Spatial Bandwidth of Bilateral Near-Field Channels for Linear Large-Scale Antenna Array System

Hongkang Yu; Jun-Bo Wang; Yijian Chen; Yijin Pan; Zhen Wang

REVIEW 3 major objections 4 minor 17 references

Spatial Bandwidth of Bilateral Near-Field Channels for Linear Large-Scale Antenna Array System

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper derives an exact closed-form expression for the local spatial bandwidth of a 3D line-of-sight linear-array channel and proves it is maximized only when the receive array lies in the transmit array's plane and is perpendicular…

desk verdict Solid exact local-bandwidth result; the EDoF-maximization headline outruns the proof via an unvalidated center-point approximation. read the letter →

arxiv 2412.05058 v1 pith:GX55H4Z3 submitted 2024-12-06 cs.IT eess.SPmath.IT

Zhen Wang , Yijin Pan , Jun-Bo Wang , Yijian Chen , Hongkang Yu This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords spatialbandwidtheffectivedegreesoffreedomline-of-sightMIMOnear-fieldcommunicationslarge-scaleantennaarraysKnumberarrayorientationoptimizationmassive

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

Large antenna arrays communicating in line of sight can still carry many independent data streams because near-field spherical wavefronts give each transmit-receive pair a distinct phase. This paper derives an exact piecewise closed-form expression for the local spatial bandwidth at any point in 3D space for such a channel, showing exactly how transmit array length, receive position, and receive orientation set the usable spatial degrees of freedom. The paper proves that for a given receive point the bandwidth reaches its largest value only when the receive array is coplanar with the transmit array and directed perpendicular to the line joining their centers. From this, it derives an approximate K-number expression and argues that the effective degrees of freedom of the line-of-sight channel are approximately maximized under the same alignment.

What carries the argument

The central object is the local spatial bandwidth $\omega_{\hat{\mathbf{v}}}(\mathbf{p}_0,L_s)$, defined as the difference between the maximum and minimum spatial frequencies $k_0\hat{\mathbf{r}}^T\hat{\mathbf{v}}$ over all source points on the transmitting array. The argument is carried by a geometric construction: connecting the receive point P to the transmit array endpoints A and B forms a triangle whose circumcircle intersects the transmit array's perpendicular bisector at M and N, defining the angles $\alpha = \angle APB$ and $\beta = \angle PMN$, with $\hat{\mathbf{v}}_{NP}$ pointing from P to N. Spherical-coordinate parametrization of the receive orientation decouples the two orientation angles and reduces the max-min optimization to elementary trigonometry, yielding the piecewise closed form and the sharp condition for its maximum.

What would settle it

Numerically evaluate the exact K-number integral in Eq. (15) for a receive array whose length is not small relative to the propagation distance, such as $L_p = R = 100\lambda$, maximize it over all receive orientations, and compare the maximizing orientation with the $\hat{\mathbf{v}}_{NP}$ direction predicted by Proposition 1; any significant mismatch would falsify the approximate maximal-EDoF claim. A direct check would be computing the singular values of the channel matrix in Eq. (18) at the predicted optimal orientation and at small orientation offsets to see whether any offset yields a higher EDoF threshold.

Watch

Extended reading notes

Core claim

The central result is Eq. (12), an exact piecewise closed form for the local spatial bandwidth $\omega(\psi,\varphi';\alpha,\beta)$ at a point receiving from a linear transmitting array in 3D free space, expressed as a function of the receiving array's orientation angles and the receiving point's geometric parameters $\alpha$ and $\beta$. Proposition 1 then states that the local spatial bandwidth at a point is maximized if and only if the receiving direction is $\hat{\mathbf{v}} = \pm\hat{\mathbf{v}}_{NP}$, with maximum value $\omega_{\max}(\alpha,\beta) = 2k_0\sin(\alpha/2)$, where $\alpha$ is the angle subtended at the receive point by the two ends of the transmit array and $\hat{\mathbf{v}}_{NP}$ points from the receive point to one of the two intersections of the circumcircle of the triangle formed by the receive point and the transmit array endpoints with the transmit array's perpendicular bisector. Approximating the K number by the center-point bandwidth, the paper obtains $K_2^{\max} = k_0 L_p \sin(\alpha/2)/\pi$ and, through singular-value comparisons of the near-field channel matrix, concludes that the effective degrees of freedom are approximately maximized when the transmit and receive arrays are coplanar and the receive array is perpendicular to the axis joining the array centroids.

Load-bearing premise

The conclusion that coplanar-perpendicular alignment maximizes the effective degrees of freedom rests on treating the spatial bandwidth at the center of the receive array as representative of the whole array, an approximation with no stated error bound, and on accepting the K number as a faithful proxy for the effective degrees of freedom.

Editorial extensions

If this is right

For any placement of the receive array, the orientation that maximizes the local spatial bandwidth is fully determined by geometry: the receive array should lie in the transmit array's plane and point perpendicular to the centroid-axis projection, i.e. along $\hat{\mathbf{v}}_{NP}$.
All receive points on the same circular arc through the transmit array endpoints share the same maximum spatial bandwidth, so rotating a receive array around the transmit array along such an arc can preserve the achievable degrees of freedom.
The approximate maximal K number $k_0 L_p \sin(\alpha/2)/\pi$ grows with the receive aperture and with the angle subtended by the transmit array, and the paper's simulations indicate that antenna spacing and antenna count do not change the K number or EDoF when the array dimensions are fixed.
The effective degrees of freedom decrease monotonically as the distance between the arrays grows or as the receive array moves off the broadside direction, with the maximum occurring when the arrays directly face each other in a coplanar perpendicular configuration.
Misaligning the receive array in either the elevation direction or the azimuth direction lowers both the K number and the singular-value threshold of the channel, so the closed-form bandwidth expression gives a direct design rule for array orientation in line-of-sight massive MIMO.

Reading between the lines

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

The center-point approximation in Eq. (16) has no stated error bound, so for receive arrays whose length is comparable to the propagation distance the true K-number integral in Eq. (15) could have a slightly different maximizing orientation; a finite-length correction would settle how much the approximate optimality claim shifts.
Because the closed-form bandwidth applies to any point in space, it can be integrated along curved or planar receive apertures, not only straight arrays, which suggests a way to optimize non-linear array shapes for higher effective degrees of freedom.
The decoupling of the two orientation angles implies that elevation and azimuth misalignments affect EDoF independently, so a sensitivity analysis based on Eq. (12) could yield simple misalignment tolerances for array placement in near-field systems.
The equal-maximum spatial bandwidth along circular arcs offers a testable geometric prediction: a receive array moved along such an arc should retain the same approximate EDoF even as the transmit-receive distance changes, which could be checked directly with singular-value simulations.

Share X Bluesky LinkedIn Reddit HN

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

Quick take: Eq. (12) and Proposition 1 are the real content. The exact piecewise closed form for local spatial bandwidth is a genuine improvement over the approximate expressions in [15] and [16], and the proof in Appendix A is an elementary but correct max/min argument. The geometric interpretation — bandwidth maximum when the receive orientation is ±v_NP, with value 2k0 sin(α/2) — is clean and likely useful for deployment intuition and fast simulation. The paper earns its place on that basis alone.

The soft spot is exactly where the reader and stress-test note point. The step from pointwise bandwidth to EDoF-maximizing geometry is not proved. Eq. (16) replaces the defining integral for K by the center value times aperture, justified when the local bandwidth is roughly constant across the receive array. No error bound is given, and the paper itself shows in Fig. 5 that the match is good mainly for R > 300λ. For smaller R the approximation degrades. More importantly, even a numerically close K2 does not guarantee that its argmax equals the argmax of K: the direction that maximizes the integrand at the center need not maximize the integral. That is a real logical gap, not a nitpick.

There are also smaller issues. The K number itself is an imported proxy for EDoF from [15]; the paper validates it visually against singular value plots rather than quantitatively. The abstract and conclusion state the EDoF-maximization result as proved, with no caveat on R or Lp. That overstates what the mathematics shows. No code or data are supplied, so I could not reproduce the figures, though the derivations are parameter-free and the visual evidence is consistent in the shown regime.

Who this is for: people working on near-field massive MIMO/THz array geometry, especially those who want a simple closed-form spatial bandwidth expression. The exact local result is worth having even if the EDoF claim needs a tighter statement. I would send it to peer review, but with a clear request: either prove the K/EDoF maximization for finite arrays under explicit conditions, or soften the claim and add quantitative error bounds and simulation coverage in the near-intermediate regime.

Recommendation: serious referee, not desk reject; expect major revision on the EDoF claim.

Referee Report

3 major / 4 minor

Summary. The paper analyzes the local spatial bandwidth of line-of-sight (LoS) channels between two linear large-scale antenna arrays in 3D space. It derives a piecewise closed-form expression for the local spatial bandwidth at an arbitrary observation point, Eq. (12), and proves in Proposition 1 that this bandwidth is maximized if and only if the receive array orientation is aligned with the angle-bisector direction v_NP, with maximum value 2k0 sin(α/2). The paper then uses the center-point bandwidth to approximate the K number via Eq. (16), and from this approximation concludes that the effective degrees of freedom (EDoF) of the LoS channel are approximately maximized when the arrays are coplanar and the receive array is perpendicular to the centroid-to-centroid axis. Numerical comparisons with singular values of simulated LoS channel matrices are presented in Figs. 6 and 7.

Significance. The exact local spatial bandwidth formula is a genuine contribution: it is derived from first principles without fitted parameters, and the piecewise optimization in Appendix A is internally consistent. The geometric interpretation in terms of the angles α and β, and the decoupling of ψ and φ', is useful for near-field XL-MIMO system design and may accelerate system-level simulations. However, the paper's broader claim about EDoF maximization is not established with the same rigor: it rests on the unquantified center-point approximation of Eq. (16) and on an imported K-number-to-EDoF proxy, and the numerical validation is visual rather than quantitative. The manuscript would be suitable for publication if the EDoF claim is either proved under explicit conditions or substantially tempered, with the rigorous content focused on the local spatial bandwidth result.

major comments (3)

[Section III-A, Eq. (16)] The replacement of the exact K-number integral (15) by K2 = (Lp/2π)ω_v(p0) is justified only by the qualitative statement that Lp is small relative to R, with no explicit validity region and no error bound. Figure 5 itself shows that the match between the approximate and numerical maximum K values is good only for R > 300λ in the simulated geometry (Ls = Lp = 100λ); at smaller R the curves diverge visibly, especially for larger θ. Since the abstract and Section IV state the EDoF-maximization result without this restriction, the central claim is not established for finite arrays with R comparable to Lp.
[Section III-B, Eqs. (16)-(17)] Even if K2 were numerically close to K, maximizing K2 over the receive orientation is not equivalent to maximizing the exact K. The pointwise argmax of the integrand at p0 need not be the argmax of the integral (15), because the bandwidth profile along Lp can be asymmetric and orientation-dependent. No monotonicity, concavity, or unimodality result is proved for the exact K(ψ,φ), and Fig. 5 compares only the maximum values after separate maximizations, not the maximizing directions. To support the claim that the coplanar-perpendicular orientation maximizes EDoF, the paper should either prove that the exact K's argmax equals ±v_NP under stated conditions, or provide exhaustive numerical evidence over the full (ψ,φ) space for a range of R, Lp, and θ.
[Abstract and Section IV] The phrase 'as proved in this work' applied to EDoF maximization is too strong. Proposition 1 proves only the pointwise maximum of the local spatial bandwidth at the center of the receive array; the step from that result to the K-number and EDoF maximum is an approximation whose fidelity is not rigorously quantified. Moreover, the K-number-to-EDoF relation is imported from [15], and the validation in Figs. 6 and 7 is visual (singular-value knee positions) rather than a quantitative comparison of EDoF across all orientations. The conclusion should be rephrased as a conditionally validated approximation or conjecture, unless a proof or error bound is added.

minor comments (4)

[Section II.A, first paragraph] The sentence 'with dimensions Lp and Lq' appears to contain a typo: the two array dimensions should be Ls and Lp, since Lq is never defined in the manuscript.
[Remark 1] In Remark 1, 'the orientation v of Ls' should read 'the orientation v of Lp', because Ls is the fixed transmit array oriented along the z-axis.
[Eq. (5)] The notation is slightly confusing: f_hat(v)(p0,s) is defined as a spatial frequency, but Eq. (5) writes it as k0 times a cosine and then denotes it by f(ψ,φ,γ). Clarifying that the right-hand side already includes k0 would avoid ambiguity.
[Fig. 5] The horizontal axis label appears to be missing the wavelength symbol (it renders as 'R ( )' in the text). Please ensure the axis is labeled 'R/λ' or 'R (λ)' consistently.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the closed-form spatial bandwidth is derived from the definitions of spatial frequency and bandwidth, while the EDoF connection is validated against simulated channel singular values.

full rationale

The paper's central derivation is self-contained: the local spatial bandwidth formula (Eq. 12) follows directly from Definition 1 (spatial frequency as the inner product of the propagation direction and the receive orientation), Definition 2 (bandwidth as the max-minus-min of those frequencies), and elementary geometry of the angular range of the propagation direction. Proposition 1 (Eq. 14) is then a direct maximization of the piecewise expression in Eq. (12), with no fitted constants and no imported uniqueness theorem. The subsequent K-number approximation in Eq. (16) is explicitly an approximation: it replaces the integral in Eq. (15) by the center-point bandwidth under the stated condition that the local bandwidth is approximately constant over the receive array, and the paper validates this approximation against numerically computed K numbers (Fig. 5) and against the singular-value decay of the simulated LoS channel matrix (Fig. 6). The K-number-to-EDoF relation is imported from an external reference [15], not from the authors' own prior work, and the paper checks it against an independent channel simulation rather than defining EDoF to be the K number by construction. The optimal-orientation conclusion inherits the approximation's limitations, but that is a correctness or robustness concern, not circularity: the result is not forced by definition, by a fitted parameter, or by a self-citation chain.

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

The central derivation rests on standard electromagnetic geometry and two imported approximations (K-number equals EDoF, center-point bandwidth represents the array). There are no fitted parameters and no invented physical entities.

assumptions (5)

domain assumption Ideal isotropic point sources with LoS free-space propagation; no scattering, mutual coupling, or polarization effects.
Invoked in Section II system model and in the channel model Eq. (18). The spatial bandwidth analysis and the EDoF claim depend on this idealization.
domain assumption The local spatial bandwidth at a point is determined by the extremal propagation directions only (Definition 2), with uniform amplitude weighting across the aperture.
Amplitude variations in near-field are neglected in the bandwidth definition; the simulations use the full amplitude model Eq. (18), so the match is empirical.
domain assumption The K number, defined as the integral of local spatial bandwidth divided by 2π, approximates the EDoF of the LoS MIMO channel.
Imported from [15] and used in Eq. (15) and Section III-B. The paper validates this visually against singular values but does not prove the equivalence.
domain assumption The local spatial bandwidth at the center of the receiving array represents the whole receiving array in Eq. (16), requiring Lp much smaller than R.
This is the basis for K2 and for the maximum-EDoF claim. No error bound is provided; accuracy is checked only for selected geometries in Figs. 5-7.
standard math Rotation about the z-axis maps any observation point into the yOz plane without changing the field, due to cylindrical symmetry of the linear array with isotropic sources.
Used in Section II to justify the WLOG placement of P in the first quadrant of the yOz plane.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Spatial Bandwidth of Bilateral Near-Field Channels for Linear Large-Scale Antenna Array System." pith.science (2026). https://pith.science/paper/GX55H4Z3

@misc{pith2026241205058,
  author       = {Pith},
  title        = {Pith review of: Spatial Bandwidth of Bilateral Near-Field Channels for Linear Large-Scale Antenna Array System},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GX55H4Z3}},
  note         = {Machine review of arXiv:2412.05058}
}

read the original abstract

This paper analyzes the spatial bandwidth of line-of-sight (LoS) channels in massive MIMO systems. For the linear large-scale antenna arrays (LSAA) of transceivers placed in random locations in 3D space, a simple but accurate closed-form expression is derived to characterize the spatial bandwidth. Subsequent analysis of the LSAA's spatial bandwidth properties is also provided, leading to the formulation of an approximate expression for the effective degrees of freedom (EDoF) of bilateral near-field channels. Interestingly, as proved in this work, when the transmit and receive arrays are coplanar, with the receive array positioned perpendicular to the axis joining the centroids of the transmit and receive arrays, the EDoF of the LoS channel is found to be approximately maximized.

Figures

Figures reproduced from arXiv: 2412.05058 by the authors.

**Figure 2.** The range of variation of the propagation direction vector [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 4.** The maximum of local spatial bandwidth at different observation [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 3.** Figure 3: The relationship between local spatial bandwidth and receiving [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]

**Figure 5.** Figure 5: The maximum K number corresponding to the receiving array at [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 7.** Figure 7: The relationship between the singular values of the LoS MIMO [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 12 canonical work pages

[15]

Degrees of freedom in 3D linear large-scale antenna array communications—a spatial bandwidth approach,

L. Ding, E. G. Str ¨om, and J. Zhang, “Degrees of freedom in 3D linear large-scale antenna array communications—a spatial bandwidth approach,” IEEE J. Sel. Areas Commun. , vol. 40, no. 10, pp. 2805– 2822, 2022

work page 2022
[16]

Spatial bandwidth asymptotic analysis for 3D large-scale antenna array communications,

L. Ding, J. Zhang, and E. G. Str ¨om, “Spatial bandwidth asymptotic analysis for 3D large-scale antenna array communications,” IEEE Trans. Wireless Commun., 2023

work page 2023
[1]

Communicating with large intelligent surfaces: Fundamen- tal limits and models,

D. Dardari, “Communicating with large intelligent surfaces: Fundamen- tal limits and models,” IEEE J. Sel. Areas Commun. , vol. 38, no. 11, pp. 2526–2537, 2020

work page 2020
[2]

Task-oriented semantic communication over rate splitting enabled wireless control systems for URLLC services,

C. Zeng, J.-B. Wang, M. Xiao, C. Ding, Y . Chen, H. Yu, and J. Wang, “Task-oriented semantic communication over rate splitting enabled wireless control systems for URLLC services,” IEEE Trans. Commun. , vol. 72, no. 2, pp. 722–739, 2024

2024
[3]

Combating the distance problem in the millimeter wave and terahertz frequency bands,

I. F. Akyildiz, C. Han, and S. Nie, “Combating the distance problem in the millimeter wave and terahertz frequency bands,” IEEE Commun. Mag., vol. 56, no. 6, pp. 102–108, 2018

work page 2018
[4]

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

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

work page 2021
[5]

Line-of-sight extra-large MIMO systems with angular- domain processing: Channel representation and transceiver architecture,

A. Tang, J.-B. Wang, Y . Pan, W. Zhang, Y . Chen, H. Yu, and R. C. De Lamare, “Line-of-sight extra-large MIMO systems with angular- domain processing: Channel representation and transceiver architecture,” IEEE Trans. Commun. , 2023

work page 2023
[6]

Tse and P

D. Tse and P. Viswanath, Fundamentals of wireless communication . Cambridge university press, 2005

2005

Show all 17 references

[7]

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

H. Lu, Y . Zeng, C. You, Y . Han, J. Zhang, Z. Wang, Z. Dong, S. Jin, C.-X. Wang, T. Jiang et al. , “A tutorial on near-field XL-MIMO communications towards 6G,” IEEE Commun. Surv. Tutorials , 2024

2024
[8]

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

A. Tang, J.-B. Wang, Y . Pan, W. Zhang, X. Zhang, Y . Chen, H. Yu, and R. C. De Lamare, “Joint visibility region and channel estimation for extremely large-scale MIMO systems,” IEEE Trans. Commun. , 2024

2024
[9]

RIS-aided near-field localization and channel estimation for the terahertz system,

Y . Pan, C. Pan, S. Jin, and J. Wang, “RIS-aided near-field localization and channel estimation for the terahertz system,” IEEE J. Sel. Topics Signal Process., vol. 17, no. 4, pp. 878–892, 2023

2023
[10]

Near-field communications: A comprehensive survey,

Y . Liu, C. Ouyang, Z. Wang, J. Xu, X. Mu, and A. L. Swindlehurst, “Near-field communications: A comprehensive survey,” arXiv preprint arXiv:2401.05900, 2024

2024 arXiv
[11]

Degree of freedom analysis for holographic MIMO based on a mutual-coupling-compliant channel model,

Y . Sun, M. Jian, J. Yang, Y . Zhao, and Y . Chen, “Degree of freedom analysis for holographic MIMO based on a mutual-coupling-compliant channel model,” ZTE Communications , vol. 22, no. 1, p. 34, 2024

2024
[12]

Electromagnetic effective degree of freedom of an MIMO system in free space,

S. S. Yuan, Z. He, X. Chen, C. Huang, and E. Wei, “Electromagnetic effective degree of freedom of an MIMO system in free space,” IEEE Antennas Wirel. Propag. Lett. , vol. 21, no. 3, pp. 446–450, 2021

2021
[13]

Communication modes with large intelligent surfaces in the near field,

N. Decarli and D. Dardari, “Communication modes with large intelligent surfaces in the near field,” IEEE Access , vol. 9, pp. 165 648–165 666, 2021

2021
[14]

Franceschetti, Wave theory of information

M. Franceschetti, Wave theory of information . Cambridge University Press, 2017

2017
[17]

Line-of-sight MIMO via intelligent reflecting surface,

H. Do, N. Lee, and A. Lozano, “Line-of-sight MIMO via intelligent reflecting surface,” IEEE Trans. Wireless Commun. , vol. 22, no. 6, pp. 4215–4231, 2022

2022

Pith tools

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

[1] [15]

Degrees of freedom in 3D linear large-scale antenna array communications—a spatial bandwidth approach,

L. Ding, E. G. Str ¨om, and J. Zhang, “Degrees of freedom in 3D linear large-scale antenna array communications—a spatial bandwidth approach,” IEEE J. Sel. Areas Commun. , vol. 40, no. 10, pp. 2805– 2822, 2022

work page 2022

[2] [16]

Spatial bandwidth asymptotic analysis for 3D large-scale antenna array communications,

L. Ding, J. Zhang, and E. G. Str ¨om, “Spatial bandwidth asymptotic analysis for 3D large-scale antenna array communications,” IEEE Trans. Wireless Commun., 2023

work page 2023

[3] [1]

Communicating with large intelligent surfaces: Fundamen- tal limits and models,

D. Dardari, “Communicating with large intelligent surfaces: Fundamen- tal limits and models,” IEEE J. Sel. Areas Commun. , vol. 38, no. 11, pp. 2526–2537, 2020

work page 2020

[4] [2]

Task-oriented semantic communication over rate splitting enabled wireless control systems for URLLC services,

C. Zeng, J.-B. Wang, M. Xiao, C. Ding, Y . Chen, H. Yu, and J. Wang, “Task-oriented semantic communication over rate splitting enabled wireless control systems for URLLC services,” IEEE Trans. Commun. , vol. 72, no. 2, pp. 722–739, 2024

2024

[5] [3]

Combating the distance problem in the millimeter wave and terahertz frequency bands,

I. F. Akyildiz, C. Han, and S. Nie, “Combating the distance problem in the millimeter wave and terahertz frequency bands,” IEEE Commun. Mag., vol. 56, no. 6, pp. 102–108, 2018

work page 2018

[6] [4]

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

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

work page 2021

[7] [5]

Line-of-sight extra-large MIMO systems with angular- domain processing: Channel representation and transceiver architecture,

A. Tang, J.-B. Wang, Y . Pan, W. Zhang, Y . Chen, H. Yu, and R. C. De Lamare, “Line-of-sight extra-large MIMO systems with angular- domain processing: Channel representation and transceiver architecture,” IEEE Trans. Commun. , 2023

work page 2023

[8] [6]

Tse and P

D. Tse and P. Viswanath, Fundamentals of wireless communication . Cambridge university press, 2005

2005