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arxiv: 2605.04380 · v1 · submitted 2026-05-06 · 📡 eess.SP

Near-Field Channel Estimation for Extremely Large-Scale Circular RIS-Aided mmWave MIMO-NOMA System with Beam Squint Effect

Wanyuan Cai , Shunli Hong , Youming Li , Menglei Sheng , Mingjun Huang This is my paper

Pith reviewed 2026-05-08 17:03 UTC · model grok-4.3

classification 📡 eess.SP
keywords RISnear-fieldchannel estimationMIMO-NOMAbeam squintmmWavetensor decomposition
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The pith

A circular extremely large-scale RIS creates an angle-invariant near-field region enabling unified channel modeling for mmWave MIMO-NOMA systems.

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

This paper proposes an extremely large-scale circular RIS architecture to create an angle-invariant near-field region in mmWave MIMO-NOMA systems. By keeping the effective aperture constant, it supports a single channel model even under beam squint in wideband signals. The received signal is cast as a third-order tensor to enable a multi-stage estimation scheme that splits the task into simpler subproblems while automatically aligning parameters from the same paths. A Cramer-Rao bound is provided for performance limits, and simulations validate the gains over other techniques.

Core claim

The central discovery is that the proposed XL-CRIS architecture constructs an angle-invariant near-field region by maintaining a constant effective aperture, which permits a unified channel modeling framework for the MIMO-NOMA system. Modeling the wideband received signal as a third-order tensor then allows a multi-stage channel estimation framework that decomposes the multi-variable problem into low-dimensional sub-problems while preserving path-wise parameter pairing through a shared permutation matrix. A vector-form CRB is derived as the theoretical benchmark.

What carries the argument

The extremely large-scale circular RIS (XL-CRIS) architecture that maintains constant effective aperture, paired with the third-order tensor representation of the received MIMO-NOMA signal for multi-stage decomposition.

Load-bearing premise

The proposed circular RIS truly maintains a constant effective aperture in the near-field region across varying user angles and operating frequencies.

What would settle it

If the effective aperture size changes with angle in simulations or measurements of the XL-CRIS, or if the channel estimation error exceeds the derived CRB significantly due to pairing issues, the claims would be falsified.

Figures

Figures reproduced from arXiv: 2605.04380 by Menglei Sheng, Mingjun Huang, Shunli Hong, Wanyuan Cai, Youming Li.

Figure 1
Figure 1. Figure 1: System model. A. Channel Modeling Owing to the rotational symmetry of XL-CRIS, the bound￾ary of the effective Rayleigh distance is angle-invariant, which can cover a region of a cellular cell and eliminate complex far-field and near-field hybrid channel modeling [24]. Thus, all UEs in the considering model can be within the near￾field region. Besides, the wideband signals will cause beam squint effect, whi… view at source ↗
Figure 2
Figure 2. Figure 2: Performance comparison for channel estimation versus SNR. view at source ↗
Figure 3
Figure 3. Figure 3: Performance comparison for channel estimation versus view at source ↗
Figure 4
Figure 4. Figure 4: Performance comparison for channel estimation versus view at source ↗
read the original abstract

Near-field channel estimation under beam squint effect is critical to future 6G millimeter-wave (mmWave) systems equipped with reconfigurable intelligent surfaces (RIS). In this paper, firstly, we design an extremely large-scale circular RIS (XL-CRIS) architecture to construct an angle-invariant near-field region for MIMO-NOMA system, which can maintain a constant effective aperture, allowing for a unified channel modeling framework. Then, to enable efficient parameter extraction, we model the received wideband MIMO-NOMA signal as a third-order tensor which is used to develop a multi-stage channel estimation framework. Accordingly, we decompose the multi-variable problem into several low-dimensional sub-problems, while naturally preserving path-wise parameter pairing through the shared permutation matrix. Finally, we derive a vector-form CRB as a theoretical performance benchmark. To illustrate the effectiveness of the proposed method, numerical experiments are carried out and compared with the discussed methods.

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

2 major / 2 minor

Summary. The paper proposes an extremely large-scale circular RIS (XL-CRIS) architecture for mmWave MIMO-NOMA systems that is claimed to produce an angle-invariant near-field region with constant effective aperture, enabling a single unified channel model. The received wideband signal is modeled as a third-order tensor, from which a multi-stage estimation algorithm is derived that decomposes the problem into low-dimensional subproblems while preserving path-wise parameter pairing via a shared permutation matrix. A vector-form Cramér-Rao bound (CRB) is derived as a benchmark, and numerical results are presented comparing the method to existing approaches.

Significance. If the geometric invariance property holds, the work would offer a concrete architecture and tensor-based estimator that jointly addresses near-field effects, beam squint, and NOMA in extremely large RIS deployments. The tensor decomposition with explicit parameter pairing and the closed-form CRB are methodologically sound contributions that could serve as useful benchmarks for future near-field RIS papers.

major comments (2)
  1. [§2] §2 (XL-CRIS architecture and near-field region definition): The central claim that the circular geometry produces an angle-invariant near-field region and constant effective aperture is asserted without an explicit derivation showing that the Fresnel-zone boundary and projected aperture remain independent of incidence angle. Standard array theory indicates that both quantities vary with the cosine of the angle of arrival; the manuscript must supply the angle-independent distance threshold or radius condition that cancels this dependence, otherwise the unified channel model and subsequent tensor construction rest on an unverified premise.
  2. [§3] §3 (tensor signal model and shared permutation matrix): The third-order tensor construction and the claim that the shared permutation matrix naturally preserves path-wise parameter pairing assume that the XL-CRIS geometry has already rendered all paths angle-invariant. If the invariance does not hold, the pairing guaranteed by the common permutation matrix no longer corresponds to physically consistent parameters across subcarriers, undermining the multi-stage solver's correctness.
minor comments (2)
  1. [§2] Notation for the effective aperture and Fresnel distance should be introduced with explicit dependence on array radius and element spacing before the invariance claim is made.
  2. [§5] The numerical experiments section would benefit from an additional ablation that varies the incidence angle to directly test the claimed angle-invariance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback. Below we provide point-by-point responses to the major comments and outline the revisions we will implement.

read point-by-point responses

  1. Referee: §2 (XL-CRIS architecture and near-field region definition): The central claim that the circular geometry produces an angle-invariant near-field region and constant effective aperture is asserted without an explicit derivation showing that the Fresnel-zone boundary and projected aperture remain independent of incidence angle. Standard array theory indicates that both quantities vary with the cosine of the angle of arrival; the manuscript must supply the angle-independent distance threshold or radius condition that cancels this dependence, otherwise the unified channel model and subsequent tensor construction rest on an unverified premise.

    Authors: We acknowledge that the derivation of the angle-invariance property was not presented with sufficient explicit detail in the original Section 2. In the revised manuscript we will insert a dedicated geometric analysis proving that the circular RIS symmetry cancels the cos(theta) dependence of the projected aperture. The Fresnel-zone boundary is thereby shown to reduce to the angle-independent expression d_NF = 2R^2 / lambda (R = RIS radius), which directly justifies the unified near-field channel model employed in the subsequent tensor construction. revision: yes

  2. Referee: §3 (tensor signal model and shared permutation matrix): The third-order tensor construction and the claim that the shared permutation matrix naturally preserves path-wise parameter pairing assume that the XL-CRIS geometry has already rendered all paths angle-invariant. If the invariance does not hold, the pairing guaranteed by the common permutation matrix no longer corresponds to physically consistent parameters across subcarriers, undermining the multi-stage solver's correctness.

    Authors: The tensor model and the shared-permutation-matrix mechanism for path-wise pairing are predicated on the angle-invariance property. Once the explicit derivation is added to Section 2, all paths satisfy the same angle-independent near-field condition across subcarriers, rendering the pairing physically consistent. We will revise Section 3 to include a short paragraph that explicitly links the invariance result to the correctness of the multi-stage decomposition and the shared permutation matrix. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper introduces the XL-CRIS architecture as an explicit design choice to achieve the claimed angle-invariant near-field region and constant effective aperture, then constructs the third-order tensor model directly from the received wideband MIMO-NOMA signal structure, decomposes the estimation into sub-problems while using a shared permutation matrix to preserve path pairing, and derives the vector-form CRB as an independent theoretical benchmark. None of these steps reduce by construction to fitted inputs renamed as predictions, self-definitional loops, or load-bearing self-citations. The geometric invariance is asserted as a property of the proposed architecture rather than derived from prior fitted parameters or external uniqueness theorems by the same authors. The central modeling and estimation framework remains independent of the target performance metrics.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents identification of specific free parameters or axioms; no invented entities are mentioned.

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discussion (0)

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Reference graph

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