Near-field Physical Layer Security: Robust Beamforming under Location Uncertainty

Changsheng You; Chao Zhou; Chengwen Xing; Cong Zhou; Jianhua Zhang

REVIEW 3 major objections 5 minor 32 references

Near-field Physical Layer Security: Robust Beamforming under Location Uncertainty

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read Infinite near-field secrecy constraints can be reduced to a finite set of 4-by-4 matrix inequalities by partitioning the eavesdropper's location-uncertainty region and linearizing the near-field steering vector around each sub-region's surr

desk verdict Clever partition-and-refined-LMI idea with a real angular-error amplification insight, but the worst-case secrecy guarantee does not follow as written — the ellipsoid in Prop. 3 is an inner approximation of the actual uncertainty region. read the letter →

arxiv 2601.13549 v1 pith:DQRS2VK7 submitted 2026-01-20 eess.SP cs.ITmath.IT

Chao Zhou , Changsheng You , Cong Zhou , Chengwen Xing , Jianhua Zhang This is my paper · ORCID

classification eess.SPcs.ITmath.IT

keywords near-fieldcommunicationsphysicallayersecurityrobustbeamforminglocationuncertaintyextremelylarge-scalearrayslinearmatrixinequalitiesTaylorapproximationangularerroramplification

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

Extremely large antenna arrays create near-field spherical wavefronts that let a base station focus signals in both angle and range, but they also make secure beamforming fragile: small errors in an eavesdropper's location produce large angle errors, and conventional robust designs either fail to guarantee secrecy or drain the transmit power. The paper claims that this fragility can be overcome by partitioning the eavesdropper's location-uncertainty region into fan-shaped sub-regions and using a first-order Taylor expansion of the near-field steering vector around a surrogate location in each sub-region. Under conditions that make the Taylor approximation accurate, the infinite family of worst-case eavesdropping-rate constraints is recast as a finite set of deterministic 4-by-4 linear matrix inequalities, with complexity independent of the array size. The paper argues this yields a superior trade-off between sum-rate and secrecy robustness and carries over to multiple users and multiple eavesdroppers.

What carries the argument

The engine is the near-field steering vector a(θ,r) with Fresnel phase approximation, together with its gradient matrix J_s = [∇_r a, ∇_θ a] at a surrogate location. The paper combines three tools: (1) Proposition 2's accuracy conditions (Δr/r̂ ≤ 0.1 and sin(θ̂+Δθ)−sin θ̂ ≤ 1/(2N)) that justify the linearization; (2) the fan-shaped partition of the uncertainty region into 2S+1 sub-regions, each with a surrogate location and a bounding ellipse Σ_s for the range–angle error; and (3) the GSD lemma applied to convert the worst-case quadratic constraint into the 4×4 LMI (40). The argument works because the partition makes the linearization uniform, so the only uncertainty that survives in each su

What would settle it

Run the proposed algorithm for a small array (e.g., N=16) with an eavesdropper whose uncertainty region straddles a sub-region corner, then compute the exact worst-case leakage max_{q∈A_E} |a(q)^H w|² by dense grid sampling and compare it with the threshold Γ; a violation at any grid point while all 4×4 LMIs hold would falsify the claim that the LMI reformulation enforces the original security constraint.

Watch

Extended reading notes

Core claim

The central claim is that the near-field steering vector a(θ,r) can be locally linearized as a(φ_s, r_s) + J_s ζ_s in each partitioned sub-region, where ζ_s is a 2-dimensional range–angle error vector bounded by an ellipsoid Σ_s. Recasting the worst-case leakage constraint |w^H (a(φ_s,r_s)+J_s ζ_s)|² ≤ Γ for all ζ_s^T Σ_s^{-1} ζ_s ≤ 1, the general sign-definiteness lemma transforms this infinite family into 2S+1 LMIs of size 4 (Proposition 3). The structural discovery is that the LMI dimension drops from N+2 (the error-bound method, which characterizes the N-dimensional steering-vector error) to 4 (the two-dimensional physical error), making robust near-field beamforming affordable for extre

Load-bearing premise

The whole guarantee rests on the claim that after partitioning, the first-order Taylor residual is negligible everywhere in each sub-region; the proof of that claim itself uses the same small-angle linearization, and the optimization never bounds the residual.

Editorial extensions

If this is right

Robust near-field PLS beamforming scales to extremely large arrays: per iteration the algorithm needs only 4×4 LMIs and one SOC constraint, independent of the number of antennas.
Secrecy robustness is no longer bought by collapsing transmit power; the proposed beamformer shapes the leakage pattern over the whole uncertainty region instead of inflating an error bound.
The method extends to K Bobs and M Eves, with one 4×4 LMI per (Bob, Eve, sub-region) triple, covering multi-user secure networks.
The accuracy conditions give an explicit recipe to set the number of sub-regions from N and the uncertainty radius, making the robustness–rate trade-off tunable.

Reading between the lines

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

The paper proves the reformulation is exact under the Taylor assumption but never quantifies the residual; a testable extension is to fold a worst-case second-order residual bound into the LMI as slack, converting the heuristic guarantee into a certified one.
The same partition-and-linearize template likely applies to other near-field problems with location uncertainty—ISAC beam tracking, near-field localization, and near-field NOMA—where the physical error dimension is also two.
The angular-error amplification effect suggests a design maxim beyond this paper: near-field robust designs should treat uncertainty in polar coordinates rather than in Cartesian CSI error, because the mapping between them is strongly anisotropic.
One concrete stress test is near sub-region corners: if secure transmission probability dips at the fan boundaries, the partition should be refined adaptively rather than uniformly.

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

The angular-error amplification effect (close Eves turn small position errors into large angle errors) is a genuine and useful observation, and the two-stage idea — partition the location-uncertainty region into fan subregions sized by the 1/(2N) Taylor-accuracy condition, then apply a 4x4 LMI per subregion — is a real step beyond the N-dimensional error-bound LMI used in prior work. The complexity reduction and the numerical results (rates near the sampling benchmark without the transmit-power collapse) are attractive.

But the stress-test note is correct, and it lands on a load-bearing step. Prop. 3 replaces the constraint over the rectangle A_s (or the actual ball intersection) with a constraint over the ellipse ζ_s^T Σ_s^{-1} ζ_s ≤ 1. That ellipse is inscribed in the rectangle, not a superset. A point at the angular boundary and range boundary of a subregion can lie in the original uncertainty ball but outside the ellipse, so satisfying the LMI (40) does not guarantee the worst-case leakage constraint (17b). This is not a Taylor-residual issue; it is a mismatch between the uncertainty set used in the reformulation and the one in the problem statement. The authors would need an outer ellipsoid (e.g., scaled by √2) or an additional argument to actually bound the eavesdropping rate over A_s.

Prop. 2's proof is also partly circular: Appendix E approximates sinθ - sinθ̂ ≈ cosθ̂Δθ inside the residual bound, so the “accuracy condition” is not independently established. The Taylor residual itself is never bounded in the optimization, so even if the ellipsoid issue were fixed, the guarantee would still be approximate unless a residual term is added.

The “secure transmission probability of 1” claim is conditioned on the 95% ball, but the design does not theoretically guarantee even that ball; the Monte Carlo metric is undefined. On the minor side, the reader's block-size worry about b_s^(r) is unfounded — b_s^(r) is a 2-vector, so the 4x4 claim holds.

Who gets value: researchers in near-field PLS and robust beamforming will find the angular-error amplification and partition heuristic worth reading. The central worst-case guarantee, however, is not proven as written. This deserves peer review with major revision — the fixes are local (use an outer approximation, quantify the residual, state the guarantee as approximate) but they are necessary before the main claim can be taken at face value.

Referee Report

3 major / 5 minor

Summary. The paper studies robust beamforming for near-field physical-layer security under imperfect Eve location information. The authors formulate a worst-case sum-rate maximization problem with a constraint on the maximum eavesdropping rate over a bounded location-uncertainty region. They first reveal a near-field angular-error amplification effect, then propose a two-stage method: (i) partition the uncertainty region into fan-shaped sub-regions in which a first-order Taylor approximation of the near-field steering vector is asserted to be accurate; (ii) apply the general sign-definiteness (GSD) lemma to convert the infinite worst-case secrecy constraints into 2S+1 deterministic 4×4 LMIs, yielding a convex SCA algorithm. The method is extended to multiple Bobs/Eves and to multi-path scenarios. Numerical results claim a superior trade-off between rate and robustness compared with sampling-based and error-bound-based benchmarks.

Significance. If the two-stage LMI reformulation were valid, this would be a valuable contribution: it addresses the practical and difficult scenario of Eve location uncertainty in near-field XL-array systems, and it proposes a complexity reduction from N-dimensional LMIs to 4×4 LMIs, avoiding the transmit-power collapse of error-bound methods. The angular-error amplification insight and the uncertainty-partitioning idea are conceptually interesting. However, the central reformulation contains a logical gap that undermines the worst-case guarantee, and the Taylor-accuracy proof is not rigorous. The significance is therefore conditional on substantial revision.

major comments (3)

[Section III-B2, Proposition 3, Eqs. (38)-(40)] The reformulation of the worst-case constraint (38) over the fan-shaped sub-region A_s as the ellipsoidal constraint (39) is not valid. A_s is a rectangle in (θ,r) and, in the local polar coordinates around the surrogate, the uncertainty set from the Cartesian ball is approximately the ellipse Δr^2 + (r̂Δφ)^2 ≤ Υ^2. The ellipsoid in (39), ζ_s^T Σ_s^{-1}ζ_s ≤ 1 with Σ_s = diag(ϵ_s^2, ϑ_s^2), is inscribed in that rectangle, not a superset. For a central sub-region, ϵ_s ≈ Υ and ϑ_s ≈ 1/(2N), which is typically much smaller than Υ/r̂. A point on the boundary of the original ball with Δφ=ϑ_s has Δr ≈ sqrt(Υ^2 − (r̂ϑ_s)^2) ≈ Υ, so (Δr/ϵ_s)^2 + (Δφ/ϑ_s)^2 ≈ 2 > 1. Such a point lies in A_s and in the original uncertainty ball but is outside the ellipsoid. Consequently, a beamformer satisfying the LMIs (40) can violate the worst-case eavesdropping constraint (17b). This is a load-bearing error in
[Proposition 2 / Appendix E] The proof that the first-order Taylor approximation is 'largely accurate' under Δr/r̂ ≤ 0.1 and sinθ_E − sinθ̂ ≤ 1/(2N) is circular. Steps (e)-(g) in Appendix E use the same small-angle linearization (e.g., sinθ_E − sinθ̂ ≈ cosθ̂ Δθ) and small-range assumptions to show the residual is negligible; they do not bound the second-order remainder. No quantitative upper bound on ||Δa_E||_2 is provided. Thus the worst-case constraint (38) may be violated even if the LMI (40) is satisfied, because the Taylor approximation is not guaranteed to be accurate at all points of the sub-region, especially at corners or for smaller N. A rigorous error bound is needed to support the claimed guarantee.
[Section V, Figs. 7 and 10] The 'secure transmission probability' metric is not defined in the manuscript. If it is computed by Monte Carlo sampling of Eve locations, it does not validate the worst-case constraint (17b); a sampled probability of 1 is not a guarantee. The numerical results should be accompanied by a definition of this metric and, ideally, a separate check of the worst-case constraint on a dense grid or via an exact worst-case computation.

minor comments (5)

[Section III-B2, Eq. (40) and Section IV, Eq. (47)] The block structure of H_s and H_{m,k,s_m} is ambiguous. Read as a 4×4 block matrix with b_s^(r) and b_s^(θ) as 2×1 blocks, the dimension is 4, not 6. However, the notation 'b_s^(r) = [∇_r a^H w, 0]^H' is confusing; it should be written with parentheses, e.g., [(∇_r a)^H w, 0]^H, and it should be clarified that the second row of the top-right block is zero.
[Section II-D, Eq. (15)] The confidence level α is introduced but its choice and effect are not discussed. A short remark on how α relates to the practical guarantee would be useful.
[Section V-A] In Fig. 10, the x-axis label says 'location error' but the caption says 'versus location error'; the caption in Fig. 11 says 'versus power ratio'. Please ensure the axes and captions are consistent.
[Appendix A] The proof of Proposition 1 uses a determinant argument but is not fully rigorous; in particular, the step 'det(A B; C D) = det(A) det(D − C A^{-1} B)' requires A to be invertible, which is not guaranteed. A cleaner proof via Schur complement is recommended.
[References] Reference [18] is an arXiv preprint; if it has been published in the interim, please update. Also, reference [1] is cited for XL-array transceiver technologies; consider citing a more specific work on near-field XL-array systems in the introduction.

Circularity Check

1 steps flagged · score 3.0 of 10

Partial circularity in the Taylor-accuracy proposition; the LMI reformulation itself is not circular.

other [Appendix E, Eq. (56), supporting Proposition 2 (Section III-B1)]
"2R{a^H(θ_E,r̂)∇_θ a|(θ̂,r̂)Δθ_E} ... (f)≈2R{ (j/N)Σ e^{j(2π/λ)u_n cosθ̂Δθ_E} · (2π/λ)u_n cosθ̂Δθ_E } (g)≈2Σ(2π/λ u_n cosθ̂Δθ_E)^2/N = 2ε^2_{θ,Tayl}, (56)"

Proposition 2 aims to prove that the first-order CSV Taylor expansion is accurate, i.e., ∥Δa_θ∥₂²≈0. Its proof in Appendix E computes the inner product in (56) by first replacing sinθ_E−sinθ̂ with its first-order approximation cosθ̂Δθ_E and then replacing the phase exponential e^{jx} with 1. These are exactly the linearizations whose accuracy is at issue. Forcing the cross term to equal 2ε²_{θ,Tayl} makes the residual vanish by construction rather than by a quantified second-order remainder bound. The range-domain residual is deferred ('details omitted for brevity'). Thus the accuracy claim is partly self-supporting, although the 1/(2N) cutoff itself has independent support from Lemma 2.

full rationale

Most of the derivation chain is self-contained. The Cartesian-to-polar uncertainty bounds (16), the fan-shaped partition, and the range intersections (35) come from exact geometry. Lemmas 1–2 derive the 1/(2N) mainlobe threshold from exact CSV inner products, not from the Taylor surrogate. Proposition 3/Appendix F then converts the per-subregion box bounds |Δr_s|≤ε_s, |Δφ_s|≤ϑ_s into the 4×4 LMIs via the GSD lemma, which is an external tool, and the numerical benchmarks are external prior-art schemes. Self-citations ([1], [18], [32]) are background/convergence items and are not load-bearing. The only genuinely circular content is in Proposition 2's proof: Appendix E establishes that the first-order Taylor residual is small by using the same first-order linearization of the phase factors, so Eq. (56) and the resulting ∥Δa_θ∥₂²≈0 are forced by construction rather than bounded. This weakens the 'Taylor approximation is largely accurate' precondition for the whole two-stage method, but it does not make the LMI reformulation itself circular. The Proposition 3 ellipsoid/box mismatch is a reformulation-sufficiency/correctness concern rather than a by-construction circularity, and Remark 4's deferral of Bob-location uncertainty is a scope limitation, not a circular step. Overall, partial circularity, confined to one load-bearing accuracy lemma, giving a moderate score.

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

No new physical entities are postulated; the "fan-shaped sub-regions" are algorithmic constructs. The load-bearing assumptions are the Fresnel/LoS channel model, the Gaussian location-error model, and the GSD/SCA machinery taken from cited prior work. The hand-chosen thresholds 0.1·r̂ and 1/(2N) shape the validity region of the central Taylor-accuracy claim.

free parameters (4)

Taylor-accuracy range threshold (Δr/r̂ ≤ 0.1) = 0.1
Hand-chosen in Lemma 1/Prop. 2 to declare the range-domain linearization accurate; the method's validity region and subregion design depend on it.
Taylor-accuracy angle threshold S_θ = 1/(2N) = 1/(2N) ≈ 0.00195 for N=256
Eq. (32). Derived from the Dirichlet-kernel analysis in Lemma 2, but the exact cutoff where the Taylor fit is declared accurate is a modeling choice that sets the number of fan subregions and hence the complexity.
Uncertainty-region confidence α = 0.05 (95% ball, Υ = σ_c√χ²_{0.95}(2) ≈ 2.448σ_c)
Eq. (15). Design choice inherited from [29]; ties the "worst-case" guarantee to a probability over the Gaussian location-error model.
NLoS-to-LoS power ratio κ_{E,m} = simulated over a range
Remark 3 / Eq. (49). Scenario parameter controlling the conservative NLoS bound; not fitted but load-bearing for the multi-path extension and Fig. 11.

assumptions (6)

domain assumption Fresnel (parabolic) approximation of distances, Eq. (3)
Underlies the CSV model (5); standard in XL-array near-field literature [2] but an approximation that limits the accuracy of the whole chain.
domain assumption LoS-dominant single-path channel for Eves and Bobs, Eqs. (1),(6)
High-frequency band justification; NLoS power is only handled as a bound in Remark 3, while the main results and simulations assume LoS-only channels.
domain assumption Gaussian location error with known zero-mean covariance, Eq. (10)
Inherited from non-cooperative localization [27],[28]; the entire uncertainty model (15)-(16) and the angular-amplification effect depend on it.
domain assumption Eves cancel all multi-user interference, Eq. (14)
Worst-case assumption from [16],[18]; converts secrecy constraints into per-stream null constraints.
standard math General sign-definiteness (GSD) lemma and its LMI reformulation, Eqs. (22)/(40)
Cited from [13] and used without proof for the core constraint transformation.
standard math Fixed-point iteration / SCA convergence of the concave surrogate, Eq. (43)
Standard SCA argument [32]; convergence claimed in Remark 2.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Near-field Physical Layer Security: Robust Beamforming under Location Uncertainty." pith.science (2026). https://pith.science/paper/DQRS2VK7

@misc{pith2026260113549,
  author       = {Pith},
  title        = {Pith review of: Near-field Physical Layer Security: Robust Beamforming under Location Uncertainty},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DQRS2VK7}},
  note         = {Machine review of arXiv:2601.13549}
}

read the original abstract

In this paper, we study robust beamforming design for near-field physical-layer-security (PLS) systems, where a base station (BS) equipped with an extremely large-scale array (XL-array) serves multiple near-field legitimate users (Bobs) in the presence of multiple near-field eavesdroppers (Eves). Unlike existing works that mostly assume perfect channel state information (CSI) or location information of Eves, we consider a more practical and challenging scenario, where the locations of Bobs are perfectly known, while only imperfect location information of Eves is available at the BS. We first formulate a robust optimization problem to maximize the sum-rate of Bobs while guaranteeing a worst-case limit on the eavesdropping rate under location uncertainty. By transforming Cartesian position errors into the polar domain, we reveal an important near-field angular-error amplification effect: for the same location error, the closer the Eve, the larger the angle error, severely degrading the performance of conventional robust beamforming methods based on imperfect channel state information. To address this issue, we first establish the conditions for which the first-order Taylor approximation of the near-field channel steering vector under location uncertainty is largely accurate. Then, we propose a two-stage robust beamforming method, which first partitions the uncertainty region into multiple fan-shaped sub-regions, followed by the second stage to formulate and solve a refined linear-matrix-inequality (LMI)-based robust beamforming optimization problem. In addition, the proposed method is further extended to scenarios with multiple Bobs and multiple Eves. Finally, numerical results validate that the proposed method achieves a superior trade-off between rate performance and secrecy robustness, hence significantly outperforming existing benchmarks under Eve location uncertainty.

Figures

Figures reproduced from arXiv: 2601.13549 by the authors.

**Figure 2.** Schematic of near-field angular-error amplification. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 5.** Schematic of the sub-region partitioning. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

Figures from the paper (5 more)

**Figure 6.** Figure 6: Beam patterns of different methods. much higher secure transmission rate. Proposition 3 (Refined LMI reformulation). Based on the Taylor approximation of CSV in (20), constraint (38) can be rewritten as max ζT s Σ−1 s ζs≤1, ∀s∈S [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: Achievable rate and secure transmission probability [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: Achievable sum-rate versus iteration number. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: Beam pattern of the proposed scheme. errors σc,1 = σc,2 = σc = 0.1 m. The Bobs are randomly distributed within a circular region of radius ΥB = 3 m, which is centered at (50, 0) m. Unless otherwise specified, the system parameters are set as Pmax = 1 W, Rmax = 1 bps/Hz…

**Figure 10.** Figure 10: Achievable rate and secure transmission probability [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references · 3 linked inside Pith

[1]

Next generation advanced transceiver technologies for 6G and beyond,

C. Youet al., “Next generation advanced transceiver technologies for 6G and beyond,”IEEE J. Sel. Areas Commun., vol. 43, no. 3, pp. 582–627, Mar. 2025

2025
[2]

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, Apr. 2022

2022
[3]

Channel measurement, modeling, and simulation for 6G: A survey and tutorial,

J. Zhanget al., “Channel measurement, modeling, and simulation for 6G: A survey and tutorial,”arXiv preprint arXiv:2305.16616, 2023

arXiv 2023
[4]

Sub-6 GHz to mmWave for 5G-advanced and beyond: Channel measurements, characteristics and impact on system perfor- mance,

H. Miaoet al., “Sub-6 GHz to mmWave for 5G-advanced and beyond: Channel measurements, characteristics and impact on system perfor- mance,”IEEE J. Sel. Areas Commun., vol. 41, no. 6, pp. 1945–1960, Jun. 2023

1945
[5]

Spatial non-stationary near-field channel modeling and validation for massive MIMO systems,

Z. Yuanet al., “Spatial non-stationary near-field channel modeling and validation for massive MIMO systems,”IEEE Trans. Antennas Propag., vol. 71, no. 1, pp. 921–933, Jan. 2022

2022
[6]

Physical layer security in near-field communications,

Z. Zhang, Y . Liu, Z. Wang, X. Mu, and J. Chen, “Physical layer security in near-field communications,”IEEE Trans. Veh. Technol., vol. 73, no. 7, pp. 10 761–10 766, Jul. 2024

2024
[7]

Near-field integrated sensing and communication: Opportunities and challenges,

J. Conget al., “Near-field integrated sensing and communication: Opportunities and challenges,”IEEE Wireless Commun., vol. 31, no. 6, pp. 162–169, Dec. 2024

2024
[8]

Unveiling the potential of NOMA: A journey to next generation multiple access,

A. Ahmedet al., “Unveiling the potential of NOMA: A journey to next generation multiple access,”IEEE Commun. Surv. Tut., pp. 1–1, 2024

2024

Show all 32 references

[9]

The wire-tap channel,

A. D. Wyner, “The wire-tap channel,”Bell Syst. Tech. J., vol. 54, no. 8, pp. 1355–1387, 1975

1975
[10]

Secure precoding aided spatial modulation via transmit antenna selection,

Y . Huang, M. Wen, B. Zheng, X. Cheng, L. Yang, and F. Ji, “Secure precoding aided spatial modulation via transmit antenna selection,”IEEE Trans. Veh. Technol., vol. 68, no. 9, pp. 8893–8905, Sep. 2019

2019
[11]

New viewpoint and algorithms for water-filling solutions in wireless communications,

C. Xing, Y . Jing, S. Wang, S. Ma, and H. V . Poor, “New viewpoint and algorithms for water-filling solutions in wireless communications,” IEEE Trans. Signal Process., vol. 68, pp. 1618–1634, Feb. 2020

2020
[12]

Intelligent reflecting surface-enabled anti-detection for secure sensing and communications,

B. Zhenget al., “Intelligent reflecting surface-enabled anti-detection for secure sensing and communications,”IEEE Wireless Commun., vol. 32, no. 2, pp. 156–163, Apr. 2025

2025
[13]

A framework of robust transmission design for IRS- aided MISO communications with imperfect cascaded channels,

G. Zhouet al., “A framework of robust transmission design for IRS- aided MISO communications with imperfect cascaded channels,”IEEE Trans. Signal Process, vol. 68, pp. 5092–5106, 2020

2020
[14]

Secrecy-energy efficient hybrid beamforming for satellite- terrestrial integrated networks,

Z. Linet al., “Secrecy-energy efficient hybrid beamforming for satellite- terrestrial integrated networks,”IEEE Trans. Commun., vol. 69, no. 9, pp. 6345–6360, Sep. 2021

2021
[15]

Robust transmit and reflect beamforming design for IRS- assisted offshore NOMA communication systems,

K. Liet al., “Robust transmit and reflect beamforming design for IRS- assisted offshore NOMA communication systems,”IEEE Trans. Veh. Technol., vol. 73, no. 1, pp. 783–798, Jan. 2023

2023
[16]

Robust and secure wireless communications via intelligent reflecting surfaces,

X. Yu, D. Xu, Y . Sun, D. W. K. Ng, and R. Schober, “Robust and secure wireless communications via intelligent reflecting surfaces,”IEEE J. Sel. Areas Commun., vol. 38, no. 11, pp. 2637–2652, Nov. 2020

2020
[17]

New mid-band for 6G: Several considerations from the channel propagation characteristics perspective,

J. Zhanget al., “New mid-band for 6G: Several considerations from the channel propagation characteristics perspective,”IEEE Commun. Mag., vol. 63, no. 1, pp. 175–180, Jan. 2024

2024
[18]

Performance analysis and low-complexity beamforming design for near-field physical layer security,

Y . Zhang, Y . Fang, C. You, Y .-J. A. Zhang, and H. C. So, “Performance analysis and low-complexity beamforming design for near-field physical layer security,”arXiv preprint arXiv:2407.13491, 2024

2024 arXiv
[19]

Physical layer security for near-field communications via directional modulation,

J. Chen, Y . Xiao, K. Liu, Y . Zhong, X. Lei, and M. Xiao, “Physical layer security for near-field communications via directional modulation,” IEEE Trans. Veh. Technol., vol. 73, no. 8, pp. 12 242–12 246, Aug. 2024

2024
[20]

Near-field wideband secure communications: An analog beamfocusing approach,

Y . Zhang, H. Zhang, S. Xiao, W. Tang, and Y . C. Eldar, “Near-field wideband secure communications: An analog beamfocusing approach,” IEEE Trans. Signal Process, vol. 72, pp. 2173–2187, 2024

2024
[21]

Physical-layer security in mixed near-field and far-field communication systems,

T. Liuet al., “Physical-layer security in mixed near-field and far-field communication systems,”arXiv preprint arXiv:2504.19555, 2025

2025 arXiv
[22]

Robust beamfocusing for secure NFC with imperfect CSI,

W. Chen, Z. Wei, and Z. Yang, “Robust beamfocusing for secure NFC with imperfect CSI,”Sensors, vol. 25, no. 4, p. 1240, 2025

2025
[23]

Robust beamforming design for secure near-field ISAC systems,

Z. Chen, F. Wang, G. Han, X. Wang, and V . K. N. Lau, “Robust beamforming design for secure near-field ISAC systems,”IEEE Wireless Commun. Lett., pp. 1–1, 2025

2025
[24]

Location-driven beam- forming for RIS-assisted near-field communications,

X. Zheng, W. Cheng, J. Wang, and W. Zhang, “Location-driven beam- forming for RIS-assisted near-field communications,”IEEE Commun. Mag., vol. 63, no. 1, pp. 44–50, Jan. 2025

2025
[25]

Robust beamforming design for near-field DMA-NOMA mmwave communications with imperfect position information,

Y . Xiuet al., “Robust beamforming design for near-field DMA-NOMA mmwave communications with imperfect position information,”IEEE Trans. Wireless Commun., vol. 24, no. 2, pp. 1678–1692, Feb. 2025

2025
[26]

A tutorial on MIMO-OFDM ISAC: From far-field to near-field,

Q. Daiet al., “A tutorial on MIMO-OFDM ISAC: From far-field to near-field,”arXiv preprint arXiv:2504.19091, 2025

2025
[27]

RIS-assisted robust hybrid beamforming against simul- taneous jamming and eavesdropping attacks,

Y . Sunet al., “RIS-assisted robust hybrid beamforming against simul- taneous jamming and eavesdropping attacks,”IEEE Trans. Wireless Commun., vol. 21, no. 11, pp. 9212–9231, Nov. 2022

2022
[28]

Location-based secure transmission for wiretap channels,

C. Liu, N. Yang, J. Yuan, and R. Malaney, “Location-based secure transmission for wiretap channels,”IEEE J. Sel. Areas Commun., vol. 33, no. 7, pp. 1458–1470, Jul. 2015

2015
[29]

Altman, D

D. Altman, D. Machin, T. Bryant, and M. Gardner,Statistics with confidence: confidence intervals and statistical guidelines. London, UK: BMJ Books, 2000

2000
[30]

Optimal sampling in spherical near-field antenna measurements by utilizing the information content of spherical wave harmonics,

H. R. Behjoo, A. Pirhadi, and R. Asvadi, “Optimal sampling in spherical near-field antenna measurements by utilizing the information content of spherical wave harmonics,”IEEE Trans. Antennas Propag., vol. 70, no. 5, pp. 3762–3771, May 2022

2022
[31]

A new approach to robust beamforming in the presence of steering vector errors,

M. H. Er and B. Ng, “A new approach to robust beamforming in the presence of steering vector errors,”IEEE Trans. Signal Process, vol. 42, no. 7, pp. 1826–1829, Jul. 1994

1994
[32]

Transmit power minimiza- tion for STAR-RIS empowered symbiotic radio communications,

C. Zhou, B. Lyu, Y . Feng, and D. T. Hoang, “Transmit power minimiza- tion for STAR-RIS empowered symbiotic radio communications,”IEEE Trans. Cogn. Commun. Netw., vol. 9, no. 6, pp. 1641–1656, Dec. 2023

2023

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

Next generation advanced transceiver technologies for 6G and beyond,

C. Youet al., “Next generation advanced transceiver technologies for 6G and beyond,”IEEE J. Sel. Areas Commun., vol. 43, no. 3, pp. 582–627, Mar. 2025

2025

[2] [2]

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, Apr. 2022

2022

[3] [3]

Channel measurement, modeling, and simulation for 6G: A survey and tutorial,

J. Zhanget al., “Channel measurement, modeling, and simulation for 6G: A survey and tutorial,”arXiv preprint arXiv:2305.16616, 2023

arXiv 2023

[4] [4]

Sub-6 GHz to mmWave for 5G-advanced and beyond: Channel measurements, characteristics and impact on system perfor- mance,

H. Miaoet al., “Sub-6 GHz to mmWave for 5G-advanced and beyond: Channel measurements, characteristics and impact on system perfor- mance,”IEEE J. Sel. Areas Commun., vol. 41, no. 6, pp. 1945–1960, Jun. 2023

1945

[5] [5]

Spatial non-stationary near-field channel modeling and validation for massive MIMO systems,

Z. Yuanet al., “Spatial non-stationary near-field channel modeling and validation for massive MIMO systems,”IEEE Trans. Antennas Propag., vol. 71, no. 1, pp. 921–933, Jan. 2022

2022

[6] [6]

Physical layer security in near-field communications,

Z. Zhang, Y . Liu, Z. Wang, X. Mu, and J. Chen, “Physical layer security in near-field communications,”IEEE Trans. Veh. Technol., vol. 73, no. 7, pp. 10 761–10 766, Jul. 2024

2024

[7] [7]

Near-field integrated sensing and communication: Opportunities and challenges,

J. Conget al., “Near-field integrated sensing and communication: Opportunities and challenges,”IEEE Wireless Commun., vol. 31, no. 6, pp. 162–169, Dec. 2024

2024

[8] [8]

Unveiling the potential of NOMA: A journey to next generation multiple access,

A. Ahmedet al., “Unveiling the potential of NOMA: A journey to next generation multiple access,”IEEE Commun. Surv. Tut., pp. 1–1, 2024

2024