Channel Estimation for Beyond Diagonal Reconfigurable Intelligent Surfaces with Group-Connected Architectures

TL;DR

This work addresses channel estimation for beyond-diagonal BD-RIS with group-connected architectures in a BD-RIS–aided MISO setting. It develops an LS-based estimator for the cascaded BD-RIS channel $\mathbf{Q}$, derives a closed-form MSE lower bound, and provides a constructive, low-complexity BD-RIS design that achieves this bound using a Kronecker decomposition and DFT/Hadamard bases. The main contributions include a rigorous MSE analysis, a practical training design minimizing overhead $T^{\min} = G\bar{M}^2$, and a provably optimal BD-RIS pattern that attains the bound, validated by simulations showing excellent agreement with the theory. The results offer a pathway to efficient CSI acquisition and beamforming for BD-RIS systems, enabling improved coverage and wave manipulation with manageable circuit complexity.

Abstract

We study channel estimation for a beyond diagonal reconfigurable intelligent surface (BD-RIS) aided multiple input single output system. We first describe the channel estimation strategy based on the least square (LS) method, derive the mean square error (MSE) of the LS estimator, and formulate the BD-RIS design problem that minimizes the estimation MSE with unique constraints induced by group-connected architectures of BD-RIS. Then, we propose an efficient BD-RIS design which theoretically guarantees to achieve the MSE lower bound. Finally, we provide simulation results to verify the effectiveness of the proposed channel estimation scheme.

Figures (2)

• Figure 1: A paradigm of a BD-RIS assisted MISO system.
• Figure 2: MSE versus $P$ for BD-RIS with single-, group-, and fully-connected architectures (The group size for group- and fully-connected architectures are $\bar{M} =2$ and $\bar{M}=M$).