# Lossy Beyond Diagonal Reconfigurable Intelligent Surfaces: Modeling and Optimization

arXiv: https://arxiv.org/abs/2504.19744 · HTML: https://mlsanity.com/paper/2504.19744/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2025.

## Built on by (most cited first, 2 of 2)

- [Beyond-Diagonal RIS Under Non-Idealities: Learning-Based Architecture Discovery and Optimization](https://mlsanity.com/paper/2510.15701/) (2025)
- [Quantization-Aware EE Optimization and SE-EE Tradeoff for MiLAC-Aided MU-MISO Beamforming](https://mlsanity.com/paper/2604.24538/) (2026)

## Abstract (arXiv)

Beyond diagonal reconfigurable intelligent surface (BD-RIS) has emerged as an advancement and generalization of the conventional diagonal RIS (D-RIS) by introducing tunable interconnections between RIS elements, enabling smarter wave manipulation and enlarged coverage. While BD-RIS has demonstrated advantages over D-RIS in various aspects, most existing works rely on the assumption of a lossless model, leaving practical considerations unaddressed. This paper thus proposes a lossy BD-RIS model and develops corresponding optimization algorithms for various BD-RIS-aided communication systems. First, by leveraging admittance parameter analysis, we model each tunable admittance based on a lumped circuit with losses and derive an expression of a circle characterizing the real and imaginary parts of each tunable admittance. We then consider the received signal power maximization in single-user single-input single-output (SISO) systems with the proposed lossy BD-RIS model. To solve the optimization problem, we design an effective algorithm by carefully exploiting the problem structure. Specifically, an alternating direction method of multipliers (ADMM) framework is custom-designed to deal with the complicated constraints associated with lossy BD-RIS. Furthermore, we extend the proposed algorithmic framework to more general multiuser multiple-input single-output (MU-MISO) systems, where the transmit precoder and BD-RIS scattering matrix are jointly designed to maximize the sum-rate of the system. Finally, simulation results demonstrate that all BD-RIS architectures still outperform D-RIS in the presence of losses, but the optimal BD-RIS architectures in the lossless case are not necessarily optimal in the lossy case, e.g. group-connected BD-RIS can outperform fully- and tree-connected BD-RISs in SISO systems with relatively high losses, whereas the opposite always holds true in the lossless case.