Joint Active/Passive Beamforming Optimization via RWMMSE and Gradient Projection for Downlink IRS-Aided MU-MISO Systems

Metamaterials are significantly advancing the way we wirelessly transmit electromagnetic signals between communicating devices. Specifically, intelligent reflecting surfaces (IRS), a metamaterial-derived technology with multiple passive reconfigurable reflecting elements, facilitate a wide array of novel opportunities. The proper reconfiguration of its elements, which is the primary task towards achieving these prospects, has been previously explored by many researchers, where most proposals are characterized by high computational complexity. This study builds upon previous research on downlink IRS-assisted multi-user multiple-input single-output (MISO) systems by introducing innovative methods to accelerate their operations. Specifically, we introduce a weighted sum rate problem and utilize the reduced weighted minimum mean square error (RWMMSE) algorithm to determine active precoders, alongside the employment of gradient projection (GP) method to enhance passive beamforming techniques. These two techniques undergo a novel restructuring process, where the RWMMSE framework, originally designed for MIMO systems, is transformed to work with a MISO system. The GP framework is enhanced with a Barzilai-Borwein method for the step size selection that ensures a fast convergence of the proposed algorithm, resulting in lower complexity. Ultimately, the numerical findings confirm our assertion, demonstrating the efficacy of our suggested algorithm in achieving performance similar to benchmark methods while significantly reducing complexity.