Channel Estimation for Beyond Diagonal RIS Exploiting Core Tensor Sparsity

TL;DR

This paper introduces a novel compressive sensing framework for channel estimation in beyond diagonal RIS systems, exploiting tensor sparsity and structure to improve accuracy and reduce measurements in mmWave/sub-THz networks.

Contribution

It proposes two algorithms, STORM and STAR, that leverage tensor sparsity and subspace techniques for efficient channel estimation in complex BD-RIS scenarios.

Findings

STAR achieves oracle LS performance at moderate-to-high SNR

Significantly fewer measurements are needed compared to baseline methods

Enables practical BD-RIS deployment in next-generation networks

Abstract

Beyond diagonal reconfigurable intelligent surface (BD-RIS)s enhance wave manipulation through inter-element couplings but pose significant channel estimation challenges due to cascaded channels and block-Kronecker structures. This paper proposes a compressive sensing framework exploiting sparse Tucker decomposition of the measurement tensor and the Kronecker rank-one structure of channel components. Two algorithms are developed: Sparse Tensor Orthogonal Recovery Method (STORM), which uses orthogonal matching pursuit (OMP) for greedy support recovery, and Sparse Tensor subspace- Aided Recovery (STAR), which leverages subspace-based projection for enhanced noise robustness. Both perform joint sparse support identification, followed by a Kronecker rank-one factorization via singular value decomposition (SVD) to recover the channel parameters. Simulations show that STAR achieves oracle-assisted least squares (LS) performance at moderate-to-high signal-to-noise ratio (SNR) with significantly fewer measurements than baseline methods, enabling practical BD-RIS deployment in next-generation millimeter wave (mmWave)/sub-terahertz (sub-THz) networks.