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arxiv: 2512.08469 · v3 · pith:6QQX7RUMnew · submitted 2025-12-09 · 📡 eess.SP

Aliasing in Near-Field Array Ambiguity Functions: a Spatial Frequency-Domain Framework

Gilles Monnoyer , J\'er\^ome Louveaux , Laurence Defraigne , Baptiste Sambon , Luc Vandendorpe This is my paper

Pith reviewed 2026-05-22 12:24 UTC · model grok-4.3

classification 📡 eess.SP
keywords near-fieldambiguity functiongrating lobesaliasingXL-arraysspatial frequency analysisuniform linear arrayuniform circular array
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The pith

Near-field grating lobes arise as aliasing artifacts that local spatial-frequency analysis can model and avoid in thinned XL-arrays.

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

The paper establishes a general framework for modeling grating lobes in the near-field ambiguity functions of thinned extremely large arrays as aliasing effects. It uses local spatial-frequency analysis of the steering signals to derive this systematically, which matters for designing cost-effective XL-arrays in next-generation communication and localization systems where near-field operation introduces spherical wavefront complexities. The framework quantifies the aliasing structure, supplies design guidelines for safe regions, recovers far-field principles as a special case, and provides closed-form aliasing-free regions for uniform linear and circular arrays.

Core claim

Using a local spatial-frequency analysis of steering signals, the paper derives a systematic methodology to model near-field grating lobes as aliasing artifacts. This quantifies their structure on the ambiguity function and provides design guidelines for XL-arrays operating within aliasing-safe regions. The framework connects to established far-field principles and yields closed-form expressions for aliasing-free regions in uniform linear arrays and uniform circular arrays.

What carries the argument

Local spatial-frequency analysis of steering signals, which treats near-field grating lobes as aliasing artifacts in the ambiguity function.

If this is right

  • The structure of near-field grating lobes on the ambiguity function is quantified directly as aliasing.
  • Design guidelines identify aliasing-safe operating regions for XL-arrays.
  • Established far-field principles appear as the limiting case of the near-field framework.
  • Closed-form expressions give aliasing-free regions for uniform linear arrays and uniform circular arrays.

Where Pith is reading between the lines

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

  • The framework could guide selection of thinning patterns to enlarge aliasing-free zones in practical deployments.
  • The same local-frequency approach may apply to planar or 3D array geometries beyond the linear and circular cases shown.
  • Beam pattern optimization routines could incorporate the derived safe regions to reduce sidelobe control effort.

Load-bearing premise

The local spatial-frequency analysis sufficiently captures the essential aliasing behavior in the near-field regime without geometry-specific adjustments.

What would settle it

Direct numerical computation of the ambiguity function for a thinned near-field array, checking whether grating lobes appear exactly at the locations and strengths predicted by the aliasing analysis outside the closed-form safe regions.

Figures

Figures reproduced from arXiv: 2512.08469 by Baptiste Sambon, Gilles Monnoyer, J\'er\^ome Louveaux, Laurence Defraigne, Luc Vandendorpe.

Figure 1
Figure 1. Figure 1: Schematic representation of the uplink scenario studied in this paper. (a) A case where the antenna array is defined over a curve [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Ambiguity functions for (top) a horizontal ULA with length 20 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: a shows the spectra G(ω; x˜, x) obtained in the context of our toy example, for multiple tested locations x˜. The reference spectrum obtained when x˜ = x exhibits a strong unit-height peak in ω = 0, yielding A(x, x) = 1. As x˜ becomes further away from x, the spectral energy in G(ω; x˜, x) is both frequency-spread and shifted, lowering its value in ω = 0 and hence the value of A(x˜, x). Let us now analyze … view at source ↗
Figure 4
Figure 4. Figure 4: Representation of the spreading of the spectrum [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Representation of the chirp-structured matched signal [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Schematic representation of a ULA operating in the NF regime. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Discrete-space AFs obtained for a horizontal ULA of length [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Geometry of the ULA-eyes. (a) representation of its width [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Ambiguity functions for a ULA with length [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Ambiguity functions for a ULA with length [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Schematic representation of a UCA VI. DISTRIBUTED UNIFORM CIRCULAR ARRAY Circular arrays constitute a natural reference for theoretical studies on XL-arrays [14], [28], due to their inherent isotropic geometry providing a 360-degree coverage. As such, this topology can be considered as the canonical example of the “perfectly” distributed XL-array. This simple geometry en￾ables the derivation of closed-for… view at source ↗
Figure 14
Figure 14. Figure 14: Discrete-space AFs, |AS(x˜, x = 0)|, for a UCA of radius Ruca = 10, 000λc and multiple apertures ψ. (top) uniform angular spacing ∆ = 2π/2000. (bottom) ∆ = 2π/200). the aliasing structure one observes for a non-infinite radius satisfying Ruca ≫ max{∥x∥ : x ∈ X }. (55) Under the infinite-radius condition, the matched signal’s am￾plitude, given in (19), is asymptotically constant, causing Gα(ω) to be a Dira… view at source ↗
read the original abstract

Next-generation communication and localization systems increasingly rely on extremely large-scale arrays (XL-arrays), which promise unprecedented spatial resolution and new functionalities. These gains arise from their inherent operation in the near field (NF) regime, where the spherical nature of the wavefront can no longer be ignored; consequently, characterizing the ambiguity function -- which amounts to the matched beam pattern -- is considerably more challenging. Implementing very wide apertures with half-wavelength element spacing is costly and complex. This motivates thinning the array (removing elements), which introduces intricate aliasing structures, i.e., grating lobes. Whereas prior work has addressed this challenge using approximations tailored to specific array geometries, this paper develops a general framework that reveals the fundamental origins and geometric behavior of grating lobes in near-field ambiguity functions. Using a local spatial-frequency analysis of steering signals, we derive a systematic methodology to model NF grating lobes as aliasing artifacts, quantifying their structure on the AF, and providing design guidelines for XL-arrays that operate within aliasing-safe regions. We further connect our framework to established far-field principles. Finally, we demonstrate the practical value of the approach by deriving closed-form expressions for aliasing-free regions in canonical uniform linear arrays and uniform circular arrays.

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 develops a spatial frequency-domain framework for modeling grating lobes in near-field (NF) ambiguity functions of extremely large arrays (XL-arrays) as aliasing artifacts. It uses local spatial-frequency analysis of steering signals to derive a general methodology for quantifying their structure, provides design guidelines for aliasing-safe operation, connects the approach to far-field principles, and derives closed-form expressions for aliasing-free regions in uniform linear arrays (ULAs) and uniform circular arrays (UCAs).

Significance. If the local approximation holds with quantifiable error bounds, the framework offers a geometry-agnostic tool for thinned XL-array design in NF regimes, extending far-field aliasing concepts to spherical-wave scenarios and enabling closed-form region predictions without geometry-specific fitting. This addresses a practical challenge in wide-aperture systems for communications and localization.

major comments (1)
  1. [Local spatial-frequency analysis section] The central derivation relies on the local spatial-frequency analysis remaining accurate across the full array aperture. For XL-arrays where aperture size approaches the Fresnel distance, accumulated phase errors from higher-order spherical-wave curvature terms could shift or split predicted aliasing lobes in ways not captured by the linearization; a quantitative error bound or validation against full-wave simulations in § on the approximation validity would be required to support the claim that NF grating lobes are modeled purely as aliasing artifacts.
minor comments (2)
  1. [Framework derivation] Clarify the exact definition of the local wavenumber and its relation to the steering vector phase in the derivation of the aliasing structure.
  2. [Closed-form expressions] Add a brief discussion of how the closed-form expressions for ULAs and UCAs reduce to known far-field grating-lobe locations as range tends to infinity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The point raised about the accuracy of the local spatial-frequency approximation for large apertures is well taken, and we have revised the paper to address it directly.

read point-by-point responses

  1. Referee: [Local spatial-frequency analysis section] The central derivation relies on the local spatial-frequency analysis remaining accurate across the full array aperture. For XL-arrays where aperture size approaches the Fresnel distance, accumulated phase errors from higher-order spherical-wave curvature terms could shift or split predicted aliasing lobes in ways not captured by the linearization; a quantitative error bound or validation against full-wave simulations in § on the approximation validity would be required to support the claim that NF grating lobes are modeled purely as aliasing artifacts.

    Authors: We agree that quantifying the validity of the local linearization is essential, especially when the array aperture becomes comparable to the Fresnel distance. In the revised manuscript we have inserted a dedicated subsection (now §III-C) that derives a rigorous error bound on the phase approximation error using the Lagrange form of the remainder in the Taylor expansion of the spherical-wave distance term. The bound is expressed in closed form as a function of normalized aperture size and range, and we show that it remains below a prescribed threshold (e.g., π/8) inside the aliasing-free regions previously derived. In addition, we now include a set of full-wave numerical validations (new Fig. 8) that compare the predicted aliasing-lobe locations obtained from the local spatial-frequency model against exact spherical-wave ambiguity-function computations for both ULAs and UCAs at aperture sizes up to 0.8 times the Fresnel distance. These results confirm that, within the operating regimes for which the closed-form aliasing-free regions are claimed, the modeling of near-field grating lobes as aliasing artifacts holds with quantifiable and acceptably small distortion. revision: yes

Circularity Check

0 steps flagged

Local spatial-frequency derivation is self-contained with no reduction to inputs by construction

full rationale

The paper's central methodology starts from a local spatial-frequency analysis of steering signals to model NF grating lobes as aliasing, then connects explicitly to far-field principles and derives closed-form aliasing-free regions for ULA and UCA geometries. No quoted step reduces a prediction or uniqueness claim to a fitted parameter, self-definition, or load-bearing self-citation chain; the framework is presented as an independent analytic tool rather than a renaming or tautological restatement of its inputs. The skeptic concern addresses approximation validity (correctness), not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, new axioms, or invented entities are identifiable; the work appears to build on standard concepts in array signal processing.

axioms (1)
  • standard math Standard assumptions in array signal processing for steering vectors and ambiguity functions in near-field regimes.
    Invoked implicitly when analyzing steering signals and connecting to far-field principles.

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Reference graph

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