A Two-Layer Iterative Algorithm for Max-Min Rate Optimization in IRS Assisted Multiuser Systems With Improper Gaussian Signaling

In this paper, we consider an intelligent reflecting surface (IRS) assisted downlink multiuser communication system with improper Gaussian signaling (IGS) that serves as generalized Gaussian signaling and can effectively combat multiuser interference. We focus on the max-min achievable rate optimization problem by jointly optimizing the transmit beamforming vectors and reflecting phase shifts, subject to the transmit power budget constraint at the access point (AP). We propose a low-complexity iterative algorithm based on a two-layer iterative procedure, which differs from these existing algorithms that rely on inefficient alternating optimization framework and high computational complexity convex optimization tools. Specifically, in the outer layer procedure, we employ a tractable lower bound of user communication rate to reformulate the original problem and repeatedly update the lower bound in each iteration. In the inner layer procedure, based on the alternating direction method of multipliers (ADMM), we decompose the reformulated problem into several convex sub-problems, which can be alternately solved by closed-form solutions. Furthermore, we study the initialization, convergence, and computational complexity of the proposed algorithm. Additionally, we simplify the algorithm to make it applicable for the cases of conventional proper Gaussian signaling (PGS) and without IRS. Finally, numerical results validate the advantages of the proposed algorithm over benchmarking algorithm in terms of rate performance and average execution time.