# Multi-beam Beamforming in RIS-aided MIMO Subject to Reradiation Mask Constraints -- Optimization and Machine Learning Design

arXiv: https://arxiv.org/abs/2507.15367 · HTML: https://mlsanity.com/paper/2507.15367/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 62 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 30 of 36)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming](https://mlsanity.com/paper/1810.03961/) (2018)
- [Graph Neural Networks for Wireless Communications: From Theory to Practice](https://mlsanity.com/paper/2203.10800/) (2022)
- [Wireless Networks Design in the Era of Deep Learning: Model-Based, AI-Based, or Both?](https://mlsanity.com/paper/1902.02647/) (2019)
- [Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces: How it Works, State of Research, and Road Ahead](https://mlsanity.com/paper/2004.09352/) (2020)
- [Intelligent Reflecting Surface Aided Wireless Communications: A Tutorial](https://mlsanity.com/paper/2007.02759/) (2020)
- [Hybrid Beamforming for Reconfigurable Intelligent Surface based Multi-user Communications: Achievable Rates with Limited Discrete Phase Shifts](https://mlsanity.com/paper/1910.14328/) (2019)
- [A Survey on Model-based, Heuristic, and Machine Learning Optimization Approaches in RIS-aided Wireless Networks](https://mlsanity.com/paper/2303.14320/) (2023)
- [Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts](https://mlsanity.com/paper/1906.03165/) (2019)
- [Model-Driven Deep Learning Based Channel Estimation and Feedback for Millimeter-Wave Massive Hybrid MIMO Systems](https://mlsanity.com/paper/2104.11052/) (2021)
- [Deep Denoising Neural Network Assisted Compressive Channel Estimation for mmWave Intelligent Reflecting Surfaces](https://mlsanity.com/paper/2006.02201/) (2020)
- [Multicell MIMO Communications Relying on Intelligent Reflecting Surface](https://mlsanity.com/paper/1907.10864/) (2019)
- [Capacity Characterization for Intelligent Reflecting Surface Aided MIMO Communication](https://mlsanity.com/paper/1910.01573/) (2019)
- [Modeling and Architecture Design of Reconfigurable Intelligent Surfaces Using Scattering Parameter Network Analysis](https://mlsanity.com/paper/2011.11362/) (2020)
- [Learning to Estimate RIS-Aided mmWave Channels](https://mlsanity.com/paper/2107.12631/) (2021)
- [Deep Learning-Based Rate-Splitting Multiple Access for Reconfigurable Intelligent Surface-Aided Tera-Hertz Massive MIMO](https://mlsanity.com/paper/2209.08456/) (2022)
- [Sum Rate Optimization for Two Way Communications with Intelligent Reflecting Surface](https://mlsanity.com/paper/2003.00918/) (2020)
- [Path Loss Modeling and Measurements for Reconfigurable Intelligent Surfaces in the Millimeter-Wave Frequency Band](https://mlsanity.com/paper/2101.08607/) (2021)
- [Low-Complexity Joint Beamforming for RIS-Assisted MU-MISO Systems Based on Model-Driven Deep Learning](https://mlsanity.com/paper/2311.15313/) (2023)
- [LiFi Through Reconfigurable Intelligent Surfaces: A New Frontier for 6G?](https://mlsanity.com/paper/2104.02390/) (2021)
- [On the Enabling of Multi-receiver Communications with Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2106.06789/) (2021)
- [Reradiation and Scattering from a Reconfigurable Intelligent Surface: A General Macroscopic Model](https://mlsanity.com/paper/2107.12773/) (2021)
- [Joint Active and Passive Beamforming Design for IRS-Aided Radar-Communication](https://mlsanity.com/paper/2203.14532/) (2022)
- [Design of Reconfigurable Intelligent Surfaces by Using S-Parameter Multiport Network Theory -- Optimization and Full-Wave Validation](https://mlsanity.com/paper/2311.06648/) (2023)
- [A Survey on Integrated Sensing and Communication with Intelligent Metasurfaces: Trends, Challenges, and Opportunities](https://mlsanity.com/paper/2401.15562/) (2024)
- [Communication Models for Reconfigurable Intelligent Surfaces: From Surface Electromagnetics to Wireless Networks Optimization](https://mlsanity.com/paper/2110.00833/) (2021)
- [Reconfigurable Intelligent Surfaces: Performance Assessment Through a System-Level Simulator](https://mlsanity.com/paper/2111.10791/) (2021)
- [RIS Partitioning Based Scalable Beamforming Design for Large-Scale MIMO: Asymptotic Analysis and Optimization](https://mlsanity.com/paper/2203.08377/) (2022)
- [Beamforming Optimization for Active Intelligent Reflecting Surface-Aided SWIPT](https://mlsanity.com/paper/2203.16093/) (2022)

## Abstract (arXiv)

Reconfigurable intelligent surfaces (RISs) are an emerging technology for improving spectral efficiency and reducing power consumption in future wireless systems. This paper investigates the joint design of the transmit precoding matrices and the RIS phase shift vector in a multi-user RIS-aided multiple-input multiple-output (MIMO) communication system. We formulate a max-min optimization problem to maximize the minimum achievable rate while considering transmit power and reradiation mask constraints. The achievable rate is simplified using the Arimoto-Blahut algorithm, and the problem is broken into quadratic programs with quadratic constraints (QPQC) sub-problems using an alternating optimization approach. To improve efficiency, we develop a model-based neural network optimization that utilizes the one-hot encoding for the angles of incidence and reflection. We address practical RIS limitations by using a greedy search algorithm to solve the optimization problem for discrete phase shifts. Simulation results demonstrate that the proposed methods effectively shape the multi-beam radiation pattern towards desired directions while satisfying reradiation mask constraints. The neural network design reduces the execution time, and the discrete phase shift scheme performs well with a small reduction of the beamforming gain by using only four phase shift levels.