Joint Beamforming and Phase Shift Design in Intelligent Reflecting Surface-Assisted Wireless Communications

Intelligent reflecting surface technology (IRS) is emerging as a major innovation in wireless communications due to its unique advantages. It takes advantage of a large number of low-cost passive elements with adjustable phase-shift capabilities, which can reflect incident signals independently. When these elements work together, IRSs can achieve three-dimensional passive beamforming without the use of any transmit RF link. This mechanism not only enhances spectrum efficiency but also reduces the energy consumption of communication systems. Based on this advantage of IRSs, the paper explores IRS-assisted multiuser wireless systems, where IRSs are cleverly deployed between a multi-antenna access point (AP) and multiple single-antenna users. By jointly optimizing the transmission beamforming of active antenna array of the AP and the passive phase-shift beamforming of the IRSs, the objective is to minimize the total transmit power of APs, while ensuring that each user’s signal-to-interference-plus-noise ratio (SINR) requirement is met. The optimization problem is challenging to solve, as it is a nonconvex quadratically constrained quadratic programming problem, and the optimization variables are highly coupled with each other. To address this challenge, a low-complexity and efficient optimization algorithm, known as the linearized alternating direction multiplier method (LADMM) algorithm is proposed to address the transmit power minimization problem. The simulation results indicate that the LADMM algorithm provides superior system performance and significantly lower complexity compared to other existing methods.