Joint Training Scattering Matrix Learning and Channel Estimation for Beyond-Diagonal Reconfigurable Intelligent Surfaces

TL;DR

This paper introduces a novel learning-based framework for channel estimation in BD-RIS-aided MU-MIMO systems, significantly reducing pilot overhead and improving estimation accuracy by jointly optimizing the scattering matrix and channel estimation process.

Contribution

It proposes the JTSMLCEF framework that jointly optimizes the scattering matrix and cascaded channel estimation using a two-phase protocol with attention modules, outperforming existing methods.

Findings

Reduces pilot overhead by 80% in simulations.

Decreases NMSE by over 82% and 92% in different scenarios.

Demonstrates superior performance over state-of-the-art methods.

Abstract

Beyond-diagonal reconfigurable intelligent surface (BD-RIS) generalizes the conventional diagonal RIS (D-RIS) by introducing tunable inter-element connections, offering enhanced wave manipulation capabilities. However, realizing the advantages of BD-RIS requires accurate channel state information (CSI), whose acquisition becomes significantly more challenging due to the increased number of channel coefficients, leading to prohibitively large pilot training overhead in BD-RIS-aided multi-user multiple-input multiple-output (MU-MIMO) systems. Existing studies reduce pilot overhead by exploiting the channel correlations induced by the Kronecker-product or multi-linear structure of BD-RIS-aided channels, which neglect the spatial correlation among antennas and the statistical correlation across RIS-user channels. In this paper, we propose a learning-based channel estimation framework, namely the joint training scattering matrix learning and channel estimation framework (JTSMLCEF), which jointly optimizes the BD-RIS training scattering matrix and estimates the cascaded channels in an end-to-end manner to achieve accurate channel estimation and reduce the pilot overhead. The proposed JTSMLCEF follows a two-phase channel estimation protocol to enable adaptive training scattering matrix optimization with a training scattering matrix optimizer (TSMO) and cascaded channel estimation with a dual-attention channel estimator (DACE). Specifically, the DACE is designed with intra-user and inter-user attention modules to capture the multi-dimensional correlations in multi-user cascaded channels. Simulation results demonstrate the superiority of JTSMLCEF. Compared with the current state-of-the-art method, it reduces the pilot overhead by $80\%$ while further reducing the normalized mean squared error (NMSE) by $82.6\%$ and $92.5\%$ in indoor and urban micro-cell (UMi) scenarios, respectively.