Exploiting Mutual Coupling Characteristics for Channel Estimation in Holographic MIMO

Emil Bj\"ornson; Nikolaos Kolomvakis

REVIEW 3 major objections 4 minor 1 cited by

Exploiting Mutual Coupling Characteristics for Channel Estimation in Holographic MIMO

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Mutual coupling, not user-specific scattering, is the prior a dense-array receiver must know to estimate channels accurately.

desk verdict Useful closed-form correlation result and an important question, but the mutual coupling covariance model is not a valid covariance for dipole arrays, so the quantitative claims in this version are ungrounded. read the letter →

arxiv 2412.13683 v1 pith:UNGT46EV submitted 2024-12-18 eess.SP

Nikolaos Kolomvakis , Emil Björnson This is my paper · ORCID

classification eess.SP

keywords holographicMIMOmutualcouplingchannelestimationMMSEestimatorleastsquaresspatialcorrelationdipoleantennaarraycovariancematrix

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

The paper tries to establish which statistical knowledge a base station actually needs to estimate channels in holographic MIMO, where antennas are packed much closer than half a wavelength. Its central finding is that mutual coupling between antennas is a first-order effect for the MMSE estimator: an estimator that ignores coupling and uses only the array-geometry covariance loses roughly 8 and 16 dB in MSE at 10 and 20 dB pilot SNR in isotropic scattering, and about 12 and 19 dB in clustered scattering. Knowing the user-specific spatial correlation is much less important, costing about 4 dB when coupling is already known. The least-squares estimator needs no coupling or correlation statistics and is therefore robust, but it only becomes competitive at high SNR. If true, this redirects practical holographic MIMO design toward coupling calibration rather than elaborate scattering modeling.

What carries the argument

The central object is the mutual-coupling matrix $\mathbf{C} = (\mathbf{Z} + R_d\mathbf{I})^{-1}$, which enters the channel model as $\mathbf{h}_{\mathrm{mc}} = \mathbf{C}^{1/2}\mathbf{h}$ and transforms the coupling-free covariance into $\mathbf{R}_{\mathrm{mc}} = \mathbf{C}^{1/2}\mathbf{R}\mathbf{C}^{1/2}$. This matrix does the work of changing the subspace in which plausible channel estimates live: Proposition 2 shows that an estimator built on $\mathbf{R}_{\mathrm{iso}}$ spans only the isotropic column space, while one built on $\mathbf{C}^{1/2}\mathbf{R}_{\mathrm{iso}}\mathbf{C}^{1/2}$ spans the physically possible coupled dimensions. The eigenbasis MSE formula in Proposition 3 and Corollary 1 then quantifies the penalty as an SNR-dependent mismatch between the estimator eigenbasis and the true channel eigenbasis, which is why ignoring coupling hurts most at high SNR.

What would settle it

Build or simulate the 10x10 $\lambda/5$ dipole array, compute $\mathbf{C}$ from the mutual-impedance formulas, test whether $\mathbf{C}$ is Hermitian positive semidefinite, and compare the measured MMSE gap against the predicted 8 and 16 dB losses; a non-PSD matrix or a missing gap would refute the central numerical claim.

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Extended reading notes

Core claim

On its own terms, the paper demonstrates that the effective channel in a dense array is $\mathbf{h}_{\mathrm{mc}} = \mathbf{C}^{1/2}\mathbf{h}$, with covariance $\mathbf{R}_{\mathrm{mc}} = \mathbf{C}^{1/2}\mathbf{R}\mathbf{C}^{1/2}$, and that an MMSE-structured estimator using $\hat{\mathbf{R}} = \mathbf{R}_{\mathrm{iso}}$ instead of $\mathbf{R}_{\mathrm{mc}}$ projects the received signal onto the wrong subspace. The numerical consequence is an SNR-dependent MSE penalty: about 8 and 16 dB at 10 and 20 dB SNR under isotropic scattering, and about 12 and 19 dB under clustered scattering. The paper also shows that substituting the user-specific correlation with the isotropic correlation costs only about 4 dB once coupling is known, while the least-squares estimator avoids coupling information altogether but pays a large low-SNR penalty. The conclusion is that mutual coupling awareness is essential for MMSE channel estimation in holographic MIMO, and that spatial correlation knowledge is secondary.

Load-bearing premise

The numerical results assume the mutual-coupling matrix $\mathbf{C} = (\mathbf{Z} + R_d\mathbf{I})^{-1}$ is a valid covariance matrix with a square root; the paper states this model but never proves that the inverse of an impedance matrix plus dissipation resistance is Hermitian positive semidefinite.

Editorial extensions

If this is right

A holographic MIMO receiver that wants MMSE-quality channel estimates must know or estimate the mutual-coupling matrix $\mathbf{C}$; array-geometry information alone is not enough.
At low pilot SNR the penalty for ignoring coupling is small, so simpler coupling-agnostic estimators can be used in that regime without much loss.
Exchanging user-specific channel statistics for isotropic statistics costs roughly 4 dB once coupling is known, so the more important prior to acquire is the coupling matrix.
The LS estimator is a viable coupling-agnostic fallback, but only when the SNR is high enough that its $M/\rho$ error floor is acceptable.
Channel estimation algorithms for dense arrays should be designed around coupling-aware covariance models rather than purely geometry-based models.

Reading between the lines

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

A natural next step the paper leaves implicit is to reuse a single calibration of $\mathbf{C}$ across all served users, since coupling is a property of the array rather than of any propagation environment.
The roughly 4 dB cost of replacing user-specific correlation with isotropic correlation suggests that, once coupling is known, coarse scattering knowledge may be enough in dense arrays; this extrapolates from two scattering models to a design rule.
Because the paper only treats uplink pilot estimation, the same coupling-aware covariance logic should carry over to downlink precoder design under TDD reciprocity, but that transfer is not proven here.
A direct experimental check on a small fabricated array of $\lambda/5$ dipoles could confirm whether the predicted 8 and 16 dB MSE gaps appear as the array geometry is held fixed and only the scattering model changes.

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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,

The short version: the paper is worth reading for its new closed-form spatial correlation expression for half-wavelength dipoles under isotropic scattering (Prop. 1), but the mutual coupling model in Eqs. (9)–(11) is mathematically invalid for the physical setup, and the paper's main quantitative claims lean on it.

What's new and good: Prop. 1 is a genuine extension of the correlation model in [3], and the derivation in Appendix A checks out. The conceptual comparison between MMSE-structured estimators that do or do not account for coupling is the right question for holographic MIMO, and the paper is cleanly written. There are no fitted constants; the figures come from a fixed channel model, so the circularity burden is low.

The soft spot is not soft: Eq. (9) defines hmc = C^{1/2}h with C = (Z + R_d I)^{-1}. For a dipole array, Z is a complex symmetric matrix, not Hermitian. Adding a scalar dissipation resistance R_d preserves that: C is complex symmetric, generally non-Hermitian, and not positive semidefinite in the matrix sense. Consequently, a Hermitian square root C^{1/2} does not exist in the usual sense, and even if you take a principal square root (which is complex symmetric), the covariance of hmc is C^{1/2} R (C^{1/2})^H, not C^{1/2} R C^{1/2}. The paper's Eq. (10) is simply not a valid covariance matrix. This is load-bearing: Prop. 2's subspace argument and Prop. 3's eigen-decomposition both assume Rmc is Hermitian positive semidefinite, and the MSE losses quoted for Fig. 1 are computed from a matrix that isn't the covariance of the channel. The alternative—use T = C^{1/2} (or the standard circuit-theory coupling matrix T = C) and form T R T^H—is the physically consistent fix. The qualitative conclusion that MMSE needs coupling awareness will probably survive that fix, but the dB numbers in this version are ungrounded.

Minor issues: the exact dipole geometry (length, radius) used for Z is not stated, so the curves can't be reproduced; and the notation in Cor. 1 is a little sloppy (lambda_w vs eigenvalues of R_hat). Both are fixable.

Bottom line: This paper deserves a serious referee—the question matters and Prop. 1 is a useful standalone result—but as written the central statistical model is wrong. I'd want the authors to redo the analysis with the correct covariance transformation before trusting any of the performance claims. If they do, the paper could be solid.

Recommendation: accept for peer review with a clear flag that the covariance model needs a major revision.

Referee Report

3 major / 4 minor

Summary. The paper studies uplink channel estimation in a holographic MIMO system whose base station is a uniform planar array of closely spaced half-wavelength dipoles. It models spatially correlated Rayleigh fading with covariance R, introduces mutual coupling through h_mc = C^{1/2}h and R_mc = C^{1/2}RC^{1/2} with C=(Z+R_d I)^{-1}, and compares the LS estimator with MMSE-structured estimators that use different assumed covariance matrices: the true R_mc, a coupling-aware isotropic covariance C^{1/2}R_isoC^{1/2}, and a coupling-ignoring isotropic covariance R_iso. The paper derives a closed-form isotropic spatial correlation expression, column-space containment results for the estimators, and eigen-expressions for the MSE, and reports numerical MSE curves claiming that ignoring mutual coupling costs roughly 8 and 16 dB at 10 and 20 dB SNR in isotropic scattering and 12 and 19 dB in clustered scattering, while LS is resilient to coupling ignorance but useful mainly at high SNR.

Significance. If the results were correct, the paper would provide concrete design guidance: a holographic MIMO receiver using an MMSE-structured estimator must know or estimate the mutual coupling matrix, while LS provides a coupling-robust fallback at high SNR. The paper also contributes a closed-form, parameter-free spatial correlation series for isotropic scattering with dipole elements, and the numerical study is reproducible from the stated model and parameters with no fitted constants. However, the central quantitative conclusions rest on a mutual-coupling covariance model that is not justified, and one of the main MSE formulas contains an algebraic inconsistency. The qualitative message may survive a corrected treatment, but the paper as written does not establish its headline dB-loss claims.

major comments (3)

[II-B, Eqs. (9)-(11)] The model h_mc = C^{1/2}h and R_mc = C^{1/2}RC^{1/2} with C=(Z+R_d I)^{-1} is a valid covariance model only if C is Hermitian positive semidefinite, so that C^{1/2} can be taken as a Hermitian square root and R_mc is the covariance of C^{1/2}h. The paper never states or proves this property. For the thin-dipole mutual impedances cited in [7], Z is complex symmetric with nonzero imaginary parts, so (Z+R_d I)^{-1} is generally not Hermitian; consequently C^{1/2}RC^{1/2} need not be Hermitian and is not the covariance of C^{1/2}h. The correct covariance would be R_mc = T R T^H with T=(Z+R_d I)^{-1}. This issue propagates to Appendix B, where the equality R_mc = C^{1/2}R^{1/2}(C^{1/2}R^{1/2})^T is asserted, and to the eigen-decomposition used in Proposition 3 and Corollary 1. Since all numerical curves in Fig. 1 are generated from this covariance model, the reported 8/16 dB and 12/19 dB losses are not grounded. The authors must either prove the required positive semidefiniteness under their antenna assumptions or re-derive the results using the physical covariance R_mc = T R T^H and rerun the numerical study.
[III-C, Corollary 1, Eq. (19)] Equation (19) is not consistent with Proposition 3 as written. In Proposition 3, lambda_{w,k} denotes an eigenvalue of the estimator matrix W. For the MMSE-structured estimator W = sqrt(rho) \hat{R}(rho\hat{R}+I)^{-1}, substituting lambda_w = sqrt(rho)\hat{lambda}/(rho\hat{lambda}+1) into the beta expression of Proposition 3 does not yield Eq. (19) for an arbitrary \hat{R}. For example, in the matched case \hat{R}=R_mc with rho=1 and lambda_h=1, Proposition 3 gives beta = -0.5, while Eq. (19) gives -4/9. The formula appears to mix eigenvalues of W with eigenvalues of \hat{R}. Because the numerical MSE values in Fig. 1 are likely computed from this formula or from the associated eigen-expansion, the reported quantitative losses are not substantiated until Eq. (19) is corrected and the curves are regenerated.
[II-A, Prop. 1 and Appendix A] The closed-form spatial correlation formula in Eq. (5) omits the wavelength normalization that is explicitly introduced in Appendix A, where d_y^{nm} = (r_y(n)-r_y(m))d_y/lambda and d_z^{nm} = (r_z(n)-r_z(m))d_z/lambda. If d_y and d_z in Eq. (5) are meant to be normalized by the wavelength, this should be stated; otherwise the formula is inconsistent with its own derivation. This is relevant because R_iso is used both in Proposition 2 and in the numerical experiments, so an unstated normalization convention can change the correlation matrix and the resulting MSE curves.

minor comments (4)

[III-A, Proposition 2] The first scenario writes \hat{R} = C^{1/2}R^{1/2}C^{1/2}, but the surrounding text says this is the true MMSE estimator, which would require \hat{R}=R_mc=C^{1/2}RC^{1/2}. The notation should be corrected to avoid ambiguity.
[III-C, Proposition 3] Proposition 3 is stated for an arbitrary linear estimator W, but its eigen-expansion with orthonormal eigenvectors and the inner-product term |<u_{w,k},u_{hmc,l}>|^2 is only valid when W has an orthonormal eigenbasis, for example when W is Hermitian. The statement should be qualified accordingly.
[References] Reference [8] is listed with year 2006, but the cited book by Björnson and Demir appears to be a recent publication; the year should be checked and corrected.
[IV-A, Fig. 1] The text says the LS estimator exhibits degradation and then says the gap narrows; consider rephrasing for clarity. Also, the figure caption does not specify whether the curves come from Monte Carlo simulation or from the analytical MSE expressions, which should be stated.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the numerical claims follow from the stated model and estimator equations, with only minor self-citations and a separate modeling-validity caveat.

full rationale

The paper's derivation chain is not circular. The spatial correlation matrices are either derived from the assumed scattering function in Proposition 1 or imported from published channel models in [3]; the MMSE-structured and LS estimators in (14)-(16) and the MSE expressions in (17)-(19) are standard definitions and algebraic consequences. The Fig. 1 dB-loss claims are computed by evaluating the closed-form MSE for fixed choices of the covariance matrix Rhat (Riso, C^{1/2}RisoC^{1/2}, Rmc), with no parameter fitted to the plotted outputs. Therefore, the conclusion that neglecting mutual coupling degrades MMSE estimation is an analytical consequence of covariance mismatch under the stated model, not a prediction forced by construction. The self-citations that appear ([3], [6], [8]) supply channel-model ingredients or a subspace-spanning lemma; they are not the target result and do not smuggle in the paper's main conclusion. A separate correctness caveat, not a circularity, is that Eqs. (9)-(11) write hmc = C^{1/2}h and Rmc = C^{1/2}RC^{1/2} with C = (Z + RdI)^{-1}, which is a valid covariance transformation only if C is Hermitian positive semidefinite; the paper never states or proves this property, and for coupled thin dipoles Z is complex symmetric rather than Hermitian. If the physically consistent covariance were T R T^H with T = (Z + RdI)^{-1}, the Fig. 1 curves would need re-computation. That is a modeling-validity concern, not a circular-reasoning concern.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claims rest on standard Rayleigh fading plus two nonstandard assumptions: the Hermitian PSD behavior of C and the isotropic subspace inclusion from [3]. The numerical results also rely on unstated dipole geometry and R_d values.

free parameters (6)

Antenna spacing d_y = d_z = lambda/5 (0.2 lambda)
Set in Sec. IV for the 10 by 10 UPA; all dB loss numbers in Fig. 1 depend on this choice.
Array size M = 100 (10 by 10)
Numerical configuration in Sec. IV; MSE curves and dB gaps are for this size.
Dipole dissipation resistance R_d = not specified in the paper
Required in Eq. (11) to build C; exact numerical results cannot be reproduced without it.
Dipole geometry (length and radius) for mutual impedance Z = not specified
Mutual impedance closed forms in [7] depend on dipole geometry; unspecified, affecting C and all quantitative claims.
Angular cluster parameters for non-isotropic scenario = N=20, sigma_phi = sigma_theta = 2 degrees, ITU urban macro (sub-6 GHz)
Taken from [12]; chosen scenario in Sec. IV-B, affects non-isotropic curves.
Directivity coefficient in dipole pattern = 1.67
Approximation from [7] used in Eq. (4); this constant enters the closed-form R_iso in Prop. 1.

assumptions (4)

domain assumption Rayleigh correlated fading: h = R^{1/2} h_iid
Sec. II, Eq. (2). Standard model; the whole MSE analysis assumes Gaussian channels.
domain assumption Mutual coupling enters as hmc = C^{1/2}h with C = (Z + R_d I)^{-1}, and C^{1/2} is used as a covariance square root.
Sec. II-B, Eqs. (9)-(11). Load-bearing but unproven; requires C to be Hermitian PSD, which is not established for complex mutual impedance Z.
domain assumption For the given array geometry, Range(R) is a subset of Range(R_iso) for any physical scattering R.
Invoked in Prop. 2 and Appendix B via [3, Lemma 3]. If false, the estimator with R_hat = C^{1/2}R_iso C^{1/2} may miss channel dimensions.
domain assumption Half-wave dipole directivity can be approximated by D = 1.67 cos^3(theta), giving f = 1.67/(2 pi) cos^4(theta).
Sec. II-A, Eq. (4). Used to derive Prop. 1; approximation accuracy is not quantified.

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Cite this review

Pith. "Pith review of Exploiting Mutual Coupling Characteristics for Channel Estimation in Holographic MIMO." pith.science (2026). https://pith.science/paper/UNGT46EV

@misc{pith2026241213683,
  author       = {Pith},
  title        = {Pith review of: Exploiting Mutual Coupling Characteristics for Channel Estimation in Holographic MIMO},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UNGT46EV}},
  note         = {Machine review of arXiv:2412.13683}
}

read the original abstract

Holographic multiple-input multiple-output (MIMO) systems represent a spatially constrained MIMO architecture with a massive number of antennas with small antenna spacing as a close approximation of a spatially continuous electromagnetic aperture. Accurate channel modeling is essential for realizing the full potential of this technology. In this paper, we investigate the impact of mutual coupling and spatial channel correlation on the estimation precision in holographic MIMO systems, as well as the importance of knowing their characteristics. We demonstrate that neglecting mutual coupling can lead to significant performance degradation for the minimum mean squared error estimator, emphasizing its critical consideration when designing estimation algorithms. Conversely, the least-squares estimator is resilient to mutual coupling but only yields good performance in high signal-to-noise ratio regimes. Our findings provide insights into how to design efficient estimation algorithms in holographic MIMO systems, aiding its practical implementation.

Figures

Figures reproduced from arXiv: 2412.13683 by the authors.

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Forward citations

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Reference graph

Works this paper leans on

14 extracted references · 13 canonical work pages · cited by 1 Pith paper

[3]

Channel m odeling and channel estimation for holographic massive MIMO with plana r arrays,

O. T. Demir, E. Bj¨ ornson, and L. Sanguinetti, “Channel m odeling and channel estimation for holographic massive MIMO with plana r arrays,” IEEE Wireless Commun. Lett. , vol. 11, no. 5, pp. 997–1001, 2022

work page 2022
[7]

C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed . John Wiley & Sons, Inc., 2016

work page 2016
[1]

Massive MIMO is a reality—what is next?: Five pro mis- ing research directions for antenna arrays,

E. Bj¨ ornson, L. Sanguinetti, H. Wymeersch, J. Hoydis, a nd T. L. Marzetta, “Massive MIMO is a reality—what is next?: Five pro mis- ing research directions for antenna arrays,” Digital Signal Processing , vol. 94, pp. 3–20, 2019

2019
[2]

Fourier pl ane-wave series expansion for holographic MIMO communications,

A. Pizzo, L. Sanguinetti, and T. L. Marzetta, “Fourier pl ane-wave series expansion for holographic MIMO communications,” IEEE Trans. on Wireless Commun., vol. 21, no. 9, pp. 6890–6905, 2022

work page 2022
[4]

DFT-based c hannel estimation for holographic MIMO,

A. A. D’Amico, G. Bacci, and L. Sanguinetti, “DFT-based c hannel estimation for holographic MIMO,” in Proc. Asilomar Conf. Signals, Syst., Comput. , 2023, pp. 353–357

work page 2023
[5]

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

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

work page 2022
[6]

Rayleigh fading model ing and channel hardening for reconﬁgurable intelligent surfaces,

E. Bj¨ ornson and L. Sanguinetti, “Rayleigh fading model ing and channel hardening for reconﬁgurable intelligent surfaces,” IEEE Wireless Com- mun. Lett. , vol. 10, no. 4, pp. 830–834, 2021

work page 2021
[8]

Bj¨ ornson and O

E. Bj¨ ornson and O. T. Demir, Introduction to Multiple Antenna Commu- nications and Reconﬁgurable Surfaces . Boston-Delft: now publishers, 2006

work page 2006

Show all 14 references

[9]

Toward a circuit theory of communi- cation,

M. T. Ivrlaˇ c and J. A. Nossek, “Toward a circuit theory of communi- cation,” IEEE Trans. Circuits Syst. I, Reg. Papers , vol. 57, no. 7, pp. 1663–1683, 2010

2010
[10]

Holographic MIMO com munica- tions: What is the beneﬁt of closely spaced antennas?

A. A. D’Amico and L. Sanguinetti, “Holographic MIMO com munica- tions: What is the beneﬁt of closely spaced antennas?” IEEE Transac- tions on Wireless Communications , pp. 1–1, 2024

2024
[11]

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimatio n Theory, vol. 1 . Englewood Cliffs, NJ, USA: Prentice-Hall, 1993

1993
[12]

Guidelines for evaluation of radio interfa ce technologies for IMT-2020,

M. Series, “Guidelines for evaluation of radio interfa ce technologies for IMT-2020,” Report ITU , 2017

2020
[13]

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products. Elsevier/Academic Press, Amsterdam, 2007

2007
[14]

Strang, Linear Algebra and Its Applications, 4th ed

G. Strang, Linear Algebra and Its Applications, 4th ed . Thomson, Brooks/Cole, 2006

2006

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [3]

Channel m odeling and channel estimation for holographic massive MIMO with plana r arrays,

O. T. Demir, E. Bj¨ ornson, and L. Sanguinetti, “Channel m odeling and channel estimation for holographic massive MIMO with plana r arrays,” IEEE Wireless Commun. Lett. , vol. 11, no. 5, pp. 997–1001, 2022

work page 2022

[2] [7]

C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed . John Wiley & Sons, Inc., 2016

work page 2016

[3] [1]

Massive MIMO is a reality—what is next?: Five pro mis- ing research directions for antenna arrays,

E. Bj¨ ornson, L. Sanguinetti, H. Wymeersch, J. Hoydis, a nd T. L. Marzetta, “Massive MIMO is a reality—what is next?: Five pro mis- ing research directions for antenna arrays,” Digital Signal Processing , vol. 94, pp. 3–20, 2019

2019

[4] [2]

Fourier pl ane-wave series expansion for holographic MIMO communications,

A. Pizzo, L. Sanguinetti, and T. L. Marzetta, “Fourier pl ane-wave series expansion for holographic MIMO communications,” IEEE Trans. on Wireless Commun., vol. 21, no. 9, pp. 6890–6905, 2022

work page 2022

[5] [4]

DFT-based c hannel estimation for holographic MIMO,

A. A. D’Amico, G. Bacci, and L. Sanguinetti, “DFT-based c hannel estimation for holographic MIMO,” in Proc. Asilomar Conf. Signals, Syst., Comput. , 2023, pp. 353–357

work page 2023

[6] [5]

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

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

work page 2022

[7] [6]

Rayleigh fading model ing and channel hardening for reconﬁgurable intelligent surfaces,

E. Bj¨ ornson and L. Sanguinetti, “Rayleigh fading model ing and channel hardening for reconﬁgurable intelligent surfaces,” IEEE Wireless Com- mun. Lett. , vol. 10, no. 4, pp. 830–834, 2021

work page 2021

[8] [8]

Bj¨ ornson and O

E. Bj¨ ornson and O. T. Demir, Introduction to Multiple Antenna Commu- nications and Reconﬁgurable Surfaces . Boston-Delft: now publishers, 2006

work page 2006