# A Low-Complexity Beamforming Design for Beyond-Diagonal RIS aided Multi-User Networks

arXiv: https://arxiv.org/abs/2307.09807 · HTML: https://mlsanity.com/paper/2307.09807/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [Quantum Intelligence Meets BD-RIS-Enabled AmBC: Challenges, Opportunities, and Practical Insights](https://mlsanity.com/paper/2512.23400/) (2025)

## Abstract (arXiv)

Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has been proposed recently as a novel and generalized RIS architecture that offers enhanced wave manipulation flexibility and large coverage expansion. However, the beyond-diagonal mathematical model in BD-RIS inevitably introduces additional optimization challenges in beamforming design. In this letter, we derive a closed-form solution for the BD-RIS passive beamforming matrix that maximizes the sum of the effective channel gains among users. We further propose a computationally efficient two-stage beamforming framework to jointly design the active beamforming at the base station and passive beamforming at the BD-RIS to enhance the sum-rate for a BD-RIS aided multi-user multi-antenna network.Numerical results show that our proposed algorithm achieves a higher sum-rate while requiring less computation time compared to state-of-the-art algorithms. The proposed algorithm paves the way for practical beamforming design in BD-RIS aided wireless networks.