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Near-Field Terahertz Communications: Model-Based and Model-Free Channel Estimation

Ahmet M. Elbir, Wei Shi, Anastasios K. Papazafeiropoulos, Pandelis Kourtessis, Symeon Chatzinotas

TL;DR

A model-based and a model-free techniques for wideband THz channel estimation in the presence of NB, based on orthogonal matching pursuit (OMP) algorithm, for which an NB-aware dictionary is designed and the key idea is to exploit the angular and range deviations due to the NB.

Abstract

Terahertz (THz) band is expected to be one of the key enabling technologies of the sixth generation (6G) wireless networks because of its abundant available bandwidth and very narrow beam width. Due to high frequency operations, electrically small array apertures are employed, and the signal wavefront becomes spherical in the near-field. Therefore, near-field signal model should be considered for channel acquisition in THz systems. Unlike prior works which mostly ignore the impact of near-field beam-split (NB) and consider either narrowband scenario or far-field models, this paper introduces both a model-based and a model-free techniques for wideband THz channel estimation in the presence of NB. The model-based approach is based on orthogonal matching pursuit (OMP) algorithm, for which we design an NB-aware dictionary. The key idea is to exploit the angular and range deviations due to the NB. We then employ the OMP algorithm, which accounts for the deviations thereby ipso facto mitigating the effect of NB. We further introduce a federated learning (FL)-based approach as a model-free solution for channel estimation in a multi-user scenario to achieve reduced complexity and training overhead. Through numerical simulations, we demonstrate the effectiveness of the proposed channel estimation techniques for wideband THz systems in comparison with the existing state-of-the-art techniques.

Near-Field Terahertz Communications: Model-Based and Model-Free Channel Estimation

TL;DR

A model-based and a model-free techniques for wideband THz channel estimation in the presence of NB, based on orthogonal matching pursuit (OMP) algorithm, for which an NB-aware dictionary is designed and the key idea is to exploit the angular and range deviations due to the NB.

Abstract

Terahertz (THz) band is expected to be one of the key enabling technologies of the sixth generation (6G) wireless networks because of its abundant available bandwidth and very narrow beam width. Due to high frequency operations, electrically small array apertures are employed, and the signal wavefront becomes spherical in the near-field. Therefore, near-field signal model should be considered for channel acquisition in THz systems. Unlike prior works which mostly ignore the impact of near-field beam-split (NB) and consider either narrowband scenario or far-field models, this paper introduces both a model-based and a model-free techniques for wideband THz channel estimation in the presence of NB. The model-based approach is based on orthogonal matching pursuit (OMP) algorithm, for which we design an NB-aware dictionary. The key idea is to exploit the angular and range deviations due to the NB. We then employ the OMP algorithm, which accounts for the deviations thereby ipso facto mitigating the effect of NB. We further introduce a federated learning (FL)-based approach as a model-free solution for channel estimation in a multi-user scenario to achieve reduced complexity and training overhead. Through numerical simulations, we demonstrate the effectiveness of the proposed channel estimation techniques for wideband THz systems in comparison with the existing state-of-the-art techniques.
Paper Structure (21 sections, 1 theorem, 34 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 21 sections, 1 theorem, 34 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. Outline and Notation
  5. Outline
  6. Notation
  7. System Model
  8. THz Channel Model
  9. Near-field Array Model
  10. Problem Formulation
  11. NB Model
  12. Model-Based Solution: NBA-OMP
  13. NBA Dictionary Design
  14. Near-field Channel Estimation
  15. Model-Free Solution: NBA-OMP-FL
  16. ...and 6 more sections

Key Result

Theorem 1

Denote $\mathbf{u}\in \mathbb{C}^N$ and $\mathbf{v}_m \in \mathbb{C}^N$ as the arbitrary near-field steering vectors corresponding to the physical (i.e., $\{\phi_{k,l},r_{k,l}\}$) and spatial (i.e., $\{\bar{\phi}_{k,m,l}, \bar{r}_{k,m,l}\}$) locations given in (steeringVectorPhy2) and (steeringVecto where $\eta_m = \frac{f_c}{f_m}$ represents the proportional deviation of DoA/ranges.

Figures (6)

  • Figure 1: Path loss (in dB) due to molecular absorption for various transmission ranges.
  • Figure 2: Normalized array gain with respect to spatial direction at low, center and high end subcarriers for (left) $3.5$ GHz, $B=0.1$ GHz; (middle) $28$ GHz, $B=2$ GHz; and (right) $300$ GHz, $30$ GHz, respectively.
  • Figure 3: Array gains $G(\phi_{1,1},r_{1,1},{m})$ in Cartesian coordinates for a single user ($K=1$, $L=1$) located in the far-field $(45^\circ,6000\text{m})$ (left) and near-field $(45^\circ,6\text{m})$ (right), respectively. Here, $M=3$, $f_c=300$ GHz, and $B=30$ GHz. The top panel shows the gain for different subcarriers which are summed up to produce a composite array gain at the bottom for both far- and near-field cases clearly showing the beam-split. The square represents the user location while the triangles correspond to the spatial locations (where the maximum array gain is achieved) at different subcarriers. Whereas the far-field beam-split is only angular, the near-field split is across both range and angular domains.
  • Figure 4: Near-field THz wideband channel estimation NMSE versus SNR. $N=256$, $f_c=300$ GHz, $M=128$ and $B=30$ GHz.
  • Figure 5: Near-field THz wideband channel estimation NMSE versus bandwidth when $\mathrm{SNR}=10$ dB.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof