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RIS-aided MIMO Beamforming: Piece-Wise Near-field Channel Model

Weijian Chen, Zai Yang, Zhiqiang Wei, Derrick Wing Kwan Ng, Michail Matthaiou

TL;DR

This work tackles the robustness of RIS-aided MIMO beamforming under CEEs by introducing a piece-wise near-field channel model that partitions the RIS into subsurfaces, balancing modeling accuracy and parameter complexity. It formulates a joint active and passive beamforming problem, converts it to an MSE minimization via auxiliary variables, and solves it with a BCD framework augmented by ADPM for RIS phase optimization. The results show the piece-wise near-field model achieves higher SE and better robustness than conventional near-field or far-field models, especially in the presence of CEEs, while offering favorable DoF gains. The approach provides a practical pathway to robust RIS deployment in high-frequency, large-array scenarios, and points to data-driven methods for optimal subsurface partitioning as future work.

Abstract

This paper proposes a joint active and passive beamforming design for reconfigurable intelligent surface (RIS)-aided wireless communication systems, adopting a piece-wise near-field channel model. While a traditional near-field channel model, applied without any approximations, offers higher modeling accuracy than a far-field model, it renders the system design more sensitive to channel estimation errors (CEEs). As a remedy, we propose to adopt a piece-wise near-field channel model that leverages the advantages of the near-field approach while enhancing its robustness against CEEs. Our study analyzes the impact of different channel models, including the traditional near-field, the proposed piece-wise near-field and far-field channel models, on the interference distribution caused by CEEs and model mismatches. Subsequently, by treating the interference as noise, we formulate a joint active and passive beamforming design problem to maximize the spectral efficiency (SE). The formulated problem is then recast as a mean squared error (MSE) minimization problem and a suboptimal algorithm is developed to iteratively update the active and passive beamforming strategies. Simulation results demonstrate that adopting the piece-wise near-field channel model leads to an improved SE compared to both the near-field and far-field models in the presence of CEEs. Furthermore, the proposed piece-wise near-field model achieves a good trade-off between modeling accuracy and system's degrees of freedom (DoF).

RIS-aided MIMO Beamforming: Piece-Wise Near-field Channel Model

TL;DR

This work tackles the robustness of RIS-aided MIMO beamforming under CEEs by introducing a piece-wise near-field channel model that partitions the RIS into subsurfaces, balancing modeling accuracy and parameter complexity. It formulates a joint active and passive beamforming problem, converts it to an MSE minimization via auxiliary variables, and solves it with a BCD framework augmented by ADPM for RIS phase optimization. The results show the piece-wise near-field model achieves higher SE and better robustness than conventional near-field or far-field models, especially in the presence of CEEs, while offering favorable DoF gains. The approach provides a practical pathway to robust RIS deployment in high-frequency, large-array scenarios, and points to data-driven methods for optimal subsurface partitioning as future work.

Abstract

This paper proposes a joint active and passive beamforming design for reconfigurable intelligent surface (RIS)-aided wireless communication systems, adopting a piece-wise near-field channel model. While a traditional near-field channel model, applied without any approximations, offers higher modeling accuracy than a far-field model, it renders the system design more sensitive to channel estimation errors (CEEs). As a remedy, we propose to adopt a piece-wise near-field channel model that leverages the advantages of the near-field approach while enhancing its robustness against CEEs. Our study analyzes the impact of different channel models, including the traditional near-field, the proposed piece-wise near-field and far-field channel models, on the interference distribution caused by CEEs and model mismatches. Subsequently, by treating the interference as noise, we formulate a joint active and passive beamforming design problem to maximize the spectral efficiency (SE). The formulated problem is then recast as a mean squared error (MSE) minimization problem and a suboptimal algorithm is developed to iteratively update the active and passive beamforming strategies. Simulation results demonstrate that adopting the piece-wise near-field channel model leads to an improved SE compared to both the near-field and far-field models in the presence of CEEs. Furthermore, the proposed piece-wise near-field model achieves a good trade-off between modeling accuracy and system's degrees of freedom (DoF).
Paper Structure (22 sections, 1 theorem, 47 equations, 6 figures, 1 table, 2 algorithms)

This paper contains 22 sections, 1 theorem, 47 equations, 6 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. System Model
  4. Channel Models
  5. Analysis of Interference Distribution for Different Channel Models
  6. Channel Estimation Error Models
  7. Covariance Matrix of the Interference-plus-Noise Signal
  8. Problem Formulation
  9. Proposed Solution
  10. Update the Auxiliary Variables Matrices $\boldsymbol{Z}$ and $\boldsymbol{\Omega}$
  11. Update the Active Beamforming Matrix $\boldsymbol{W}$
  12. Update the Passive Beamforming Matrix $\boldsymbol{\Phi}$
  13. Update $\boldsymbol\phi_0$
  14. Update $\boldsymbol\phi$
  15. Overall Algorithm and Complexity Analysis
  16. ...and 7 more sections

Key Result

Lemma 1

For a matrix $\boldsymbol{X}\in \mathbb{C}^{n \times m}$, which obeys the distribution $\boldsymbol{X} \sim {\mathcal{CN}_{n,m}}(\hat{\boldsymbol X}, \boldsymbol{R}_n\otimes\boldsymbol{R}_m)$, where $\boldsymbol{R}_m\in \mathbb{C}^{m \times m}$ and $\boldsymbol{R}_n\in \mathbb{C}^{n \times n}$ repre

Figures (6)

  • Figure 1: The RIS-aided P2P wireless communication system.
  • Figure 2: Convergence behavior when $d_{\rm BR}=20$ m and SNR = 10 dB.
  • Figure 3: The achievable SEs versus the SNR when $\tau = 0.2$.
  • Figure 4: The achievable SEs versus the CEE variance when $K = 8$.
  • Figure 5: The achievable SEs versus the number of transmit antennas, $N_{\rm {Tx}}$, when $N_{\rm R}=256$.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Lemma 1: zhang2017matrix