# Hybrid Beamforming for Reconfigurable Intelligent Surface based Multi-user Communications: Achievable Rates with Limited Discrete Phase Shifts

arXiv: https://arxiv.org/abs/1910.14328 · HTML: https://mlsanity.com/paper/1910.14328/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2019.

## Built on by (most cited first, 15 of 15)

- [Automated Metaheuristic Algorithm Design with Autoregressive Learning](https://mlsanity.com/paper/2405.03419/) (2024)
- [GDSG: Graph Diffusion-based Solution Generator for Optimization Problems in MEC Networks](https://mlsanity.com/paper/2412.08296/) (2024)
- [Time-Varying Channel Prediction for RIS-Assisted MU-MISO Networks via Deep Learning](https://mlsanity.com/paper/2111.04971/) (2021)
- [AutoOpt: A General Framework for Automatically Designing Metaheuristic Optimization Algorithms with Diverse Structures](https://mlsanity.com/paper/2204.00998/) (2022)
- [A Robust Deep Learning-Based Beamforming Design for RIS-assisted Multiuser MISO Communications with Practical Constraints](https://mlsanity.com/paper/2111.06555/) (2021)
- [AutoOptLib: Tailoring Metaheuristic Optimizers via Automated Algorithm Design](https://mlsanity.com/paper/2303.06536/) (2023)
- [Unsupervised Learning-Based Joint Resource Allocation and Beamforming Design for RIS-Assisted MISO-OFDMA Systems](https://mlsanity.com/paper/2506.22448/) (2025)
- [Phase Shift Design in RIS Empowered Wireless Networks: From Optimization to AI-Based Methods](https://mlsanity.com/paper/2204.13372/) (2022)
- [Unlocking Metasurface Practicality for B5G Networks: AI-assisted RIS Planning](https://mlsanity.com/paper/2310.10330/) (2023)
- [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)
- [Anti-Jamming Sensing with Distributed Reconfigurable Intelligent Metasurface Antennas](https://mlsanity.com/paper/2508.04964/) (2025)
- [Sum Rate Maximization in STAR-RIS-UAV-Assisted Networks: A CA-DDPG Approach for Joint Optimization](https://mlsanity.com/paper/2512.01202/) (2025)
- [Learning to Design Convex Relaxations for Nonconvex Optimization](https://mlsanity.com/paper/2610.16948/) (2026)

## Abstract (arXiv)

Reconfigurable intelligent surface (RIS) has drawn considerable attention from the research society recently, which creates favorable propagation conditions by controlling the phase shifts of the reflected waves at the surface, thereby enhancing wireless transmissions. In this paper, we study a downlink multi-user system where the transmission from a multi-antenna base station (BS) to various users is achieved by the RIS reflecting the incident signals of the BS towards the users. Unlike most existing works, we consider the practical case where only a limited number of discrete phase shifts can be realized by the finite-sized RIS. Based on the reflection-dominated one-hop propagation model between the BS and users via the RIS, a hybrid beamforming scheme is proposed and the sum-rate maximization problem is formulated. Specifically, the continuous digital beamforming and discrete RIS-based analog beamforming are performed at the BS and the RIS, respectively, and an iterative algorithm is designed to solve this problem. Both theoretical analysis and numerical validations show that the RIS-based system can achieve a good sum-rate performance by setting a reasonable size of RIS and a small number of discrete phase shifts.