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Efficient Channel Estimation With Shorter Pilots in RIS-Aided Communications: Using Array Geometries and Interference Statistics

Özlem Tuğfe Demir, Emil Björnson, Luca Sanguinetti

TL;DR

This paper first optimize the RIS phase-shift pattern using a much-reduced pilot length to minimize the mean square error (MSE) in the channel estimation under electromagnetic interference, and proposes a novel channel estimator that requires only knowledge of the array geometry while not requiring any user-specific statistical information.

Abstract

Accurate estimation of the cascaded channel from a user equipment (UE) to a base station (BS) via each reconfigurable intelligent surface (RIS) element is critical to realizing the full potential of the RIS's ability to control the overall channel. The number of parameters to be estimated is equal to the number of RIS elements, requiring an equal number of pilots unless an underlying structure can be identified. In this paper, we show how the spatial correlation inherent in the different RIS channels provides this desired structure. We first optimize the RIS phase-shift pattern using a much-reduced pilot length (determined by the rank of the spatial correlation matrices) to minimize the mean square error (MSE) in the channel estimation under electromagnetic interference. In addition to considering the linear minimum MSE (LMMSE) channel estimator, we propose a novel channel estimator that requires only knowledge of the array geometry while not requiring any user-specific statistical information. We call this the reduced-subspace least squares (RS-LS) estimator and optimize the RIS phase-shift pattern for it. This novel estimator significantly outperforms the conventional LS estimator. For both the LMMSE and RS-LS estimators, the proposed optimized RIS configurations result in significant channel estimation improvements over the benchmarks.

Efficient Channel Estimation With Shorter Pilots in RIS-Aided Communications: Using Array Geometries and Interference Statistics

TL;DR

This paper first optimize the RIS phase-shift pattern using a much-reduced pilot length to minimize the mean square error (MSE) in the channel estimation under electromagnetic interference, and proposes a novel channel estimator that requires only knowledge of the array geometry while not requiring any user-specific statistical information.

Abstract

Accurate estimation of the cascaded channel from a user equipment (UE) to a base station (BS) via each reconfigurable intelligent surface (RIS) element is critical to realizing the full potential of the RIS's ability to control the overall channel. The number of parameters to be estimated is equal to the number of RIS elements, requiring an equal number of pilots unless an underlying structure can be identified. In this paper, we show how the spatial correlation inherent in the different RIS channels provides this desired structure. We first optimize the RIS phase-shift pattern using a much-reduced pilot length (determined by the rank of the spatial correlation matrices) to minimize the mean square error (MSE) in the channel estimation under electromagnetic interference. In addition to considering the linear minimum MSE (LMMSE) channel estimator, we propose a novel channel estimator that requires only knowledge of the array geometry while not requiring any user-specific statistical information. We call this the reduced-subspace least squares (RS-LS) estimator and optimize the RIS phase-shift pattern for it. This novel estimator significantly outperforms the conventional LS estimator. For both the LMMSE and RS-LS estimators, the proposed optimized RIS configurations result in significant channel estimation improvements over the benchmarks.

Paper Structure

This paper contains 26 sections, 6 theorems, 69 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System and Channel Modeling
  3. Pilot Transmission and Channel Estimation
  4. Pilot Transmission
  5. Linear Minimum Mean-Square Error Estimation
  6. Reduced-Subspace Least Squares Estimation
  7. Optimizing the RIS Configuration for LMMSE Estimation
  8. Optimal Structure without EMI
  9. Optimal Structure with EMI
  10. Optimizing the RIS Configuration for RS-LS Estimation
  11. Optimal Structure for the RS-LS Estimator Without EMI
  12. Optimal Structure for the RS-LS Estimator with EMI
  13. When $\tau_p=\overline{r}_{\rm hg}$
  14. When $\overline{\mathbf{U}}_{\rm hg,2}^{\hbox{\tiny $\mathrm{H}$}} \left(\mathbf{R}_{\rm w}\odot\mathbf{R}_{\rm g}\right)=\mathbf{0}_{(N-\overline{r}_{\rm hg}) \times N}$
  15. When $\overline{\mathbf{U}}_{\rm hg,1}^{\hbox{\tiny $\mathrm{H}$}} \left(\mathbf{R}_{\rm w}\odot\mathbf{R}_{\rm g}\right)=\mathbf{0}_{\overline{r}_{\rm hg} \times N}$
  16. ...and 11 more sections

Key Result

Lemma 1

Let $\overline{\mathbf{R}}_{\rm x }=\overline{\mathbf{R}}_{{\rm g}^{\prime}} \otimes \left(\overline{\mathbf{R}}_{\rm h}\odot\overline{\mathbf{R}}_{\rm g}\right)$ and $\mathbf{R}_{\rm x}=\mathbf{R}_{{\rm g}^{\prime}} \otimes \left(\mathbf{R}_{\rm h}\odot\mathbf{R}_{\rm g}\right)$ be two spatial corr

Figures (9)

  • Figure 1: NMSE versus SIR for LMMSE estimator with $\tau_p=N/2=128$.
  • Figure 2: NMSE versus SIR for LMMSE estimator with fast and slowly varying EMI when the nominal azimuth angle of the EMI spatial correlation matrix is $\varphi=0$.
  • Figure 3: NMSE versus SIR for LMMSE estimator with fast and slowly varying EMI when the nominal azimuth angle of the EMI spatial correlation matrix is $\varphi=\pi/5$.
  • Figure 4: NMSE versus SIR for LS and RS-LS estimators with $\tau_p=N=256$ and when the nominal azimuth angle of the EMI spatial correlation matrix is $\varphi=\pi/5$.
  • Figure 5: NMSE versus SIR for RS-LS estimator with fast and slowly varying EMI when the nominal azimuth angle of the EMI spatial correlation matrix is $\varphi=\pi/5$ and $\tau_p=N/2=128$.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Lemma 1
  • Remark 1
  • Remark 2
  • Lemma 2
  • Corollary 1
  • Lemma 3
  • Lemma 4
  • Remark 3
  • Lemma 5