# Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts

arXiv: https://arxiv.org/abs/1906.03165 · HTML: https://mlsanity.com/paper/1906.03165/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2019.

## Built on by (most cited first, 12 of 12)

- [Learning to Estimate RIS-Aided mmWave Channels](https://mlsanity.com/paper/2107.12631/) (2021)
- [Time-Varying Channel Prediction for RIS-Assisted MU-MISO Networks via Deep Learning](https://mlsanity.com/paper/2111.04971/) (2021)
- [A Robust Deep Learning-Based Beamforming Design for RIS-assisted Multiuser MISO Communications with Practical Constraints](https://mlsanity.com/paper/2111.06555/) (2021)
- [Ultra-Reliable Indoor Millimeter Wave Communications using Multiple Artificial Intelligence-Powered Intelligent Surfaces](https://mlsanity.com/paper/2104.00075/) (2021)
- [Collaborative Intelligent Reflecting Surface Networks with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2203.14152/) (2022)
- [Phase Shift Design in RIS Empowered Wireless Networks: From Optimization to AI-Based Methods](https://mlsanity.com/paper/2204.13372/) (2022)
- [Optimal Beamforming of RIS-Aided Wireless Communications: An Alternating Inner Product Maximization Approach](https://mlsanity.com/paper/2405.06442/) (2024)
- [Optimal Configuration of Reconfigurable Intelligent Surfaces With Non-uniform Phase Quantization](https://mlsanity.com/paper/2405.06967/) (2024)
- [Multi-beam Beamforming in RIS-aided MIMO Subject to Reradiation Mask Constraints -- Optimization and Machine Learning Design](https://mlsanity.com/paper/2507.15367/) (2025)
- [When UAV Swarm Meets IRS: Collaborative Secure Communications in Low-altitude Wireless Networks](https://mlsanity.com/paper/2510.22117/) (2025)
- [A Particle-Swarm-Assisted Gradient Meta-Learning Algorithm for Joint Transmit Precoding and STAR-RIS Coefficient Optimization](https://mlsanity.com/paper/2609.29150/) (2026)
- [A 3GPP-Compliant Benchmark Dataset for RIS-Aided Beyond 5G Networks](https://mlsanity.com/paper/2609.39058/) (2026)

## Abstract (arXiv)

Intelligent reflecting surface (IRS) is a cost-effective solution for achieving high spectrum and energy efficiency in future wireless networks by leveraging massive low-cost passive elements that are able to reflect the signals with adjustable phase shifts. Prior works on IRS mainly consider continuous phase shifts at reflecting elements, which are practically difficult to implement due to the hardware limitation. In contrast, we study in this paper an IRS-aided wireless network, where an IRS with only a finite number of phase shifts at each element is deployed to assist in the communication from a multi-antenna access point (AP) to multiple single-antenna users. We aim to minimize the transmit power at the AP by jointly optimizing the continuous transmit precoding at the AP and the discrete reflect phase shifts at the IRS, subject to a given set of minimum signal-to-interference-plus-noise ratio (SINR) constraints at the user receivers. The considered problem is shown to be a mixed-integer non-linear program (MINLP) and thus is difficult to solve in general. To tackle this problem, we first study the single-user case with one user assisted by the IRS and propose both optimal and suboptimal algorithms for solving it. Besides, we analytically show that as compared to the ideal case with continuous phase shifts, the IRS with discrete phase shifts achieves the same squared power gain in terms of asymptotically large number of reflecting elements, while a constant proportional power loss is incurred that depends only on the number of phase-shift levels. The proposed designs for the single-user case are also extended to the general setup with multiple users among which some are aided by the IRS. Simulation results verify our performance analysis as well as the effectiveness of our proposed designs as compared to various benchmark schemes.