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Low-Overhead Channel Estimation Framework for Beyond Diagonal Reconfigurable Intelligent Surface Assisted Multi-User MIMO Communication

Rui Wang, Shuowen Zhang, Bruno Clerckx, Liang Liu

TL;DR

This work tackles the CSI overhead challenge in BD-RIS aided MU-MIMO uplink. It uncovers a fundamental correlation: for each user, cascaded channels across BD-RIS elements are scaled versions of a reference channel due to a shared RIS–BS link, allowing dramatic reduction in independent unknowns. In the noise-free case, the minimum overhead is shown to be ${\bar \tau} = 2M + \lceil M(KU-1)/q \rceil$, placing BD-RIS overhead on par with conventional RIS. The authors then propose a two-phase estimation framework for the noisy setting, employing phase-wise linear estimators (LMMSE) and a structured pilot/BD-RIS design to achieve low overhead, with extensive simulations demonstrating substantial NMSE gains over existing approaches. This approach offers practical pathways to deploy BD-RIS in multi-user systems without prohibitive CSI costs, preserving the gains promised by BD-RIS architectures.

Abstract

Beyond diagonal reconfigurable intelligent surface (BD-RIS) refers to a family of RIS architectures characterized by scattering matrices not limited to being diagonal and enables higher wave manipulation flexibility and large performance gains over conventional (diagonal) RIS. To achieve those promising gains, accurate channel state information (CSI) needs to be acquired in BD-RIS assisted communication systems. However, the number of coefficients in the cascaded channels to be estimated in BD-RIS assisted systems is significantly larger than that in conventional RIS assisted systems, because the channels associated with the off-diagonal elements of the scattering matrix have to be estimated as well. Surprisingly, for the first time in the literature, this paper rigorously shows that the uplink channel estimation overhead in BD-RIS assisted systems is actually of the same order as that in the conventional RIS assisted systems. This amazing result stems from a key observation: for each user antenna, its cascaded channel matrix associated with one reference BD-RIS element is a scaled version of that associated with any other BD-RIS element due to the common RIS-base station (BS) channel. In other words, the number of independent unknown variables is far less than it would seem at first glance. Building upon this property, this paper manages to characterize the minimum overhead to perfectly estimate all the channels in the ideal case without noise at the BS, and propose a twophase estimation framework for the practical case with noise at the BS. Numerical results demonstrate outstanding channel estimation overhead reduction over existing schemes in BD-RIS assisted systems.

Low-Overhead Channel Estimation Framework for Beyond Diagonal Reconfigurable Intelligent Surface Assisted Multi-User MIMO Communication

TL;DR

This work tackles the CSI overhead challenge in BD-RIS aided MU-MIMO uplink. It uncovers a fundamental correlation: for each user, cascaded channels across BD-RIS elements are scaled versions of a reference channel due to a shared RIS–BS link, allowing dramatic reduction in independent unknowns. In the noise-free case, the minimum overhead is shown to be , placing BD-RIS overhead on par with conventional RIS. The authors then propose a two-phase estimation framework for the noisy setting, employing phase-wise linear estimators (LMMSE) and a structured pilot/BD-RIS design to achieve low overhead, with extensive simulations demonstrating substantial NMSE gains over existing approaches. This approach offers practical pathways to deploy BD-RIS in multi-user systems without prohibitive CSI costs, preserving the gains promised by BD-RIS architectures.

Abstract

Beyond diagonal reconfigurable intelligent surface (BD-RIS) refers to a family of RIS architectures characterized by scattering matrices not limited to being diagonal and enables higher wave manipulation flexibility and large performance gains over conventional (diagonal) RIS. To achieve those promising gains, accurate channel state information (CSI) needs to be acquired in BD-RIS assisted communication systems. However, the number of coefficients in the cascaded channels to be estimated in BD-RIS assisted systems is significantly larger than that in conventional RIS assisted systems, because the channels associated with the off-diagonal elements of the scattering matrix have to be estimated as well. Surprisingly, for the first time in the literature, this paper rigorously shows that the uplink channel estimation overhead in BD-RIS assisted systems is actually of the same order as that in the conventional RIS assisted systems. This amazing result stems from a key observation: for each user antenna, its cascaded channel matrix associated with one reference BD-RIS element is a scaled version of that associated with any other BD-RIS element due to the common RIS-base station (BS) channel. In other words, the number of independent unknown variables is far less than it would seem at first glance. Building upon this property, this paper manages to characterize the minimum overhead to perfectly estimate all the channels in the ideal case without noise at the BS, and propose a twophase estimation framework for the practical case with noise at the BS. Numerical results demonstrate outstanding channel estimation overhead reduction over existing schemes in BD-RIS assisted systems.

Paper Structure

This paper contains 20 sections, 2 theorems, 69 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. Prior Work
  4. Main Contributions
  5. Organization
  6. System Model
  7. Problem Statement for Channel Estimation
  8. Minimum Overhead in Special Case of A Single-Antenna User
  9. Minimum Overhead in General Case of Multiple Multi-Antenna Users
  10. Phase I: Estimation of the Cascaded Channel Associated with the 1st Antenna of User 1
  11. Phase II: Estimation of the Scaling Coefficients of the Other Antennas of User 1 and the Other Users
  12. Channel Estimation for Case with Noise at the BS
  13. Phase I: Estimation of the Cascaded Channel Associated With the 1st Antenna of User 1
  14. Phase II: Estimation of the Scaling Coefficients of the Other Antennas of User 1 and the Other Users
  15. Numerical Results
  16. ...and 5 more sections

Key Result

Theorem 1

Suppose for each time instant $t=1,\cdots,M$, ${\bm \phi}_{2,t},\cdots,{\bm \phi}_{M,t}$ are linearly independent. Then, ${\rm rank}({\bm\Theta}_1)=M-1$.

Figures (8)

  • Figure 1: A BD-RIS assisted MU-MIMO uplink communication system.
  • Figure 2: Illustration of the two-phase channel estimation protocol.
  • Figure 3: NMSE performance under different pilot sequence allocations.
  • Figure 4: NMSE performance versus total pilot length when $M=8,N=4,U=2$.
  • Figure 5: NMSE performance versus number of BD-RIS elements when $M=16,N=12,U=4$.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof