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GP Bandit-Assisted Two-Stage Sparse Phase Retrieval for Amplitude-Only Near-Field Beam Training

Zijun Wang, Shawn Tsai, Ye Hu, Rui Zhang

Abstract

The transition to Extremely Large Antenna Arrays (ELAA) in 6G introduces significant near-field effects, necessitating robust near-field beam training strategies in multi-path environments. Because signal phases are frequently compromised by hardware impairments such as phase noise and frequency offsets, amplitude-only channel recovery is a critical alternative to coherent beam training. However, existing near-field amplitude-based training methods often assume simplistic line-of-sight conditions. Conversely, far-field phase retrieval (PR) methods lack the sensing flexibility required to optimize training efficiency and are fundamentally limited by plane-wave models, making them ill-suited for near-field propagation. We propose a two-stage sparse PR framework for amplitude-only near-field beam training in multipath channels. Stage I performs adaptive support discovery on the standard 2D DFT beamspace by exploiting a physics-guided prior induced by near-field beam patterns. Stage II then refines the channel estimate by restricting sensing and sparse PR to the learned subspace. Numerical results show that the proposed adaptive pipeline consistently outperforms non-adaptive baselines, improving beamforming gain by over 70% at low SNR.

GP Bandit-Assisted Two-Stage Sparse Phase Retrieval for Amplitude-Only Near-Field Beam Training

Abstract

The transition to Extremely Large Antenna Arrays (ELAA) in 6G introduces significant near-field effects, necessitating robust near-field beam training strategies in multi-path environments. Because signal phases are frequently compromised by hardware impairments such as phase noise and frequency offsets, amplitude-only channel recovery is a critical alternative to coherent beam training. However, existing near-field amplitude-based training methods often assume simplistic line-of-sight conditions. Conversely, far-field phase retrieval (PR) methods lack the sensing flexibility required to optimize training efficiency and are fundamentally limited by plane-wave models, making them ill-suited for near-field propagation. We propose a two-stage sparse PR framework for amplitude-only near-field beam training in multipath channels. Stage I performs adaptive support discovery on the standard 2D DFT beamspace by exploiting a physics-guided prior induced by near-field beam patterns. Stage II then refines the channel estimate by restricting sensing and sparse PR to the learned subspace. Numerical results show that the proposed adaptive pipeline consistently outperforms non-adaptive baselines, improving beamforming gain by over 70% at low SNR.
Paper Structure (27 sections, 2 theorems, 93 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 27 sections, 2 theorems, 93 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Beam Pattern and Sparsity on UPA
  4. Separable Fresnel approximation
  5. 2D beam-pattern factorization and plateau support
  6. Effective sparsity level in 2D DFT beamspace
  7. Proposed Gaussian Bandit-Assisted Sparse Phase Retrieval
  8. Stage I: GP-LSE Support Discovery in 2D DFT Beamspace
  9. Stage I outputs support for Stage II.
  10. Stage I overhead in terms of information gain.
  11. Practical support truncation under a fixed probing budget
  12. Stage II: Gaussian-Masked DFT Sensing and Rician-SPARTA Refinement
  13. Simulation Results
  14. Performance under Varying SNR
  15. Ablation Study
  16. ...and 12 more sections

Key Result

Lemma 1

Fix $\delta\in(0,1)$. Choose a nondecreasing exploration sequence where $\gamma_{t}$ is the maximum information gain of kernel $k$ on $\mathcal{I}$ under noise parameter $\sigma_\varepsilon^2$. Then, conditioned on $\mathcal{E}_{\mathrm{bd}}(T_1)$, with probability at least $1-\delta$, for all $t\ge 1$ and all $i\in\mathcal{I}$, Consequently, $f(i)\in Q_t(i)$ for all $i,t$, and thus $f(i)\in C_t

Figures (7)

  • Figure 1: Diagram of the near-field communication system featuring a UPA.
  • Figure 2: Normalized DFT-beamspace magnitude on a $(128\times 128)$ UPA at $f_c=28~\mathrm{GHz}$.
  • Figure 3: 1D cuts of the normalized gain and the 6-dB lobe widths.
  • Figure 4: Mean correlation versus SNR.
  • Figure 5: Mean correlation versus SNR for ablated methods.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Lemma 2
  • proof