# MIMO Capacity Maximization with Beyond-Diagonal RIS

arXiv: https://arxiv.org/abs/2406.02170 · HTML: https://mlsanity.com/paper/2406.02170/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2024.

## 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)

This paper addresses the problem of maximizing the capacity of a multiple-input multiple-output (MIMO) link assisted by a beyond-diagonal reconfigurable intelligent surface (BD-RIS). We maximize the capacity by alternately optimizing the transmit covariance matrix, and the BD-RIS scattering matrix, which, according to network theory, should be unitary and symmetric. These constraints make the optimization of BD-RIS more challenging than that of diagonal RIS. To find a stationary point of the capacity we maximize a sequence of quadratic problems in the manifold of unitary matrices. This leads to an efficient algorithm that always improves the capacity obtained by a diagonal RIS. Through simulation examples, we study the capacity improvement provided by a passive BD-RIS architecture over the conventional RIS model in which the phase shift matrix is diagonal.