# Beyond Diagonal Reconfigurable Intelligent Surfaces: From Transmitting and Reflecting Modes to Single-, Group-, and Fully-Connected Architectures

arXiv: https://arxiv.org/abs/2205.02866 · HTML: https://mlsanity.com/paper/2205.02866/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2022.

## Built on by (most cited first, 4 of 4)

- [Meta-Learning Based Optimization for Large Scale Wireless Systems](https://mlsanity.com/paper/2407.01823/) (2024)
- [Beyond-Diagonal RIS Under Non-Idealities: Learning-Based Architecture Discovery and Optimization](https://mlsanity.com/paper/2510.15701/) (2025)
- [RIS-Enabled Smart Wireless Environments: Fundamentals and Distributed Optimization](https://mlsanity.com/paper/2512.18788/) (2025)
- [Quantum Intelligence Meets BD-RIS-Enabled AmBC: Challenges, Opportunities, and Practical Insights](https://mlsanity.com/paper/2512.23400/) (2025)

## Abstract (arXiv)

Reconfigurable intelligent surfaces (RISs) are envisioned as a promising technology for future wireless communications. With various hardware realizations, RISs can work under different modes (reflective/transmissive/hybrid) or have different architectures (single/group/fully-connected). However, most existing research focused on single-connected reflective RISs, mathematically characterized by diagonal phase shift matrices, while there is a lack of a comprehensive study for RISs unifying different modes/architectures. In this paper, we solve this issue by analyzing and proposing a general RIS-aided communication model. Specifically, we establish an RIS model not limited to diagonal phase shift matrices, a novel branch referred to as beyond diagonal RIS (BD-RIS), unifying modes and architectures. With the proposed model, we develop efficient algorithms to jointly design transmit precoder and BDRIS matrix to maximize the sum-rate for RIS-aided systems. We also provide simulation results to compare the performance of BD-RISs with different modes/architectures. Simulation results show that under the same mode, fully- and group-connected RIS can effectively increase the sum-rate performance compared with single-connected RIS, and that hybrid RIS outperforms reflective/transmissive RIS with the same architecture.