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Joint Training and Reflection Pattern Optimization for Non-Ideal RIS-Aided Multiuser Systems

Zhenyao He, Jindan Xu, Hong Shen, Wei Xu, Chau Yuen, Marco Di Renzo

TL;DR

This paper considers an RIS-aided multiuser system with non-ideal reflecting elements, each of which has a phase-dependent reflecting amplitude, and aims to minimize the mean-squared error (MSE) of the channel estimation by jointly optimizing the training signals at the user equipments (UEs) and the reflection pattern at the RIS.

Abstract

Reconfigurable intelligent surface (RIS) is a promising technique to improve the performance of future wireless communication systems at low energy consumption. To reap the potential benefits of RIS-aided beamforming, it is vital to enhance the accuracy of channel estimation. In this paper, we consider an RIS-aided multiuser system with non-ideal reflecting elements, each of which has a phase-dependent reflecting amplitude, and we aim to minimize the mean-squared error (MSE) of the channel estimation by jointly optimizing the training signals at the user equipments (UEs) and the reflection pattern at the RIS. As examples the least squares (LS) and linear minimum MSE (LMMSE) estimators are considered. The considered problems do not admit simple solution mainly due to the complicated constraints pertaining to the non-ideal RIS reflecting elements. As far as the LS criterion is concerned, we tackle this difficulty by first proving the optimality of orthogonal training symbols and then propose a majorization-minimization (MM)-based iterative method to design the reflection pattern, where a semi-closed form solution is obtained in each iteration. As for the LMMSE criterion, we address the joint training and reflection pattern optimization problem with an MM-based alternating algorithm, where a closed-form solution to the training symbols and a semi-closed form solution to the RIS reflecting coefficients are derived, respectively. Furthermore, an acceleration scheme is proposed to improve the convergence rate of the proposed MM algorithms. Finally, simulation results demonstrate the performance advantages of our proposed joint training and reflection pattern designs.

Joint Training and Reflection Pattern Optimization for Non-Ideal RIS-Aided Multiuser Systems

TL;DR

This paper considers an RIS-aided multiuser system with non-ideal reflecting elements, each of which has a phase-dependent reflecting amplitude, and aims to minimize the mean-squared error (MSE) of the channel estimation by jointly optimizing the training signals at the user equipments (UEs) and the reflection pattern at the RIS.

Abstract

Reconfigurable intelligent surface (RIS) is a promising technique to improve the performance of future wireless communication systems at low energy consumption. To reap the potential benefits of RIS-aided beamforming, it is vital to enhance the accuracy of channel estimation. In this paper, we consider an RIS-aided multiuser system with non-ideal reflecting elements, each of which has a phase-dependent reflecting amplitude, and we aim to minimize the mean-squared error (MSE) of the channel estimation by jointly optimizing the training signals at the user equipments (UEs) and the reflection pattern at the RIS. As examples the least squares (LS) and linear minimum MSE (LMMSE) estimators are considered. The considered problems do not admit simple solution mainly due to the complicated constraints pertaining to the non-ideal RIS reflecting elements. As far as the LS criterion is concerned, we tackle this difficulty by first proving the optimality of orthogonal training symbols and then propose a majorization-minimization (MM)-based iterative method to design the reflection pattern, where a semi-closed form solution is obtained in each iteration. As for the LMMSE criterion, we address the joint training and reflection pattern optimization problem with an MM-based alternating algorithm, where a closed-form solution to the training symbols and a semi-closed form solution to the RIS reflecting coefficients are derived, respectively. Furthermore, an acceleration scheme is proposed to improve the convergence rate of the proposed MM algorithms. Finally, simulation results demonstrate the performance advantages of our proposed joint training and reflection pattern designs.
Paper Structure (32 sections, 7 theorems, 70 equations, 10 figures, 2 tables, 3 algorithms)

This paper contains 32 sections, 7 theorems, 70 equations, 10 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Cascaded Channel Estimation
  5. Problem Formulation
  6. LS Channel Estimation
  7. Closed-Form Optimal Training Matrix
  8. Optimization of RIS Reflection Pattern
  9. LMMSE Channel Estimation
  10. Optimization of the Training Matrix
  11. Optimization of the RIS Reflection Pattern
  12. Accelerated MM Algorithm
  13. Simulation Results and Complexity Analysis
  14. Simulation Setup
  15. Normalized MSE Performance Comparisons
  16. ...and 17 more sections

Key Result

Theorem 1

The optimal training matrix for the LS channel estimator of the considered non-ideal RIS-assisted system satisfies the condition:

Figures (10)

  • Figure 1: The considered RIS-aided uplink multiuser communication system.
  • Figure 2: The considered practical phase shift model RISPracticalModel.
  • Figure 3: The considered channel estimation protocol.
  • Figure 4: Normalized MSE of the LS channel estimator with respect to the number of iterations and the running time in each iteration.
  • Figure 5: Normalized MSE of the LS channel estimator versus the SNR.
  • ...and 5 more figures

Theorems & Definitions (9)

  • Remark 1
  • Theorem 1
  • Proposition 1
  • Proposition 2
  • Theorem 2
  • Remark 2
  • Lemma 1
  • Proposition 3
  • Lemma 2