New Paradigm for Unified Near-Field and Far-Field Wireless Communications

Haochen Wu; Liyang Lu; Yuanbin Chen; Zhaocheng Wang

REVIEW 5 major objections 6 minor 15 references

New Paradigm for Unified Near-Field and Far-Field Wireless Communications

T0 review · 5 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A K-SVD-learned codebook trained on wavenumber-domain channel estimates can serve near-field and far-field users in multi-user MIMO with one precoding scheme, eliminating the need for the base station to classify any user's region.

desk verdict Proposes a K-SVD-learned wavenumber-domain codebook to unify near/far-field precoding; the idea is worth a serious look, but the paper is a sketch that needs training details, fair baselines, and sparsity validation before the main claim is credible. read the letter →

arxiv 2501.02730 v2 pith:SJJ6AU4R submitted 2025-01-06 eess.SP

Zhaocheng Wang , Haochen Wu , Yuanbin Chen , Liyang Lu This is my paper · ORCID

classification eess.SP

keywords near-fieldcommunicationsfar-fieldcodebookdesignwavenumberdomainK-SVDdictionarylearningmulti-userMIMOprecodingcompressivesensingchannelestimation6G

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that 5G's DFT-based Type I and Type II codebooks fail when users sit inside the Rayleigh distance, and that replacing them with a K-SVD-learned codebook trained on wavenumber-domain channel estimates unifies near-field and far-field precoding. The wavenumber-domain representation expands the channel as a sparse superposition of plane waves, so one dictionary can serve both regimes. In simulations with a 1024-antenna array serving 16 users under the standardized TR 38.901 channel model, the learned codebook outperforms DFT and polar codebooks and approaches fully digital spectral efficiency, while keeping the existing reference-signal workflow. If this holds, 6G systems could precode mixed user populations without spending pilots on region classification.

What carries the argument

The machinery is the combination of a wavenumber-domain channel representation and K-SVD dictionary learning. The wavenumber-domain representation uses a Fourier harmonic expansion of the channel as a superposition of plane waves with different wavenumbers, which the paper argues makes both near-field and far-field channels sparse and avoids the angular power diffusion of DFT processing. K-SVD then alternates between solving sparse recovery problems for the coefficient matrix $\bar{H}$ and updating the codebook matrix $A$ column by column with SVD, so the codebook is tuned to the statistics of the actual channel; a final constant-modulus projection renders the codewords feasible for hybrid analog-digital precoding.

What would settle it

Rerun the paper's 32-by-32 array, 16-UE simulations with all users placed well inside the Rayleigh distance, for example at 0.1 times the Rayleigh distance, and check whether wavenumber-domain OMP or MRF still yields lower NMSE than angular-domain OMP; if the wavenumber representation is not sparser there, the K-SVD codebook's advantage over the polar codebook should disappear.

Watch

Extended reading notes

Core claim

The central claim is that a codebook learned by K-SVD in the wavenumber domain ensures efficient precoding for all UEs in coexisting near-field and far-field multi-user MIMO, and removes the need for the base station to know which region any UE is in. The argument runs through two stages: first, the channel $H$ is estimated in the wavenumber domain, where both far-field planar waves and near-field spherical waves are represented as superpositions of plane waves via Fourier harmonic expansion, and the estimation is cast as a compressive-sensing sparse recovery problem; second, K-SVD learns a codebook matrix $A$ and a sparse coefficient matrix $\bar{H}$ by alternating sparse coding and column-wise SVD updates, and a constant-modulus projection makes the codebook usable by analog phase shifters. Reported simulations over the standardized TR 38.901 channel model, with a $32\times32$ uniform planar array serving 16 UEs in mixed, all-near-field, and all-far-field deployments, show the regression-based codebook exceeding DFT and polar codebooks and approaching the fully digital precoding bound.

Load-bearing premise

The load-bearing premise is that near-field channels from the standardized TR 38.901 model are faithfully captured as sparse superpositions of plane waves in the wavenumber domain; if that representation loses or smears near-field energy, the compressive-sensing estimates and the K-SVD codebook trained on them lose their edge.

Editorial extensions

If this is right

A single codebook trained in the wavenumber domain can precode mixed near-field and far-field UEs without the base station classifying any UE's region, eliminating the extra pilots and feedback that region-aware schemes require.
Because the workflow and reference signals stay aligned with current Type I and Type II procedures, the learned codebook is a candidate extension to existing standards rather than a new air interface.
Wavenumber-domain channel estimation reduces the angular power diffusion that near-field channels cause, which should weaken the domino effect where one user's bad CSI degrades every other user's precoding.
In the reported simulations, the K-SVD codebook outperforms both DFT and polar-domain codebooks and approaches the fully digital precoding bound under the standardized TR 38.901 channel model.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

I infer that the same K-SVD training pipeline could be run offline on site-specific or measured channel datasets, so the codebook would adapt to a deployment's actual scatterer geometry rather than to a fixed grid; the paper notes offline learning but does not develop it.
A testable extension is to scale the antenna aperture while holding the user distribution fixed: if the wavenumber-domain mechanism is what carries the gain, the regression codebook's margin over DFT should grow as the Rayleigh distance pushes more users into the near field.
The constant-modulus projection is acknowledged to erode the sparsity of the recovered channel; I infer that a systematic sweep of projection loss against array size and codebook size would reveal when hybrid precoding with a learned codebook stops being worth the learning overhead.

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Signed reviews

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

What's actually new: a single K-SVD-learned codebook, applied in the wavenumber domain, that serves mixed near-field and far-field UEs without the BS ever classifying users into regions. That is a genuine extension of the wavenumber-domain estimation developed in the authors' prior work (and Pizzo's group), and it speaks to a real 3GPP problem for the 7-24 GHz near-field study item. The paper is clearly written, and the motivation is sound: Type I/II DFT codebooks suffer power leakage for near-field UEs, and polar-domain codebooks tend to require region labels or heavy sampling. The mixture of offline dictionary learning with a standards-compatible PMI feedback flow is a sensible framing.

The soft spots are large, in proportion. The central claim is supported only by simulation curves. There are no equations for the K-SVD objective or its update rules, no hyperparameters (number of atoms, sparsity level, training set size), no variance across the 500 runs, and no code. The 'no region ID needed' claim is not tested against a region-aware baseline, so the reader cannot separate the benefit of learning from the benefit of knowing the region. The simulation description is thin: array size and cluster counts are given, but not the near-field distances or how TR 38.901 was extended to spherical wavefronts.

The deepest issue is the wavenumber-domain sparsity premise. The paper cites prior work and asserts that near-field TR 38.901 channels are sparse superpositions of plane waves. That is not automatic: a point source has a continuous plane-wave spectrum; over a 32x32 aperture, the wavenumber footprint can be broad unless the channel is dominated by a few isolated scatterers. With 4 clusters of 5 rays, each ray is a spherical wave, so discrete sparsity is not guaranteed. Fig. 2 does not settle it because it omits the channel model and the near-field configuration. The stress-test note slightly overstates by saying the method has no theoretical basis if sparsity fails—K-SVD could still learn a useful low-rank codebook—but the compressive-sensing channel estimation genuinely relies on sparsity, so the concern lands.

Who is this for: people tracking 6G codebook proposals and the 3GPP near-field study. As a proposal sketch it is a reasonable candidate; as a rigorous evaluation it is not there yet. A serious referee can force disclosure of training details, a fair region-aware comparison, and a sparsity validation. I would send it to review on those terms, but I would not cite it for the main result as it stands. Cite the underlying wavenumber-domain papers instead.

Referee Report

5 major / 6 minor

Summary. The paper proposes a unified codebook paradigm for serving coexisting near-field and far-field UEs in multi-user MIMO. The scheme combines wavenumber-domain channel estimation (imported from the authors' earlier work), K-SVD dictionary learning to generate a regression-based codebook, and standard PMI feedback/precoding, with constant-modulus projection for analog/hybrid implementations. The authors claim that the learned codebook 'removes the need for the base station to identify whether one specific UE stays in either near-field or far-field regions' and that simulations show spectral efficiency superior to DFT and polar codebooks in mixed and homogeneous near/far-field scenarios, while remaining compatible with 5G workflows and reference-signal structures.

Significance. If the central claim is substantiated, the contribution would be relevant to 3GPP Rel-19/20 discussions on near-field channel modeling and codebook design, since current Type I/Type II codebooks are far-field-centric and near-field coexistence is an acknowledged standardization gap. The idea of replacing fixed codebooks with a dictionary learned in the wavenumber domain is interesting and potentially practical, and the paper correctly identifies a real limitation of existing schemes. However, the evidence as presented is not yet sufficient: the wavenumber-domain sparsity premise is asserted rather than validated for the simulated geometry, the K-SVD optimization is not specified in enough detail to be reproduced, and the headline claim about avoiding region identification is not tested against a region-aware baseline. The paper is clearly written and the figures convey the qualitative behavior, but the technical depth is below what a journal contribution on codebook design normally requires.

major comments (5)

[III-A] The load-bearing premise that TR 38.901 near-field channels are sparse in the wavenumber domain is asserted via references [3], [14], but no derivation, transform definition, or sparsity measurement is provided for the specific array and channel geometry used in the simulations. Over a finite 32x32 UPA aperture, a near-field spherical wavefront generally has a broad wavenumber footprint; sparsity is an empirical property that must be checked under the simulated near-field distances, carrier frequency, array spacing, and cluster parameters. Since the compressive-sensing channel estimation and the K-SVD dictionary update both rely on this sparsity, the paper should either provide a rigorous justification for the wavenumber-domain representation or include a quantitative sparsity analysis (e.g., number of significant coefficients vs. distance/aperture) for the TR 38.901-based model.
[III-B] The K-SVD regression is described only in words and by an illustrative figure; there is no equation stating the optimization objective, the sparsity constraint, the dictionary update rule, or the stopping criterion. The paper also does not report the training set size, number of atoms, sparsity level, number of iterations, or the exact procedure for the constant-modulus projection. Without these details, the results in Figs. 4-5 are not reproducible, and the performance could depend critically on untested hyperparameters. In particular, the claim that the constant-modulus projection 'has an acceptable impact' needs quantitative support, since analog precoding cannot use arbitrary complex coefficients.
[III-C, Figs. 4-5] The abstract's central claim that the proposed codebook removes the need to identify the near/far-field region is not tested against a region-aware baseline. A proper comparison would include a hybrid scheme that knows each UE's region and uses, for example, a polar codebook for near-field UEs and a DFT codebook for far-field UEs, or an optimal per-region codebook selection. Without such a baseline, the simulation only shows that the learned codebook outperforms two fixed codebooks that are each mismatched to the opposite region; it does not demonstrate that region identification is unnecessary. This is a load-bearing gap for the paper's headline contribution.
[III-C] The simulation setup is underspecified. The authors state only that the BS has a 32x32 UPA, serves 16 UEs, uses 4 clusters with 5 rays per cluster, and runs 500 simulations. Missing are the carrier frequency, array element spacing, the definition of Rayleigh distance, the distribution of near-field distances, cluster angular spreads, delay spreads, and the exact way in which the TR 38.901 model is modified to include near-field spherical wavefronts. This matters because the wavenumber-domain representation and the K-SVD generalization behavior are sensitive to these parameters. Additionally, TR 38.901 as currently published does not include a mature near-field spherical-wave model; the cited study item RP-241743 is still ongoing, so the paper should clarify whether it uses the legacy far-field model with a distance-dependent steering-vector modification or a newly developed near-field model.
[III-C, Figs. 4-5] The validation is performed on the full pipeline that includes the wavenumber-domain channel estimator proposed by the same authors (refs [2], [12], [13]), and the codebook is trained and tested on channels drawn from the same simulation model. This creates a circularity risk: the benefit of the learned codebook cannot be separated from the benefit of the channel estimator, and the results may not generalize to unseen channel statistics. The authors should report tests with perfect CSI, and should also evaluate the learned codebook on a channel realization drawn from a different scenario (e.g., different near-field distances, different number of UEs, or a different cluster configuration) than the one used for training, to demonstrate that the dictionary is not overfitting the training distribution.

minor comments (6)

[Fig. 2] Figure 2 lacks the channel-model parameters and array configuration used to generate the NMSE curves; adding this information is essential for interpreting the claimed advantage of the wavenumber domain.
[Figs. 4-5] The spectral efficiency curves are presented as single average lines without variance or confidence intervals; given that only 500 simulations are mentioned and the results are the main evidence, error bars or at least a statement of variance should be included.
[III-B] There is a typo in 'sparse channel matirx' that should read 'matrix'.
[Figs. 4-5 captions] The captions and axis labels contain typos and inconsistencies: 'Spectral efficieny' appears in Figs. 4 and 5a, and the axis labels of Fig. 5b appear garbled ('olar FT P D') and should be corrected to 'Polar' and 'DFT'.
[III-C] The phrase 'proceding process' should be 'precoding process', and 'neccessary' in Section IV-D should be 'necessary'.
[II-A] The description of Type II codebook as performing 'beam sweeping' is informal and potentially misleading; Type II CSI reporting in NR is based on linear combination of a set of beams quantized from the channel eigenvectors, which is different from the beam-sweeping procedure used for beam management. The paper should align its terminology with the actual 3GPP specification.

Circularity Check

0 steps flagged · score 2.0 of 10

No definitional circularity: the codebook pipeline has external anchors (TR 38.901, K-SVD, [14]), though the paper leans on same-author prior work and leaves train/test separation unspecified.

full rationale

The paper's derivation chain is not circular in the sense of reducing an output to an input by construction. The wavenumber-domain representation is imported as a Fourier harmonic expansion with an external anchor in Pizzo et al. [14]; the same-author references [3], [12], and [13] supply prior channel-estimation algorithms, but those results are published independently of the present codebook, and Fig. 2 reproduces their comparison rather than invoking an unverified uniqueness theorem. The central codebook claim is tested against external benchmarks (DFT and polar codebooks) under the external 3GPP TR 38.901 channel model, using the external K-SVD dictionary-learning algorithm, so the spectral-efficiency comparison does not reduce to the paper's own fitted values. The legitimate concerns are validation risks rather than circularity: the paper asserts, rather than measures, that TR 38.901 near-field channels are sparse in the wavenumber domain; Fig. 2 omits the channel model, array parameters, and near-field configuration; and the simulation section does not state whether K-SVD was trained on a separate dataset from the 500 evaluation realizations, which could make the learned-codebook advantage an in-sample fit rather than a prediction. None of these is a definitional equivalence between claimed result and input, and the paper's own future-work section acknowledges open standardization issues rather than attempting to close them by fiat. Because the central claim retains independent empirical content, the circularity score is 2, reflecting only the noticeable same-author citation weight in the CSI-acquisition premise.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central performance claim is anchored in a learned codebook whose parameters and training details are not disclosed, plus a wavenumber-domain sparsity model carried over from the authors' prior work.

free parameters (3)

Learned codebook matrix A (K-SVD dictionary atoms) = not reported
The codebook is fitted to simulated channel realizations; its values, size, and training data are not specified, yet they determine the central performance claim.
Sparse channel coefficient matrix Hbar = not reported
Updated jointly with A in K-SVD; the resulting sparse coefficients are not reported but are tied to the reconstruction quality.
K-SVD hyperparameters (number of atoms, sparsity level, iterations, training set size) = not reported
These are chosen implicitly by the authors but not stated; performance may depend on them.

assumptions (5)

domain assumption Both near-field and far-field channel responses can be represented as superpositions of planar waves in the wavenumber domain via Fourier harmonic expansion.
Invoked in Section III-A citing refs [14], [3], [12], [13]; not derived in this paper, and it forms the basis for the channel estimation and codebook pipeline.
domain assumption The wavenumber-domain channel is sparse enough for compressive sensing recovery with OMP or MRF.
Needed for wavenumber-domain channel estimation in Section III-A; sparsity is asserted based on prior work by the same group.
domain assumption The 3GPP TR 38.901 stochastic channel model, extended with near-field parameters, is a valid representation of near-field propagation for these simulations.
Simulations in Section III-C use TR 38.901; the paper itself notes 3GPP is still working on near-field enhancements, so the model's validity for the simulated near-field regime is assumed.
ad hoc to paper A dictionary learned by K-SVD from a set of channel realizations generalizes to unseen channels and to the multi-UE precoding scenario.
This is the core of Section III-B; no generalization bound, no cross-validation, and the learned codebook is not released.
ad hoc to paper Constant-modulus projection of the learned codebook does not materially degrade precoding performance.
Section III-C asserts this trade-off is 'acceptable' without quantitative analysis.

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Pith. "Pith review of New Paradigm for Unified Near-Field and Far-Field Wireless Communications." pith.science (2026). https://pith.science/paper/SJJ6AU4R

@misc{pith2026250102730,
  author       = {Pith},
  title        = {Pith review of: New Paradigm for Unified Near-Field and Far-Field Wireless Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SJJ6AU4R}},
  note         = {Machine review of arXiv:2501.02730}
}

read the original abstract

Current Type I and Type II codebooks in fifth generation (5G) wireless communications are limited in supporting the coexistence of far-field and near-field user equipments, as they are exclusively designed for far-field scenarios. To fill this knowledge gap and encourage relevant proposals by the 3rd Generation Partnership Project (3GPP), this article provides a novel codebook to facilitate a unified paradigm for the coexistence of far-field and near-field contexts. It ensures efficient precoding for all user equipments (UEs), while removing the need for the base station to identify whether one specific UE stays in either near-field or far-field regions. Additionally, our proposed codebook ensures compliance with current 3GPP standards for working flow and reference signals. Simulation results demonstrate the superior performance and versatility of our proposed codebook, validating its effectiveness in unifying near-field and far-field precoding for sixth-generation (6G) multiple-input multiple-output (MIMO) systems.

Figures

Figures reproduced from arXiv: 2501.02730 by the authors.

**Figure 1.** Illustration of generation process and precoding architecture of Type I/Type II and our proposed codebooks. Firstly, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Performance comparison of different channel estima [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Illustration of the proposed codebook generation. K-SVD algorithm is leveraged to obtain our proposed codebook, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: (a) Spectral efficiency comparison with beam sweeping [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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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., to appear, 2024. [Online]. Available: https://arxiv.org/abs/2407.14815

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X. Guo, Y . Chen, Y . Wang, Z. Wang, and Z. Han, “Wavenumber domain sparse channel estimation in holographic MIMO,” in Proc. IEEE Int. Conf. Commun., Denver, CO, USA, Jun. 2024, pp. 3078–3084

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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, Apr. 2022

2022

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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, Jun. 2023

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Hybrid near-far field channel estimation for holographic MIMO communications,

S. Yue, S. Zeng, L. Liu, Y . C. Eldar, and B. Di, “Hybrid near-far field channel estimation for holographic MIMO communications,” IEEE Trans. Wireless Commun., 2024, early access

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