Spectral Efficiency for Active IRS-Aided Multi-Group Multicast Cognitive Radio Systems

Abstract

This paper investigates the spectral efficiency (SE) optimization in muti-group (MG) multicast (MC) multiple-input multiple-output (MIMO) cognitive radio (CR) systems with the assistance of an active intelligent reflecting surface (IRS). The research aims at designing the transmit precoders (TPCs) at the secondary base station (SBS) and the reflection coefficients (RCs) at the IRS to maximize either the sum rates of MC groups or the minimum rates among MC groups in the secondary network while guaranteeing transmit power (TP) budget constraints at the SBS and reflection amplitude and amplification power at the IRS, and the interference power (IP) constraints at the primary users (PUs). To address the challenges of coupled variables in the formulated design problems, we exploit the alternating optimization (AO) to decompose the design problems into amenable sub-problems. To tackle the difficulties posed by the nonconvex nature of the design problems, we derive the surrogate functions to transform the optimization problems into convex forms. Then, efficient iterative algorithms are derived to obtain the optimal SBS TPCs and IRS RCs. The numerical simulations are conducted to investigate the system performance over the various system parameters. The numerical results demonstrate that maximizing the minimum rates leads to fairer distributions of achievable rates among groups, while maximizing the sum rate offers higher achievable rates for favorable groups. The results also reveal that systems with optimized IRS RCs obtain superior rates compared to those with fixed IRS RCs.