Channel Estimation and Beamforming for Beyond Diagonal Reconfigurable Intelligent Surfaces

TL;DR

This work tackles channel estimation and beamforming for beyond diagonal reconfigurable intelligent surfaces (BD-RIS). It introduces a tile-based cascaded-channel model and an LS-based channel estimation scheme with a unitary-structured training design that achieves minimum MSE, while revealing a fundamental trade-off between training overhead and beamforming flexibility. Building on the estimated cascaded channels, the authors propose two BD-RIS beamforming pipelines: (i) reflective BD-RIS for point-to-point MIMO with a two-stage design on the Stiefel manifold and SVD-based precoding/combining, and (ii) hybrid/multi-sector BD-RIS for MU-MISO using fractional programming and manifold optimization. Simulations show that larger group-connected BD-RIS sizes improve rate but increase training overhead, and multi-sector BD-RIS offers notable gains in multi-user scenarios, highlighting practical overhead-performance trade-offs and guiding architecture choices.

Abstract

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a new advance and generalization of the RIS technique. BD-RIS breaks through the isolation between RIS elements by creatively introducing inter-element connections, thereby enabling smarter wave manipulation and enlarging coverage. However, exploring proper channel estimation schemes suitable for BD-RIS aided communication systems still remains an open problem. In this paper, we study channel estimation and beamforming design for BD-RIS aided multi-antenna systems. We first describe the channel estimation strategy based on the least square (LS) method, derive the mean square error (MSE) of the LS estimation, and formulate the joint pilot sequence and BD-RIS design problem with unique constraints induced by BD-RIS architectures. Specifically, we propose an efficient pilot sequence and BD-RIS design which theoretically guarantees to achieve the minimum MSE. With the estimated channel, we then consider two BD-RIS scenarios and propose beamforming design algorithms. Finally, we provide simulation results to verify the effectiveness of the proposed channel estimation scheme and beamforming design algorithms. We also show that more interelement connections in BD-RIS improves the performance while increasing the training overhead for channel estimation.

Figures (10)

• Figure 1: A paradigm of a BD-RIS assisted MIMO system.
• Figure 2: Illustration of BD-RIS antenna ports, groups, and tiles. Left: BD-RIS with $M=36$, $G_1=18$ and $G_2=9$; right: BD-RIS with $M=36$, $G_1=12$ and $G_2=4$. For example, in the left figure, BD-RIS antenna ports with indices $\{1,2\}$ and $\{3,4\}$ form two different groups, each of which consists of antenna ports connected to each other by reconfigurable impedance components. These two groups further form one tile, within which the groups share the same BD-RIS pattern.
• Figure 3: One transmission frame consisting of three phases with $T = T_1 + T_2 + T_3$ symbol durations.
• Figure 4: Training breaking the training time into $T_\mathrm{s}$ blocks of length $K$.
• Figure 5: Illustration of channel estimation for BD-RIS with hybrid mode.