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REVIEW 3 major objections 4 minor 31 references

Multi-User MIMO Enhancement using Metasurface Wavefront Bending (MWB)

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A passive transmissive metasurface that bends each user's spherical wavefront so it appears to come from a closer point can decorrelate range-separated users and raise spectral efficiency and effective rank in near-field MU-MIMO.

desk verdict Genuinely new metasurface mechanism (virtual-source-shift wavefront bending) with internally consistent theory for near-field MU-MIMO, but headline gains rest on an ideal angle-independent phase mask that the paper's own oblique-incidence unit-cell data only partially supports. read the letter →

arxiv 2607.29542 v1 pith:UDFVCSRJ submitted 2026-07-31 eess.SP

Xiaolu Yang , Oscar Cespedes Vicente , Christophe Caloz This is my paper · ORCID
classification eess.SP
keywords metasurfacewavefrontbendingMU-MIMOradiativenearfieldspherical-wavecurvaturechannelcorrelationgeneralizedsheettransitionconditionsphasequantizationeffectiverank
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 spherical-wave curvature is not merely a property of near-field propagation but a resource a system can engineer: a passive transmissive metasurface placed between users and a base station can bend each incident wavefront so that it appears to originate from a closer virtual source, increasing the curvature seen across the receiving array. Because the phase difference between two users then varies across the array instead of staying constant, their channel vectors become less parallel—a direct, range-dependent decorrelation mechanism that the paper derives and quantifies. The paper builds a complete user–metasurface–base-station channel model around this mask, evaluates it for a practical common mask and an ideal per-user mask, and reports higher spectral-efficiency sums and effective channel ranks than the no-metasurface baseline, including for users who share the same angle and differ only in range. If correct, this would give a simple passive way to improve spatial multiplexing in future high-frequency, large-aperture systems where more users are falling into the radiative near field.

What carries the argument

The load-bearing element is a phase-only transmission mask (Eq. 40), T_MS(x_m,y_m)=exp[-jk0( sqrt((d_i^TM/beta)^2+r_m^2) - sqrt((d_i^TM)^2+r_m^2) )], applied to every user's incident scalar spherical-wave field. It is derived from a generalized-sheet-transition-condition (GSTC) synthesis, which relates field discontinuities across a thin sheet to the required electric and magnetic surface susceptibilities, and the transmitted field is propagated to the base station with a Rayleigh-Sommerfeld scalar diffraction integral. The mask's effect is to amplify the quadratic aperture phase r_m^2/(2d) by the bending ratio beta; that amplified phase variation rotates the phasors in the correlation sum o

What would settle it

Build the eight-unit-cell aperture, place two range-separated users on the same broadside line at 10 GHz, and measure the normalized channel correlation at the base station with and without the mask. If the correlation does not drop toward the predicted ~0.1 at beta=8, or the spectral-efficiency sum does not rise, the central claim fails. A cheaper check is to recompute Eq. (22) with measured, angle-dependent unit-cell transmission responses over the full local-incidence range (0 to about 54 degrees) and see whether the predicted correlation minimum survives.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that increasing wavefront curvature lowers inter-user channel correlation, and that a thin transmissive metasurface can impose that increase. The synthesized mask, Eq. (40), converts the incident field of the reference user into the field of a virtual source at distance d_i^TM/beta, with beta>1 the bending ratio, while preserving field magnitude. In the two-user same-direction configuration, normalized correlation falls from near one to about 0.1 at beta=8 and spectral-efficiency sum rises correspondingly; in the ideal user-specific benchmark the effective channel rank reaches K, meaning user channels become orthogonal. The paper therefore p

Load-bearing premise

The whole gain rests on the assumption that a scalar, angle-independent, phase-only transmission mask accurately describes what a physical metasurface does to every user's field; in reality unit cells deviate at oblique incidence—up to about 54 degrees at the aperture corners—and the ideal mask is never validated in a full-wave system-level simulation.

Editorial extensions

If this is right

  • A single passive common mask can separate users that lie along the same angle at different ranges—a configuration where angular beamforming alone cannot help.
  • The bending ratio has an optimal value for a given geometry: increasing it first lowers correlation, then phase wrapping makes correlation rise, so the mask must be co-designed with aperture size and user spacing.
  • Three-bit (eight-state) phase quantization preserves most of the multiplexing gain, meaning the continuously synthesized mask is realizable with a finite unit-cell library.
  • The ideal per-user bending benchmark yields orthogonal user channels (effective rank equal to the number of users), setting an upper bound for future reconfigurable metasurface architectures.
  • The common-profile scheme's benefit saturates as the number of users grows, since one shared mask cannot generate an independent spatial mode for every user.

Reading between the lines

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

  • By reciprocity, the same curvature-bending mask should also decorrelate downlink channels, so MWB could be applied at the access point to serve multiple users in the same angular direction without per-user feedback of the correlation structure.
  • The gain is tied to line-of-sight spherical-wave structure; in dense multipath or scattering environments the correlation may already be low, so the incremental value of bending is likely smaller there.
  • Because Eq. (53) isolates the phase contributions, the optimal bending ratio could be derived analytically for a given aperture, array pitch, and range separation—making the nonmonotonic curves in the paper predictable rather than empirical.
  • The paper's own oblique-incidence data show the largest phase deviations at aperture edges and corners; an edge-tapered mask or a unit-cell library optimized for those angles is a natural next step to close the gap between the scalar model and a physical implementation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes metasurface wavefront bending (MWB), a passive transmissive metasurface that maps an incident spherical wavefront to one with increased curvature, as a means to improve spatial multiplexing in radiative-near-field LOS MU-MIMO systems. The authors derive a curvature-dependent normalized channel correlation, a GSTC-based synthesis procedure, and a complete user–metasurface–BS channel model. They evaluate two schemes: a practical common-profile bending (one fixed phase mask applied to all users) and an ideal user-specific benchmark where each UE gets its own bending ratio. They further propose three-bit quantized three-layer Huygens unit cells and report CST unit-cell transmission responses. The central numerical claim is that MWB reduces inter-user channel correlation and increases spectral-efficiency sum and effective channel rank compared with the no-metasurface baseline.

Significance. The curvature-correlation relation (Sec. III) and the GSTC synthesis (Sec. IV) are useful and clearly presented; the analytical SINR derivation in Appendix A is careful, and the user-specific benchmark is explicitly labeled as an ideal upper bound, which is appropriate. The phase-quantization robustness study (Sec. VII) is a useful practical step. If the predicted gains survive a realistic implementation, MWB would be a valuable passive approach to enhancing near-field MU-MIMO without requiring active RIS elements. However, the system-level results rely on an ideal phase-only, angle-independent transmission mask and a scalar channel model, while the physical validation stops at unit-cell CST simulations; this gap currently limits support for the strong 'substantial improvements' claim.

major comments (3)
  1. [Sec. IV, Eq. (34), Fig. 8; Sec. V, Eq. (40), Eq. (45)] There is an internal inconsistency between the GSTC-synthesized surface and the surface used in the system-level model. The GSTC synthesis yields a local transmission coefficient T(x,y) in Eq. (34) whose magnitude is not generally unity; Fig. 8 shows noticeable amplitude variation. Yet the system model in Eq. (45) uses the ideal phase-only mask T_MS(i,β) from Eq. (40), which has |T|=1 by construction. The paper never inserts the actual GSTC-derived T(x,y) into the channel model, nor does it quantitatively bound the difference. Since the correlation-reduction mechanism in Eq. (53) is driven by precise quadratic-phase differences across the metasurface aperture, the amplitude and phase errors of the synthesized surface could materially reduce the claimed gains. Please use the actual local transmission coefficient in the system model, or justify the ideal mask as an accurate approximation w
  2. [Appendix C, Fig. 17; Sec. VI random-sector configuration] The physical unit-cell library is characterized only up to 45° incidence, but the random-sector configuration allows d_TM down to 5λ with a 10λ aperture, and Appendix C itself computes a maximum local incidence angle of about 54°. At 45°, Cells 4 and 8 already show clear phase and amplitude deviations. The edge and corner unit cells, which are the most critical for the aperture phase profile, fall exactly in the uncharacterized angular range. Because the decorrelation gain depends on the cumulative phase across the aperture, these deviations could substantially reduce or eliminate the benefit. A full-wave simulation of a finite metasurface panel in the link, or a measurement of the complete MWB-assisted channel, is needed to support the physical claim.
  3. [Sec. V, Eq. (44)-(46); Sec. VIII] The 'complete' system-level channel model is a scalar Rayleigh-Sommerfeld diffraction formula with a local, angle-independent phase-only transmission mask. It does not include mutual coupling between the finite metasurface unit cells, edge truncation effects, or vector-field polarization effects of the dogbone particles. The paper's conclusion that MWB provides 'substantial improvements' is therefore backed only by this ideal-mask scalar model, not by a full-wave simulation of the actual metasurface-assisted link. Given that the title and abstract promise a physical enhancement mechanism, this is a load-bearing validation gap. At minimum, a representative full-wave finite-array simulation should be added for one of the claimed operating scenarios.
minor comments (4)
  1. [Sec. V, around Eq. (39)] The text says 'with r_m^2 = sqrt(x_m^2 + y_m^2)', but r_m^2 should be x_m^2 + y_m^2, consistent with Eq. (36). Please correct this typo.
  2. [Sec. II and Fig. 3] The abbreviation 'WFB' appears in the caption of Fig. 3 while the paper consistently uses 'MWB' (metasurface wavefront bending). Please unify the terminology.
  3. [Sec. III-A, near Eq. (8)] There is a duplicated article in 'the the Hermitian conjugate operation'.
  4. [Sec. VII] The software name is misspelled as 'CST Microwave Stu dio'; it should be 'CST Microwave Studio'.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the MWB gain follows from a forward electromagnetic channel model with an explicit phase-only mask; GSTC self-citations are background, and the user-specific benchmark is explicitly ideal.

full rationale

The correlation-reduction mechanism is derived analytically from spherical-wave path differences (Eqs. (1)-(3), (20)-(22)) and the SINR expression (Eq. (15)) is derived algebraically from MMSE combining in Appendix A; no parameter is fitted to the later spectral-efficiency or rank targets. The GSTC synthesis (Eqs. (23)-(34)) starts from an explicit prescription of the transmitted field and derives susceptibilities and a local transmission coefficient; this is a forward design calculation, not a result that presupposes the system-level gain. The complete system channel (Eqs. (40)-(46)) uses a deterministic phase-only mask and Rayleigh-Sommerfeld propagation, with the bending ratio beta swept rather than optimized against the reported metrics, so the common-profile improvements in Figs. 10-11 are forward simulations. The user-specific benchmark (Eq. (56)) selects beta_k to minimize pairwise correlations, but the paper explicitly labels it 'an ideal upper-bound reference' and states that such functionality 'cannot be achieved by a unique metasurface'; therefore it is not a disguised prediction. Self-citations to Caloz's GSTC work ([19], [21]) are background established synthesis theory and are not used as a load-bearing uniqueness argument. The paper's own Appendix C admits oblique-incidence deviations up to about 54 degrees and Sec. VIII defers fabrication and experimental validation; this is a physical-realizability and validation gap, not circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 1 invented entities

The central performance claims rest on the scalar-wave channel assumption and an idealized angle-independent phase mask; the bending ratios are design knobs rather than fitted constants, but the choice β=8 underlies the headline gains.

free parameters (2)
  • Bending ratio β (common profile) = 8
    Hand-chosen operating point; performance vs β is nonmonotonic (Fig. 10) and the claimed common-profile gains are evaluated at β=8.
  • User-specific bending-ratio set {β_k} = {1.00, 1.73, 3.00, 4.27, 4.64, 6.09, 6.82, 7.27, 8.00, 9.36}
    Selected by sequential minimax-correlation optimization (Eq. (56)) in the ideal benchmark; the near-orthogonality result is a consequence of this selection.
assumptions (5)
  • domain assumption Line-of-sight scalar spherical-wave channel (Eq. (6), Eq. (41))
    Each UE is modeled as an isotropic scalar point source with field C0 e^{-jkR}/R; polarization, antenna pattern and multipath are neglected in the channel model.
  • ad hoc to paper Phase-only, angle-independent metasurface transmission mask (Eq. (40))
    The system model assumes T_MS is a pure phase profile independent of incidence angle and user position; physical unit cells deviate at large oblique incidence (Appendix C), and the ideal mask is not validated in full-system simulation.
  • domain assumption Rayleigh-Sommerfeld scalar diffraction from MS to BS (Eq. (44))
    Uses scalar diffraction with obliquity factor d/R and discrete unit-cell sources; standard but approximate for near-field vector fields.
  • domain assumption Far-field dipole expressions used in GSTC synthesis (Eq. (30))
    The synthesis keeps only leading 1/R and 1/R^2 terms; for virtual-source distances as small as 1.25λ (β=8), the omitted reactive near-field terms are non-negligible.
  • domain assumption Lossless, reflectionless Huygens metasurface
    GSTC synthesis yields predominantly reactive susceptibilities and the unit cells show |T|>0.9, but losses and residual reflections are not included in the system-level spectral efficiency evaluation.
invented entities (1)
  • Virtual source at distance d_vs = d_ps/β
    purpose: Mathematical construct used to prescribe the target transmitted phase profile (Eq. (24)); not a physical radiator.
    The virtual source is a design fiction — no physical source exists there, and no falsifiable prediction is attached to it outside the metasurface design.

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Cite this review

Pith. "Pith review of Multi-User MIMO Enhancement using Metasurface Wavefront Bending (MWB)." pith.science (2026). https://pith.science/paper/UDFVCSRJ

@misc{pith2026260729542,
  author       = {Pith},
  title        = {Pith review of: Multi-User MIMO Enhancement using Metasurface Wavefront Bending (MWB)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UDFVCSRJ}},
  note         = {Machine review of arXiv:2607.29542}
}
read the original abstract

This paper introduces metasurface wavefront bending (MWB) to enhance spatial multiplexing in radiative nearfield multi-user multiple-input multiple-output (MU-MIMO) systems. By increasing spherical-wave curvature, MWB strengthens range-dependent phase variations across the receiver array, reduces inter-user channel correlation and improves user separability. The paper develops a curvature-dependent channel analysis, a generalized-sheet-transition-condition (GSTC) synthesisprocedure for MWB and a complete metasurface-assisted MUMIMO channel model. Both a practical common-profile scheme and an ideal user-specific benchmark are evaluated. The results demonstrate that MWB provides substantial improvements in spectral efficiency and effective channel rank. Finally, a threelayer transmissive Huygens metasurface architecture is proposed for physical implementation.

Figures

Figures reproduced from arXiv: 2607.29542 by the authors.

Figure 2
Figure 2. Illustration of wavefront bending (WFB) by a properly [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. The BS array is positioned in the x–y plane, with its center selected as the origin of a Cartesian coordinate system. The position of the nth BS element is denoted by rn = (xn, yn, 0), with n = 1, . . . , N. To isolate the effect of 2 [PITH_FULL_IMAGE:figures/full_fig_p002_4.png] view at source ↗
Figure 3
Figure 3. Perspective representation of the WFB metasurface in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Uplink MU-MIMO system without metasurface. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]
Figure 5
Figure 5. Figure 5: Curvature-dependent performance for two-user MIMO [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Metasurface wavefront bending (WFB) transformation [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 8
Figure 8. Figure 8: Local transmission coefficient [Eq. (34)] corresponding [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 7
Figure 7. Figure 7: GSTC-synthesized WFB metasurface susceptibilities [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 9
Figure 9. Figure 9: Metasurface assisted MU-MIMO system configuration. [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 10
Figure 10. Figure 10: Two-user MIMO performance for common-profile [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: Multi-user performance for the common-profile MWB scheme for different bending ratios [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 14
Figure 14. Figure 14: Effect of phase quantization on the common-profile [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]
Figure 12
Figure 12. Figure 12: Comparison of the multi-user performance achieved [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]
Figure 15
Figure 15. Figure 15: Metasurface scattering particle with generic variable [PITH_FULL_IMAGE:figures/full_fig_p011_15.png]
Figure 16
Figure 16. Figure 16: Simulated transmission responses of the eight three [PITH_FULL_IMAGE:figures/full_fig_p012_16.png]
Figure 17
Figure 17. Figure 17: Simulated transmission responses of the eight dog-bone unit cells under oblique incidence. The unit-cell architecture [PITH_FULL_IMAGE:figures/full_fig_p014_17.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

31 extracted references · 1 linked inside Pith

  1. [1]

    Noncooperative cellular wireless with unlimited num- bers of base station antennas,

    T. L. Marzetta, “Noncooperative cellular wireless with unlimited num- bers of base station antennas,”IEEE Trans. Wirel. Commun., vol. 9, no. 11, pp. 3590–3600, 2010

    2010

  2. [2]

    Towards 6G MIMO: Massive spatial multiplexing, dense arrays, and interplay between electromagnetics and processing,

    E. Bj ¨ornson, C.-B. Chae, R. W. Heath Jr, T. L. Marzetta, A. Mezghani, L. Sanguinetti, F. Rusek, M. R. Castellanos, D. Jun, and ¨O. T. Demir, “Towards 6G MIMO: Massive spatial multiplexing, dense arrays, and interplay between electromagnetics and processing,”arXiv preprint arXiv:2401.02844, 2024

    arXiv 2024

  3. [3]

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

    H. Lu, Y . Zeng, C. You, Y . Han, J. Zhang, Z. Wang, Z. Dong, S. Jin, C.-X. Wang, T. Jianget al., “A tutorial on near-field XL-MIMO communications toward 6G,”IEEE Commun. Surv. Tutor., vol. 26, no. 4, pp. 2213–2257, 2024

    2024

  4. [4]

    Near-field MIMO communications for 6G: Fundamentals, challenges, potentials, and future directions,

    M. Cui, Z. Wu, Y . Lu, X. Wei, and L. Dai, “Near-field MIMO communications for 6G: Fundamentals, challenges, potentials, and future directions,”IEEE Commun. Mag., vol. 61, no. 1, pp. 40–46, 2022

    2022

  5. [5]

    Analysis, rigor- ous design and characterization of a three-layer anisotropic transmitarray at 300 GHz,

    O. Koutsos, F. Manzillo, A. Clemente, and R. Sauleau, “Analysis, rigor- ous design and characterization of a three-layer anisotropic transmitarray at 300 GHz,”IEEE Trans. Antennas Propag., vol. 70, no. 7, pp. 5437– 5446, 2022

    2022

  6. [6]

    C. A. Balanis,Antenna Theory: Analysis and Design. John wiley & sons, 2016

    2016

  7. [7]

    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. Wirel. Commun., vol. 21, no. 6, pp. 4039–4053, 2022

    2022

  8. [8]

    Exploiting the depth and angular domains for massive near-field spatial multiplexing,

    P. Ramezani, A. Kosasih, A. Irshad, and E. Bj ¨ornson, “Exploiting the depth and angular domains for massive near-field spatial multiplexing,” IEEE BITS Inf. Theory Mag., vol. 3, no. 1, pp. 14–26, 2023

    2023

Show all 31 references
  1. [9]

    Beam focusing for near-field multiuser MIMO communications,

    H. Zhang, N. Shlezinger, F. Guidi, D. Dardari, M. F. Imani, and Y . C. Eldar, “Beam focusing for near-field multiuser MIMO communications,” IEEE Trans. Wirel. Commun., vol. 21, no. 9, pp. 7476–7490, 2022

    2022

  2. [10]

    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, 2023

    1918

  3. [11]

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

    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, 2022

    2022

  4. [12]

    A primer on near-field beamforming for arrays and reconfigurable intelligent surfaces,

    E. Bj ¨ornson, ¨O. T. Demir, and L. Sanguinetti, “A primer on near-field beamforming for arrays and reconfigurable intelligent surfaces,” in2021 55th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2021, pp. 105–112

    2021

  5. [13]

    On the study of reconfigurable intelligent surfaces in the near-field region,

    P. Mei, Y . Cai, K. Zhao, Z. Ying, G. F. Pedersen, X. Q. Lin, and S. Zhang, “On the study of reconfigurable intelligent surfaces in the near-field region,”IEEE Trans. Antennas Propag., vol. 70, no. 10, pp. 8718–8728, 2022

    2022

  6. [14]

    Near-field beamforming for stacked intelligent metasurfaces-assisted MIMO networks,

    A. Papazafeiropoulos, P. Kourtessis, S. Chatzinotas, D. I. Kaklamani, and I. S. Venieris, “Near-field beamforming for stacked intelligent metasurfaces-assisted MIMO networks,”IEEE Wirel. Commun. Lett., vol. 13, no. 11, pp. 3035–3039, 2024

    2024

  7. [15]

    A reconfigurable intelligent surface with surface-wave assisted beamforming capabilities,

    V . G. Ataloglou and G. V . Eleftheriades, “A reconfigurable intelligent surface with surface-wave assisted beamforming capabilities,”IEEE Trans. Antennas Propag., 2025

    2025

  8. [16]

    An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,

    C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,”IEEE Antennas Propag. Mag., vol. 54, no. 2, pp. 10–35, 2012

    2012

  9. [17]

    Synthesis of modulated-metasurface antennas with amplitude, phase, and polarization control,

    G. Minatti, F. Caminita, E. Martini, M. Sabbadini, and S. Maci, “Synthesis of modulated-metasurface antennas with amplitude, phase, and polarization control,”IEEE Trans. Antennas Propag., vol. 64, no. 9, pp. 3907–3919, 2016

    2016

  10. [18]

    Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead,

    M. Di Renzo, A. Zappone, M. Debbah, M.-S. Alouini, C. Yuen, J. De Rosny, and S. Tretyakov, “Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead,”IEEE J. Sel. Areas Commun., vol. 38, no. 11, pp. 2450–2525, 2020

    2020

  11. [19]

    Achouri and C

    K. Achouri and C. Caloz,Electromagnetic Metasurfaces: Theory and Applications. John Wiley & Sons, 2021

    2021

  12. [20]

    Thin planar metasurface lens for millimeter-wave MIMO applications,

    Z. Wani, M. P. Abegaonkar, and S. K. Koul, “Thin planar metasurface lens for millimeter-wave MIMO applications,”IEEE Trans. Antennas Propag., vol. 70, no. 1, pp. 692–696, 2021

    2021

  13. [21]

    General metasurface synthesis based on susceptibility tensors,

    K. Achouri, M. A. Salem, and C. Caloz, “General metasurface synthesis based on susceptibility tensors,”IEEE Trans. Antennas Propag., vol. 63, no. 7, pp. 2977–2991, 2015

    2015

  14. [22]

    Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,

    C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,”Phys. Rev. Lett, vol. 110, no. 19, p. 197401, 2013

    2013

  15. [23]

    Huygens’ metasurfaces via the equivalence principle: design and applications,

    A. Epstein and G. V . Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,”J. Opt. Soc. Am. B, vol. 33, no. 2, pp. A31–A50, 2016. 14

    2016

  16. [24]

    Massive MIMO networks: Spectral, energy, and hardware efficiency,

    E. Bj ¨ornson, J. Hoydis, and L. Sanguinetti, “Massive MIMO networks: Spectral, energy, and hardware efficiency,”Foundations and Trends ˆW in Signal Processing, vol. 11, no. 3-4, pp. 154–655, 2017

    2017

  17. [25]

    Tse and P

    D. Tse and P. Viswanath,Fundamentals of Wireless Communication. Cambridge university press, 2005

    2005

  18. [26]

    MMSE interference suppression for direct-sequence spread-spectrum CDMA,

    U. Madhow and M. L. Honig, “MMSE interference suppression for direct-sequence spread-spectrum CDMA,”IEEE Trans. Commun., vol. 42, no. 12, pp. 3178–3188, 1994

    1994

  19. [27]

    The effective rank: A measure of effective dimensionality,

    O. Roy and M. Vetterli, “The effective rank: A measure of effective dimensionality,” inProc. 15th Eur. Signal Process. Conf. (EUSIPCO),

  20. [28]

    M. P. Do Carmo,Differential Geometry of Curves and Surfaces. Courier Dover Publications, 2016

    2016

  21. [29]

    A study on characterization of near-field sub-regions for phased-array antennas,

    M. Monemi, S. Bahrami, M. Rasti, and M. Latva-aho, “A study on characterization of near-field sub-regions for phased-array antennas,” IEEE Trans. Commun., vol. 73, no. 5, pp. 2964–2979, 2024

    2024

  22. [30]

    Born and E

    M. Born and E. Wolf,Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Elsevier, 2013. 15

    2013

  23. [2007]

    IEEE, 2007, pp. 606–610

    2007

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