# Intelligent Reflecting Surface: Practical Phase Shift Model and Beamforming Optimization

arXiv: https://arxiv.org/abs/2002.10112 · HTML: https://mlsanity.com/paper/2002.10112/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2020.

## Built on by (most cited first, 7 of 7)

- [Pervasive Machine Learning for Smart Radio Environments Enabled by Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2205.03793/) (2022)
- [Multi-hop RIS-Empowered Terahertz Communications: A DRL-based Hybrid Beamforming Design](https://mlsanity.com/paper/2101.09137/) (2021)
- [Digital Twin-Aided Learning for Managing Reconfigurable Intelligent Surface-Assisted, Uplink, User-Centric Cell-Free Systems](https://mlsanity.com/paper/2302.05073/) (2023)
- [Channel Estimation and Hybrid Architectures for RIS-Assisted Communications](https://mlsanity.com/paper/2104.07115/) (2021)
- [Collaborative Intelligent Reflecting Surface Networks with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2203.14152/) (2022)
- [Deep Reinforcement Learning Based Joint Downlink Beamforming and RIS Configuration in RIS-aided MU-MISO Systems Under Hardware Impairments and Imperfect CSI](https://mlsanity.com/paper/2211.09702/) (2022)
- [Deep Reinforcement Learning-Based Precoding for Multi-RIS-Aided Multiuser Downlink Systems with Practical Phase Shift](https://mlsanity.com/paper/2509.25661/) (2025)

## Abstract (arXiv)

Intelligent reflecting surface (IRS) that enables the control of wireless propagation environment has recently emerged as a promising cost-effective technology for boosting the spectrum and energy efficiency in future wireless communication systems. Prior works on IRS are mainly based on the ideal phase shift model assuming the full signal reflection by each of the elements regardless of its phase shift, which, however, is practically difficult to realize. In contrast, we propose in this paper the practical phase shift model that captures the phase-dependent amplitude variation in the element-wise reflection coefficient. Based on the proposed model and considering an IRS-aided multiuser system with an IRS deployed to assist in the downlink communications from a multi-antenna access point (AP) to multiple single-antenna users, we formulate an optimization problem to minimize the total transmit power at the AP by jointly designing the AP transmit beamforming and the IRS reflect beamforming, subject to the users' individual signal-to-interference-plus-noise ratio (SINR) constraints. Iterative algorithms are proposed to find suboptimal solutions to this problem efficiently by utilizing the alternating optimization (AO) or penalty-based optimization technique. Moreover, we analyze the asymptotic performance loss of the IRS-aided system that employs practical phase shifters but assumes the ideal phase shift model for beamforming optimization, as the number of IRS elements goes to infinity. Simulation results unveil substantial performance gains achieved by the proposed beamforming optimization based on the practical phase shift model as compared to the conventional ideal model.