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arxiv: 2605.17690 · v1 · pith:6S6QQ27Fnew · submitted 2026-05-17 · 📡 eess.SP

A Framework of Near-Field Communication with Different Array Geometries: Analysis, Optimization, and General Channel Estimation Algorithms Based on Deep Learning

Kangda Zhi , Yi Song , Tianyu Yang , Tuo Wu , Tengjiao Wang , Songyan Xue , Fangzhou Wu , Giuseppe Caire This is my paper

Pith reviewed 2026-05-19 21:57 UTC · model grok-4.3

classification 📡 eess.SP
keywords near-field communicationXL-MIMOarray geometrychannel estimationdeep learninghybrid precodingspatial non-stationaritycompressed sensing
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The pith

Curved array geometries extend the near-field region in XL-MIMO while a general deep-learning estimator recovers the resulting channels for rate optimization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a framework for near-field communication in extremely large MIMO systems that incorporates different array geometries. It formulates spatially non-stationary channel models based on per-antenna distances for both planar and modular curved arrays, and demonstrates that increasing curvature while holding total antenna count and horizontal arc length fixed pushes the near-field boundary farther from the array for cell-edge users. The central technical contribution is a denoising autoencoder-aided approximated message passing algorithm that solves the compressed sensing channel estimation task for arbitrary geometries without relying on specific codebooks. The estimated channels then support joint optimization of array curvature and hybrid precoding to raise the sum rate across users.

Core claim

By fixing the total number of antennas and the horizontal arc length while varying curvature, the work shows that modular curved arrays enlarge the near-field region compared with planar arrays, and that the AE-AMP algorithm, which inserts a learned denoiser into approximated message passing, estimates the resulting non-stationary channels with robustness and generality across geometries, enabling measurable sum-rate gains when geometry and precoding are designed together.

What carries the argument

The denoising autoencoder-aided approximated message passing (AE-AMP) algorithm, which learns a regularizer to solve the compressed sensing problem for channel estimation under arbitrary array geometries and arbitrary-field channels.

If this is right

  • Increasing array curvature extends the near-field region for cell-edge users without adding antennas or widening the horizontal span.
  • The AE-AMP estimator recovers spatial non-stationary near-field channels more robustly than conventional or other deep-learning benchmarks.
  • Joint design of modular array geometry and hybrid precoding raises achievable sum user rates when the estimated channels are used.
  • The estimation approach applies to arbitrary array geometries and arbitrary-field channels without requiring geometry-specific codebooks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Future XL-MIMO base stations could adopt curved surfaces to improve coverage in regions where near-field propagation dominates.
  • The general compressed-sensing formulation with learned regularizer could be transferred to other spatially non-stationary channel models such as those arising at terahertz frequencies.
  • Hardware implementations would need to weigh the added complexity of modular curved surfaces against the reported rate improvements.

Load-bearing premise

Fixing total antenna count and horizontal arc length while varying curvature isolates the pure geometric effect without confounding changes in aperture or element spacing.

What would settle it

A measurement campaign that directly compares the distance at which spherical-wave effects dominate for planar versus modular curved arrays of identical antenna count and arc length would confirm or refute the claimed extension of the near-field region.

Figures

Figures reproduced from arXiv: 2605.17690 by Fangzhou Wu, Giuseppe Caire, Kangda Zhi, Songyan Xue, Tengjiao Wang, Tianyu Yang, Tuo Wu, Yi Song.

Figure 1
Figure 1. Figure 1: Illustration of the considered sub-connected XL-MIMO system. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The change of array curvature angle θ given fixed curve length L. have a much larger number of antennas than linear/planar arrays. Meanwhile, the complete circular/cylindrical array does not enable the investigation of the impact of array curvature on adjusting near-field region. Thus, we will fix the number of antennas (i.e., arc length) and model the change of array cur￾vature for fair comparisons betwee… view at source ↗
Figure 3
Figure 3. Figure 3: The impact of array curvature on (a) theoretical and effective Rayleigh [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The 3D curved array: (a) uniform cylindrical array; (b) modular [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Near-field boundaries in the 3D space: (a) uniform cylindrical array [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Illustration of the considered denosing AE network. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: NMSE performance versus uplink SNRs [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Correlation coefficient between estimated and true channels. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparisons with state evolution and replica bound. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Heatmap of sum data rates for users located in different M [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: NMSE performance for estimating channels of UPA and MCA. [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Rate comparison between UPA and MCA with estimated channels. [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
read the original abstract

This work establishes a framework of near-field communication under different array geometries of extremely large-scale multiple-input multiple-output (XL-MIMO). We first formulate the near-field spatial non-stationary channel model which is characterized by the distance between the user and each antenna on uniform and modular curved arrays. By fixing the total number of antennas while varying the degree of curvature, we investigate a fair case where the horizontal arc length of the curved array is the same as the planar array. We explicitly unveil the non-trivial impact of array curvature on extending the near-field region for cell edges. Then, for arbitrary array geometries and arbitrary-field channels, we estimate the spatial-domain channel by tackling a compressed sensing problem with a learned regularizer. Without relying on specific codebooks, we propose a denoising autoencoder (AE)-aided approximated message passing (AMP) algorithm and provide the corresponding theoretical replica bound. Finally, based on the estimated channel, we propose an optimization algorithm to maximize the sum user rate for sub-connected XL-MIMO systems by jointly designing the array geometry and hybrid precoding in the downlink. Numerical results demonstrate that the proposed AE-AMP algorithm can effectively estimate the spatial non-stationary near-field channels with robustness and generalities compared to several conventional and deep-learning-based benchmarks. The improvement of data rate by using modular curved arrays with the estimated channel is also validated.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper establishes a framework for near-field XL-MIMO communications across array geometries, including uniform planar and modular curved arrays. It formulates a spatial non-stationary channel model using per-antenna distances, proposes a denoising autoencoder-aided approximated message passing (AE-AMP) algorithm for general compressed-sensing channel estimation together with a replica bound, and develops a joint optimization of array geometry and hybrid precoding to maximize downlink sum rates in sub-connected systems. Numerical results claim superior estimation robustness and rate gains for curved arrays relative to planar baselines and other benchmarks.

Significance. If the central claims hold, the work supplies a geometry-agnostic estimation procedure backed by a theoretical replica bound and a practical optimization routine for hybrid precoding under near-field conditions. The AE-AMP algorithm's generality across array curvatures and the explicit replica bound constitute clear technical strengths that could support reproducible follow-on studies.

major comments (1)
  1. [Channel formulation and numerical setup] Channel formulation and numerical setup: the comparison that fixes total antenna count N and horizontal arc length while varying curvature does not control for the concomitant shortening of chord length and projected aperture. Because curvature alters the effective horizontal span and the distribution of user-to-element distances independently of the intended spherical-wave non-stationarity, the reported sum-rate improvement cannot be unambiguously attributed to the geometric effect the framework claims to isolate. An ablation that restores equivalent chord length or reports effective aperture metrics is required to substantiate the central rate-gain claim.
minor comments (2)
  1. [Abstract] The abstract states that the AE-AMP algorithm is compared against 'several conventional and deep-learning-based benchmarks' but does not name them; listing the specific baselines in the abstract would improve immediate readability.
  2. [Channel estimation section] Notation for the replica bound is introduced without an explicit statement of the underlying assumptions (e.g., large-system limit, i.i.d. entries) in the main text; a short clarifying sentence would help readers assess its applicability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address the major comment below and agree that additional analysis will strengthen the central claims. We will incorporate the suggested ablation and metrics in the revised manuscript.

read point-by-point responses

  1. Referee: Channel formulation and numerical setup: the comparison that fixes total antenna count N and horizontal arc length while varying curvature does not control for the concomitant shortening of chord length and projected aperture. Because curvature alters the effective horizontal span and the distribution of user-to-element distances independently of the intended spherical-wave non-stationarity, the reported sum-rate improvement cannot be unambiguously attributed to the geometric effect the framework claims to isolate. An ablation that restores equivalent chord length or reports effective aperture metrics is required to substantiate the central rate-gain claim.

    Authors: We thank the referee for highlighting this subtlety in our experimental design. Our decision to fix both N and the horizontal arc length was intended to provide a fair comparison for modular curved arrays, where the total physical length of the modules along the curve is held constant (reflecting practical deployment constraints on module size). We acknowledge, however, that increasing curvature necessarily reduces the chord length and projected aperture, which in turn affects the distribution of user-to-element distances. This geometric change is partly inseparable from the near-field spherical-wave effects we aim to study. To address the concern directly and strengthen the attribution of rate gains, we will add an ablation study in the revised manuscript. In this ablation we will compare configurations with matched chord lengths (by adjusting arc length as curvature varies) and will explicitly report effective aperture metrics such as the projected horizontal span for each geometry. These additions will help isolate the contribution of spatial non-stationarity from aperture variation. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper formulates a near-field channel model for different array geometries, proposes an AE-AMP algorithm for general compressed-sensing channel estimation with a replica bound, and validates performance numerically against external benchmarks. The replica bound is derived as theoretical analysis for the AMP iteration and does not reduce to a fitted parameter or self-referential input by construction. Training the autoencoder on simulated channels drawn from the stated model is standard supervised learning practice and does not equate the reported estimation accuracy or rate gains to the training data itself. The fixed-N and fixed-arc-length modeling choice is an explicit assumption for isolating curvature effects rather than a definitional loop. No load-bearing step collapses to a self-citation chain, ansatz smuggling, or renaming of known results; the central claims remain independently testable against the provided benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claims rest on the spatial non-stationary channel model being an accurate description of real propagation, on the training distribution of the autoencoder matching deployment channels, and on the fixed-arc-length comparison being a fair isolation of curvature effects.

free parameters (2)
  • degree of curvature
    Varied while keeping total antennas and horizontal arc length fixed; chosen to study geometric impact.
  • number of users and antennas
    Fixed in the fair comparison and numerical experiments; values are simulation parameters.
axioms (1)
  • domain assumption The near-field channel is fully characterized by per-antenna distances on uniform and modular curved arrays.
    Invoked in the first modeling step of the abstract.

pith-pipeline@v0.9.0 · 5806 in / 1433 out tokens · 38881 ms · 2026-05-19T21:57:53.851388+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

  1. [1]

    A general channel estimation method for spatial non- stationary mixed near- and far-field XL-MIMO channels,

    K. Zhiet al., “A general channel estimation method for spatial non- stationary mixed near- and far-field XL-MIMO channels,” 2026

    work page 2026

  2. [2]

    A tutorial on near-field XL-MIMO communications toward 6G,

    H. Lu, Y . Zeng, C. You, Y . Han, J. Zhang, Z. Wanget al., “A tutorial on near-field XL-MIMO communications toward 6G,”IEEE Commun. Surveys Tutorials, vol. 26, no. 4, pp. 2213–2257, 2024

    work page 2024

  3. [3]

    NEFT: A unified transformer framework for efficient near-field CSI feedback in XL-MIMO systems,

    T. Mao, H. Li, S. Tan, P. Wang, G. Liu, R. Liu, L. Zhang, M. Hua, D. Zheng, Z. Wanget al., “NEFT: A unified transformer framework for efficient near-field CSI feedback in XL-MIMO systems,”arXiv preprint arXiv:2509.12748, 2025

    work page arXiv 2025

  4. [4]

    Near-field channel estimation for extremely large-scale reconfigurable intelligent surface (XL-RIS)-aided wideband mmwave systems,

    S. Yang, C. Xie, W. Lyu, B. Ning, Z. Zhang, and C. Yuen, “Near-field channel estimation for extremely large-scale reconfigurable intelligent surface (XL-RIS)-aided wideband mmwave systems,”IEEE J. Sel. Areas Commun., vol. 42, no. 6, pp. 1567–1582, 2024

    work page 2024

  5. [5]

    Performance analysis and low-complexity design for XL- MIMO with near-field spatial non-stationarities,

    K. Zhiet al., “Performance analysis and low-complexity design for XL- MIMO with near-field spatial non-stationarities,”IEEE J. Sel. Areas Commun., vol. 42, no. 6, pp. 1656–1672, 2024

    work page 2024

  6. [6]

    Unified far-field and near-field in holographic MIMO: A wavenumber-domain perspective,

    Y . Chen, X. Guo, G. Zhou, S. Jin, D. W. K. Ng, and Z. Wang, “Unified far-field and near-field in holographic MIMO: A wavenumber-domain perspective,”IEEE Commun. Mag., vol. 63, no. 1, pp. 30–36, 2025

    work page 2025

  7. [7]

    A tutorial on 3GPP rel-19 channel modeling for 6G FR3 (7-24 GHz): From standard specification to simulation implementation,

    P. Tang, H. Xu, J. Zhang, X. Liuet al., “A tutorial on 3GPP rel-19 channel modeling for 6G FR3 (7-24 GHz): From standard specification to simulation implementation,”arXiv preprint arXiv:2602.07623, 2026

    work page arXiv 2026

  8. [8]

    Low-complexity iterative precoding design for near-field multiuser systems with spatial non-stationarity,

    M. Liu, C. Pan, K. Zhi, H. Ren, C.-X. Wang, J. Wang, and Y . C. Eldar, “Low-complexity iterative precoding design for near-field multiuser systems with spatial non-stationarity,”IEEE Trans. Signal Process., vol. 74, pp. 1309–1324, 2026

    work page 2026

  9. [9]

    Rotatable antenna enabled multi-cell mixed near-field and far- field communications,

    Y . Zhang, C. You, R. Zhang, B. Zheng, H. C. So, D. Niyato, and T. Q. Quek, “Rotatable antenna enabled multi-cell mixed near-field and far- field communications,”IEEE Trans. Wireless Commun., 2026

    work page 2026

  10. [10]

    Channel estimation for extremely large-scale MIMO: Far-field or near-field?

    M. Cui and L. Dai, “Channel estimation for extremely large-scale MIMO: Far-field or near-field?”IEEE Trans. Commun., vol. 70, no. 4, pp. 2663–2677, 2022

    work page 2022

  11. [11]

    Multiple access for near-field communications: Sdma or ldma?

    Z. Wu and L. Dai, “Multiple access for near-field communications: Sdma or ldma?”IEEE J. Sel. Areas Commun., vol. 41, no. 6, pp. 1918–1935, 2023

    work page 1918

  12. [12]

    Enabling more users to benefit from near-field communications: From linear to circular array,

    Z. Wu, M. Cui, and L. Dai, “Enabling more users to benefit from near-field communications: From linear to circular array,”IEEE Trans. Wireless Commun., 2023

    work page 2023

  13. [13]

    Near-field 3D localization and mimo channel estimation with sub-connected planar arrays,

    K. Zhi, T. Yang, S. Xue, and G. Caire, “Near-field 3D localization and mimo channel estimation with sub-connected planar arrays,”arXiv preprint arXiv:2510.20274, 2025

    work page arXiv 2025

  14. [14]

    Two-stage hierarchical beam training for near- field communications,

    C. Wu, C. Youet al., “Two-stage hierarchical beam training for near- field communications,”IEEE Trans. Veh. Tech., 2023

    work page 2023

  15. [15]

    Codebook design for extremely large-scale MIMO systems: Near-field and far- field,

    X. Zhang, H. Zhang, J. Zhang, C. Li, Y . Huang, and L. Yang, “Codebook design for extremely large-scale MIMO systems: Near-field and far- field,”IEEE Trans. Commun., 2023

    work page 2023

  16. [16]

    Deep learning based beam training for extremely large-scale massive MIMO in near-field domain,

    W. Liu, H. Ren, C. Pan, and J. Wang, “Deep learning based beam training for extremely large-scale massive MIMO in near-field domain,” IEEE Commun. Lett., vol. 27, no. 1, pp. 170–174, Jan. 2023

    work page 2023

  17. [17]

    Hybrid-field beam- split pattern detection-based channel estimation for THz XL-MIMO systems,

    J. Lu, J. Zhang, H. Lei, H. Xiao, Z. Lu, and B. Ai, “Hybrid-field beam- split pattern detection-based channel estimation for THz XL-MIMO systems,”IEEE Trans. Veh. Tech., 2024

    work page 2024

  18. [18]

    Joint visibility region and channel estimation for extremely large-scale MIMO systems,

    A. Tang, J.-B. Wang, Y . Panet al., “Joint visibility region and channel estimation for extremely large-scale MIMO systems,”IEEE Trans. Commun., vol. 72, no. 10, pp. 6087–6101, 2024

    work page 2024

  19. [19]

    Communicating with extremely large-scale ar- ray/surface: Unified modelling and performance analysis,

    H. Lu and Y . Zeng, “Communicating with extremely large-scale ar- ray/surface: Unified modelling and performance analysis,”IEEE Trans. Wireless Commun., vol. 21, no. 6, pp. 4039–4053, Jun. 2021

    work page 2021

  20. [20]

    Near-field boundary distance in mmwave and THz communications with misaligned antenna arrays,

    P. Zhang, V . Petrov, and E. Bj ¨ornson, “Near-field boundary distance in mmwave and THz communications with misaligned antenna arrays,” IEEE Trans. Wireless Commun., vol. 25, pp. 16 072–16 088, 2026

    work page 2026

  21. [21]

    Finite beam depth analysis for large arrays,

    A. Kosasih and E. Bj ¨ornson, “Finite beam depth analysis for large arrays,”IEEE Trans. Wireless Commun., vol. 23, no. 8, 2024

    work page 2024

  22. [22]

    Near-field communications: A degree-of-freedom perspective,

    C. Ouyang, Y . Liu, X. Zhang, and L. Hanzo, “Near-field communications: A degree-of-freedom perspective,”arXiv preprint arXiv:2308.00362, 2023

    work page arXiv 2023

  23. [23]

    Physical layer security in near-field communications,

    Z. Zhang, Y . Liu, Z. Wang, X. Mu, and J. Chen, “Physical layer security in near-field communications,”IEEE Trans. Veh. Tech., vol. 73, no. 7, pp. 10 761–10 766, 2024

    work page 2024

  24. [24]

    Near-field integrated sensing and communications,

    Z. Wang, X. Mu, and Y . Liu, “Near-field integrated sensing and communications,”IEEE Commun. Lett., vol. 27, no. 8, pp. 2048–2052, 2023

    work page 2048

  25. [25]

    Rate-splitting multiple access for near-field communications with imperfect CSIT and SIC,

    S. Zhang, F. Wang, Y . Mao, A.-L. Jin, and T. Q. Quek, “Rate-splitting multiple access for near-field communications with imperfect CSIT and SIC,”IEEE Trans. Commun., 2025

    work page 2025

  26. [26]

    Joint beamforming and antenna design for near-field fluid antenna system,

    Y . Chen, M. Chen, H. Xu, Z. Yang, K.-K. Wong, and Z. Zhang, “Joint beamforming and antenna design for near-field fluid antenna system,” IEEE Wireless Commun. Lett., vol. 14, no. 2, pp. 415–419, 2024

    work page 2024

  27. [27]

    Movable antenna enabled near-field communications: Channel modeling and performance opti- mization,

    L. Zhu, W. Ma, Z. Xiao, and R. Zhang, “Movable antenna enabled near-field communications: Channel modeling and performance opti- mization,”IEEE Trans. Commun., vol. 73, no. 9, pp. 7240–7256, 2025

    work page 2025

  28. [28]

    Near-field communication with massive movable antennas: A functional perspective,

    S. Liu, X. Yu, J. Xu, and R. Zhang, “Near-field communication with massive movable antennas: A functional perspective,”IEEE Trans. Wireless Commun., vol. 25, pp. 14 455–14 470, 2026

    work page 2026

  29. [29]

    Design of non-uniform 3D arrays for near-field XL-MIMO communications,

    Y . Guo, Y . Zhang, L. Pang, Y . Ren, Y . Chen, and Y . Liu, “Design of non-uniform 3D arrays for near-field XL-MIMO communications,”IEEE Wireless Commun. Lett., 2025

    work page 2025

  30. [30]

    Hybrid beamforming with widely-spaced-array for multi-user cross-near-and-far-field communica- tions,

    H. Shen, Y . Chen, C. Han, and J. Yuan, “Hybrid beamforming with widely-spaced-array for multi-user cross-near-and-far-field communica- tions,”IEEE Trans. Commun., 2025

    work page 2025

  31. [31]

    Sparse array enabled near-field communications: Beam pattern analysis and hybrid beamforming design,

    C. Zhou, C. You, H. Zhang, L. Chen, and S. Shi, “Sparse array enabled near-field communications: Beam pattern analysis and hybrid beamforming design,”IEEE Trans. Wireless Commun., 2025

    work page 2025

  32. [32]

    Channel estimation for extremely large-scale massive MIMO systems,

    Y . Han, S. Jin, C.-K. Wen, and X. Ma, “Channel estimation for extremely large-scale massive MIMO systems,”IEEE Wireless Commun. Lett., vol. 9, no. 5, pp. 633–637, May 2020

    work page 2020

  33. [33]

    Near- field integrated imaging and communication in distributed MIMO networks,

    K. Zhi, T. Yang, S. Li, Y . Song, A. Rezaei, and G. Caire, “Near-field integrated imaging and communication in distributed MIMO networks,” arXiv preprint arXiv:2508.17526, 2025

    work page arXiv 2025

  34. [34]

    Plug-and-play image restoration with deep denoiser prior,

    K. Zhang, Y . Li, W. Zuo, L. Zhang, L. Van Gool, and R. Timofte, “Plug-and-play image restoration with deep denoiser prior,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 44, no. 10, pp. 6360–6376, 2021

    work page 2021

  35. [35]

    An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,

    Q. Shiet al., “An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,” IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4331–4340, 2011

    work page 2011

  36. [36]

    Is RIS-aided massive MIMO promising with ZF detectors and imperfect CSI?

    K. Zhiet al., “Is RIS-aided massive MIMO promising with ZF detectors and imperfect CSI?”IEEE J. Sel. Areas Commun., vol. 40, no. 10, pp. 3010–3026, Oct. 2022

    work page 2022