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Near-Field Beam Training: Joint Angle and Range Estimation with DFT Codebook

Xun Wu, Changsheng You, Jiapeng Li, Yunpu Zhang

TL;DR

This work tackles the high training overhead of near-field beam training in XL-array systems by showing that conventional DFT codebooks can jointly estimate user angle and off-grid range. It introduces the concept of surrogate angular support width to link angle and range from the near-field energy-spread pattern, and proposes two schemes, ASW-JE and prMSE-JE, that leverage DFT codebooks for efficient angle-range estimation. Numerical results demonstrate substantial training overhead reductions and improved range accuracy, with prMSE-JE providing robustness in noisy environments and higher achievable rates at high SNR. The approach bridges near-field sensing and communication, offering practical, low-complexity beam training for high-frequency XL-array deployments.

Abstract

Prior works on near-field beam training have mostly assumed dedicated polar-domain codebook and on-grid range estimation, which, however, may suffer long training overhead and degraded estimation accuracy. To address these issues, we propose in this paper new and efficient beam training schemes with off-grid range estimation by using conventional discrete Fourier transform (DFT) codebook. Specifically, we first analyze the received beam pattern at the user when far-field beamforming vectors are used for beam scanning, and show an interesting result that this beam pattern contains useful user angle and range information. Then, we propose two efficient schemes to jointly estimate the user angle and range with the DFT codebook. The first scheme estimates the user angle based on a defined angular support and resolves the user range by leveraging an approximated angular support width, while the second scheme estimates the user range by minimizing a power ratio mean square error (MSE) to improve the range estimation accuracy. Finally, numerical simulations show that our proposed schemes greatly reduce the near-field beam training overhead and improve the range estimation accuracy as compared to various benchmark schemes.

Near-Field Beam Training: Joint Angle and Range Estimation with DFT Codebook

TL;DR

This work tackles the high training overhead of near-field beam training in XL-array systems by showing that conventional DFT codebooks can jointly estimate user angle and off-grid range. It introduces the concept of surrogate angular support width to link angle and range from the near-field energy-spread pattern, and proposes two schemes, ASW-JE and prMSE-JE, that leverage DFT codebooks for efficient angle-range estimation. Numerical results demonstrate substantial training overhead reductions and improved range accuracy, with prMSE-JE providing robustness in noisy environments and higher achievable rates at high SNR. The approach bridges near-field sensing and communication, offering practical, low-complexity beam training for high-frequency XL-array deployments.

Abstract

Prior works on near-field beam training have mostly assumed dedicated polar-domain codebook and on-grid range estimation, which, however, may suffer long training overhead and degraded estimation accuracy. To address these issues, we propose in this paper new and efficient beam training schemes with off-grid range estimation by using conventional discrete Fourier transform (DFT) codebook. Specifically, we first analyze the received beam pattern at the user when far-field beamforming vectors are used for beam scanning, and show an interesting result that this beam pattern contains useful user angle and range information. Then, we propose two efficient schemes to jointly estimate the user angle and range with the DFT codebook. The first scheme estimates the user angle based on a defined angular support and resolves the user range by leveraging an approximated angular support width, while the second scheme estimates the user range by minimizing a power ratio mean square error (MSE) to improve the range estimation accuracy. Finally, numerical simulations show that our proposed schemes greatly reduce the near-field beam training overhead and improve the range estimation accuracy as compared to various benchmark schemes.
Paper Structure (29 sections, 5 theorems, 23 equations, 13 figures, 1 table)

This paper contains 29 sections, 5 theorems, 23 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Motivations and Contributions
  4. Organization and Notations
  5. System model
  6. Benchmark Beam Training Schemes
  7. 2D Exhaustive Search under Polar-Domain Codebook
  8. Two-Phase Near-field Beam Training
  9. Near-Field Received Beam Pattern Analysis
  10. Received Beam Pattern
  11. Surrogate Angular Support
  12. Proposed joint angle and range estimation with DFT codebook
  13. Scheme 1: Angle Support Width based Joint Angle and Range Estimation
  14. Beam sweeping
  15. Joint angle and range estimation
  16. ...and 14 more sections

Key Result

Lemma 1

The function $G(\theta_{\rm u}, r_{\rm u}, \phi)$ can be approximated as where $C(\cdot)$ and $S(\cdot)$ denote the Fresnel integrals defined as $C(x)=\int_{0}^{x}\cos(\frac{\pi}{2}t^2) {\rm d} t$ and $S(x)=\int_{0}^{x}\sin(\frac{\pi}{2}t^2) {\rm d} t$, respectively, and the parameters $\mu$ and $a$ are given by

Figures (13)

  • Figure 1: A narrow-band XL-array communication system.
  • Figure 2: Received beam pattern under far-field beamformers for different user angles and ranges, where $N=256$ and $f=30$ GHz. The true user spatial angle is marked by the black dotted lines.
  • Figure 3: The beam power ratio function $G(\theta_{\rm u}, r_{\rm u}, \phi)$ versus the approximation function $L(\mu, a)$.
  • Figure 4: 3dB surrogate angular support width versus user range for three user angles, where $N=256$ and $f=30$ GHz.
  • Figure 5: Illustration of function $L(\mu, a)$ versus $\mu$, where the case 1 is $a = \bar{\theta}^{(1)}_{\rm u}-\theta_{m} = 0.1$, and the case 2 is $a = \bar{\theta}^{(1)}_{\rm u}-\theta_{m} = 0.2$.
  • ...and 8 more figures

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 1
  • proof
  • Lemma 2: Symmetricity of $L(\mu, a)$
  • proof
  • Proposition 1
  • proof
  • Corollary 1
  • ...and 3 more