# Optimal Beamforming of RIS-Aided Wireless Communications: An Alternating Inner Product Maximization Approach

arXiv: https://arxiv.org/abs/2405.06442 · HTML: https://mlsanity.com/paper/2405.06442/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 46 references that are in the map.
- First posted on arXiv 10 May 2024.

## Builds on (most cited first, 24 of 24)

- [Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming](https://mlsanity.com/paper/1810.03961/) (2018)
- [Wireless Communications Through Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/1906.09490/) (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)
- [Hybrid Beamforming for Reconfigurable Intelligent Surface based Multi-user Communications: Achievable Rates with Limited Discrete Phase Shifts](https://mlsanity.com/paper/1910.14328/) (2019)
- [RIS-Aided Wireless Communications: Prototyping, Adaptive Beamforming, and Indoor/Outdoor Field Trials](https://mlsanity.com/paper/2103.00534/) (2021)
- [Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface with Discrete Phase Shifts](https://mlsanity.com/paper/1906.03165/) (2019)
- [Latency Minimization for Intelligent Reflecting Surface Aided Mobile Edge Computing](https://mlsanity.com/paper/1910.07990/) (2019)
- [Intelligent Surfaces Empowered Wireless Network: Recent Advances and The Road to 6G](https://mlsanity.com/paper/2312.16918/) (2023)
- [Intelligent Reflecting Surface-Assisted Millimeter Wave Communications: Joint Active and Passive Precoding Design](https://mlsanity.com/paper/1908.10734/) (2019)
- [Reconfigurable Intelligent Surfaces for Localization: Position and Orientation Error Bounds](https://mlsanity.com/paper/2009.02818/) (2020)
- [Channel Estimation for Reconfigurable Intelligent Surface Aided Multi-User mmWave MIMO Systems](https://mlsanity.com/paper/1912.03619/) (2019)
- [Channel Estimation and Passive Beamforming for Intelligent Reflecting Surface: Discrete Phase Shift and Progressive Refinement](https://mlsanity.com/paper/1912.10646/) (2019)
- [Joint Active and Passive Beamforming Optimization for Intelligent Reflecting Surface Assisted SWIPT under QoS Constraints](https://mlsanity.com/paper/1910.06220/) (2019)
- [Secure Transmission for Intelligent Reflecting Surface-Assisted mmWave and Terahertz Systems](https://mlsanity.com/paper/2005.13451/) (2020)
- [A Linear Time Algorithm for the Optimal Discrete IRS Beamforming](https://mlsanity.com/paper/2211.04704/) (2022)
- [Intelligent Reflecting Surface Aided MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer](https://mlsanity.com/paper/1908.04863/) (2019)
- [Robust Beamforming Design for Intelligent Reflecting Surface Aided MISO Communication Systems](https://mlsanity.com/paper/1911.06237/) (2019)
- [Intelligent Reflecting Surface Enhanced Multi-UAV NOMA Networks](https://mlsanity.com/paper/2101.09145/) (2021)
- [Configuring Intelligent Reflecting Surface with Performance Guarantees: Optimal Beamforming](https://mlsanity.com/paper/2112.02260/) (2021)
- [High-Resolution Programmable Scattering for Wireless Coverage Enhancement: An Indoor Field Trial Campaign](https://mlsanity.com/paper/2112.11194/) (2021)
- [A Novel SCA-Based Method for Beamforming Optimization in IRS/RIS-Assisted MU-MISO Downlink](https://mlsanity.com/paper/2208.12053/) (2022)
- [Designing Unimodular Codes via Quadratic Optimization is not Always Hard](https://mlsanity.com/paper/1303.0152/) (2013)
- [Reconfigurable Intelligent Surface Aided Mobile Edge Computing](https://mlsanity.com/paper/2102.02569/) (2021)
- [Efficient DOA Estimation Method for Reconfigurable Intelligent Surfaces Aided UAV Swarm](https://mlsanity.com/paper/2203.10219/) (2022)

## Abstract (arXiv)

This paper investigates a general discrete ℓp-norm maximization problem, with the power enhancement at steering directions through reconfigurable intelligent surfaces (RISs) as an instance. We propose a mathematically concise iterative framework composed of alternating inner product maximizations, well-suited for addressing ℓ1- and ℓ2-norm maximizations with either discrete or continuous uni-modular variable constraints. The iteration is proven to be monotonically non-decreasing. Moreover, this framework exhibits a distinctive capability to mitigate performance degradation due to discrete quantization, establishing it as the first post-rounding lifting approach applicable to any algorithm intended for the continuous solution. Additionally, as an integral component of the alternating iterations framework, we present a divide-and-sort (DaS) method to tackle the discrete inner product maximization problem. In the realm of ℓ_∞-norm maximization with discrete uni-modular constraints, the DaS ensures the identification of the global optimum with polynomial search complexity. We validate the effectiveness of the alternating inner product maximization framework in beamforming through RISs using both numerical experiments and field trials on prototypes. The results demonstrate that the proposed approach achieves higher power enhancement and outperforms other competitors. Finally, we show that discrete phase configurations with moderate quantization bits (e.g., 4-bit) exhibit comparable performance to continuous configurations in terms of power gains.