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Channel Estimation for Double-BD-RIS-Assisted Multi-User MIMO Communication

Junyuan Gao, Shuowen Zhang, Liang Liu

TL;DR

This paper reveals that high-dimensional cascaded channels are characterized by five low-dimensional matrices by exploiting channel correlation properties and develops a channel estimation scheme to recover these matrices sequentially and implies the superiority of cooperative BD-RIS-aided communication over the diagonal- RIS counterpart even when channel estimation overhead is considered.

Abstract

Deploying multiple beyond diagonal reconfigurable intelligent surfaces (BD-RISs) can potentially improve the communication performance thanks to inter-element connections of each BD-RIS and inter-surface cooperative beamforming gain among BD-RISs. However, a major issue for multi-BD-RISassisted communication lies in the channel estimation overhead - the channel coefficients associated with the off-diagonal elements in each BD-RIS's scattering matrix as well as those associated with the reflection links among BD-RISs have to be estimated. In this paper, we propose an efficient channel estimation framework for double-BD-RIS-assisted multi-user multipleinput multiple-output (MIMO) systems. Specifically, we reveal that high-dimensional cascaded channels are characterized by five low-dimensional matrices by exploiting channel correlation properties. Based on this novel observation, in the ideal noiseless case, we develop a channel estimation scheme to recover these matrices sequentially and characterize the closed-form overhead required for perfect estimation as a function of the numbers of users and each BD-RIS's elements and channel ranks, which is with the same order as that in double-diagonal-RIS-aided communication systems. This exciting result implies the superiority of cooperative BD-RIS-aided communication over the diagonal- RIS counterpart even when channel estimation overhead is considered. We further extend the proposed scheme to practical noisy scenarios and provide extensive numerical simulations to validate its effectiveness.

Channel Estimation for Double-BD-RIS-Assisted Multi-User MIMO Communication

TL;DR

This paper reveals that high-dimensional cascaded channels are characterized by five low-dimensional matrices by exploiting channel correlation properties and develops a channel estimation scheme to recover these matrices sequentially and implies the superiority of cooperative BD-RIS-aided communication over the diagonal- RIS counterpart even when channel estimation overhead is considered.

Abstract

Deploying multiple beyond diagonal reconfigurable intelligent surfaces (BD-RISs) can potentially improve the communication performance thanks to inter-element connections of each BD-RIS and inter-surface cooperative beamforming gain among BD-RISs. However, a major issue for multi-BD-RISassisted communication lies in the channel estimation overhead - the channel coefficients associated with the off-diagonal elements in each BD-RIS's scattering matrix as well as those associated with the reflection links among BD-RISs have to be estimated. In this paper, we propose an efficient channel estimation framework for double-BD-RIS-assisted multi-user multipleinput multiple-output (MIMO) systems. Specifically, we reveal that high-dimensional cascaded channels are characterized by five low-dimensional matrices by exploiting channel correlation properties. Based on this novel observation, in the ideal noiseless case, we develop a channel estimation scheme to recover these matrices sequentially and characterize the closed-form overhead required for perfect estimation as a function of the numbers of users and each BD-RIS's elements and channel ranks, which is with the same order as that in double-diagonal-RIS-aided communication systems. This exciting result implies the superiority of cooperative BD-RIS-aided communication over the diagonal- RIS counterpart even when channel estimation overhead is considered. We further extend the proposed scheme to practical noisy scenarios and provide extensive numerical simulations to validate its effectiveness.
Paper Structure (23 sections, 2 theorems, 122 equations, 5 figures)

This paper contains 23 sections, 2 theorems, 122 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Prior Works
  4. Main Contributions
  5. System Model
  6. Problem Statement
  7. Channel Estimation in the Noiseless Case
  8. Phase I: Estimation of $\bar{\mathbf{Q}}_{2}$
  9. Phase II: Estimation of $\bar{\bm{r}}_{2}$
  10. Phase III: Estimation of $\bar{\mathbf{Q}}_{1}$
  11. Phase IV: Estimation of $\bar{\mathbf{B}}$
  12. Phase V: Estimation of $\bar{\mathbf{r}}_{1}$
  13. Overall Overhead
  14. Channel Estimation in the Case with Noise
  15. Phase I: Estimation of $\bar{\mathbf{Q}}_{2}$
  16. ...and 8 more sections

Key Result

Theorem 1

Given the channel matrices $\bar{\mathbf{Q}}_{1} , \bar{\mathbf{Q}}_{2},$ and $\bar{\mathbf{B}}$, the maximum rank of $\mathbf{F}$ achievable via the configuration of the scattering matrix $\bm{\Phi}_2$ is given by This maximum rank is achieved by designing $\bm{\Phi}_2$ as where $\mathbf{V}_{\tilde{\mathbf{Q}}_2} \in \mathbb{C}^{M_2\times M_2}$ is the right singular matrix of the matrix $\tilde

Figures (5)

  • Figure 1: System model of double-BD-RIS-aided communication. BD-RIS 1 is close to the users, and BD-RIS 2 is close to the BS. The BS receives signals via the user - BD-RIS 1 - BS link, user - BD-RIS 2 - BS link, and user - BD-RIS 1 - BD-RIS 2 - BS link.
  • Figure 2: Channel estimation performance versus transmit power $p$ with $T = 64, K = 8, L = 8$, and $M_1 = M_2 = 4$.
  • Figure 3: Channel estimation performance versus pilot length $T$ with $p = 30$ dBm and $K = M_1 = M_2 = 4$.
  • Figure 4: Channel estimation performance versus the number $K$ of users with $p = 30$ dBm and $L = M_1 = M_2 = 4$.
  • Figure 5: Convergence behavior versus the number $M_2$ of elements in BD-RIS 2 with $p = 30$ dBm, $T = 200$, $K = 8$, and $L = 32$.

Theorems & Definitions (5)

  • Theorem 1
  • Corollary 1
  • Remark 1
  • Remark 2
  • Remark 3