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Channel Estimation for Beyond Diagonal RIS Exploiting Core Tensor Sparsity

Daniel Costa Araújo, André L. F. de Almeida

TL;DR

A compressive sensing framework exploiting sparse Tucker decomposition of the measurement tensor and the Kronecker rank-one structure of channel components is proposed, enabling practical BD-RIS deployment in next-generation millimeter wave (mmWave)/sub-terahertz (sub-THz) 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.

Channel Estimation for Beyond Diagonal RIS Exploiting Core Tensor Sparsity

TL;DR

A compressive sensing framework exploiting sparse Tucker decomposition of the measurement tensor and the Kronecker rank-one structure of channel components is proposed, enabling practical BD-RIS deployment in next-generation millimeter wave (mmWave)/sub-terahertz (sub-THz) 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.
Paper Structure (8 sections, 10 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 8 sections, 10 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Channel Estimation
  4. Stage 1: Sparse Support Recovery
  5. Stage 2: Channel Parameter Estimation
  6. Computational Complexity Analysis
  7. Numerical Results
  8. Conclusion

Figures (4)

  • Figure 1: as a function of . Fixed: $N=32$, $M=32$, $K=64$, $N_{\text{tx}}=16$, $M_{\text{rx}}=16$; measurement size at 50% of $Q\bar{K}^2$.
  • Figure 2: as a function of the percentage of measurements relative to $Q\bar{K}^2$. Fixed: $N=32$, $M=32$, $K=64$, $N_{\text{tx}}=16$, $M_{\text{rx}}=16$.
  • Figure 3: Processing time of the algorithms as a function of $\bar{K}$. Fixed: $N=32$, $M=32$, $K=64$, $N_{\text{tx}}=16$, $M_{\text{rx}}=16$; measurement size at 50% of $Q\bar{K}^2$.
  • Figure 4: as a function of the number of paths per channel. Fixed: $N=32$, $M=32$, $K=64$, $N_{\text{tx}}=16$, $M_{\text{rx}}=16$; measurement size at 50% of $Q\bar{K}^2$.