A Discrete Passive Beamforming Technique for an IRS-aided MISO System with Imperfect CSI

This study investigates the downlink transmission of a multiple-input single-output (MISO) communication system with an intelligent reflecting surface (IRS) under channel uncertainty. The problem of maximizing the sum-rate is formulated by incorporating the channel estimation error footprints, and it is solved through joint optimization of the active precoding at the access point (AP) and passive beamforming at the IRS using the penalty dual decomposition (PDD) algorithm. The PDD algorithm is iterative, has guaranteed convergence, and yields closed-form solutions in each iteration, resulting in low computational complexity. Two cases of continuous and discrete phase shifts at the IRS are considered. Simulation results indicate the effectiveness of the proposed method in handling channel uncertainty for both continuous and discrete phase shifts.