimal design of transmit precoding (TPC) matrices at the secondary base station (SBS), the phase shift matrix at the IRS, and energy harvesting (EH) power splitting (PS) factors at the users to maximize the EE is challenging due to the fractional nature of the objective function, nonconvex constraints of coupled design variables and robust semi-infinite interference power (IP) constraints. To deal with non-convexity, we seek appropriate surrogate functions and convex inner sets. To handle the semi-infinite IP constraints, we recast them as linear matrix inequalities (LMIs). Then, we introduce an iterative algorithm utilizing alternating optimization (AO) and the Dinkelbach method to find optimal solutions. Through extensive simulations, we gain the insights into the effectiveness of the EE optimization scheme against the SE optimization approach.