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

arXiv: https://arxiv.org/abs/1907.06002 · HTML: https://mlsanity.com/paper/1907.06002/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2019.

## Built on by (most cited first, 14 of 14)

- [Pervasive Machine Learning for Smart Radio Environments Enabled by Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2205.03793/) (2022)
- [Digital Twin-Aided Learning for Managing Reconfigurable Intelligent Surface-Assisted, Uplink, User-Centric Cell-Free Systems](https://mlsanity.com/paper/2302.05073/) (2023)
- [DNN-Based Precoding in RIS-Aided mmWave MIMO Systems With Practical Phase Shift](https://mlsanity.com/paper/2507.02824/) (2025)
- [Trustworthy AI-Driven Dynamic Hybrid RIS: Joint Optimization and Reward Poisoning-Resilient Control in Cognitive MISO Networks](https://mlsanity.com/paper/2604.01238/) (2026)
- [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)
- [Beyond 5G RIS mmWave Systems: Where Communication and Localization Meet](https://mlsanity.com/paper/2109.07729/) (2021)
- [Phase Shift Design in RIS Empowered Wireless Networks: From Optimization to AI-Based Methods](https://mlsanity.com/paper/2204.13372/) (2022)
- [Deep Reinforcement Learning-Based Adaptive IRS Control with Limited Feedback Codebooks](https://mlsanity.com/paper/2205.03636/) (2022)
- [Geometry Aware Meta-Learning Neural Network for Joint Phase and Precoder Optimization in RIS](https://mlsanity.com/paper/2409.11270/) (2024)
- [Discrete Beamforming Optimization for RISs with a Limited Phase Range and Amplitude Attenuation](https://mlsanity.com/paper/2507.07342/) (2025)
- [Sustainable LSTM-Based Precoding for RIS-Aided mmWave MIMO Systems with Implicit CSI](https://mlsanity.com/paper/2509.12658/) (2025)
- [RIS-Enabled Smart Wireless Environments: Fundamentals and Distributed Optimization](https://mlsanity.com/paper/2512.18788/) (2025)
- [Optimization Algorithms for Joint OFDM Waveform Design and RIS Configuration in 6G Networks: From Convex Relaxation to Foundation Models](https://mlsanity.com/paper/2606.31334/) (2026)

## Abstract (arXiv)

Intelligent reflecting surface (IRS) that enables the control of the wireless propagation environment has been looked upon as a promising 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 a practical phase shift model that captures the phase-dependent amplitude variation in the element-wise reflection coefficient. Applying this new model to an IRS-aided wireless system, we formulate a problem to maximize its achievable rate by jointly optimizing the transmit beamforming and the IRS reflect beamforming. The formulated problem is non-convex and difficult to be optimally solved in general, for which we propose a low-complexity suboptimal solution based on the alternating optimization (AO) technique. Simulation results unveil a substantial performance gain achieved by the joint beamforming optimization based on the proposed phase shift model as compared to the conventional ideal model.