Physical-Layer Security in Mixed Near-Field and Far-Field Communication Systems

Changsheng You; Cong Zhou; Guangchi Zhang; Heng Liu; Shiqi Gong; Tianyu Liu; Yunpu Zhang

REVIEW 3 major objections 5 minor 1 cited by

Physical-Layer Security in Mixed Near-Field and Far-Field Communication Systems

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper claims that in a mixed near-field/far-field system, a far-field user's insecure-transmission region is distinctly expanded relative to far-field-only systems, because near-field eavesdroppers capture energy that a far-field…

desk verdict A genuinely new mixed near-far field PLS scenario with a plausible central claim, but the key closed-form boundary leans on an unproven Fresnel approximation that the authors should be asked to justify. read the letter →

arxiv 2504.19555 v2 pith:744PK5UC submitted 2025-04-28 eess.SP

Tianyu Liu , Changsheng You , Cong Zhou , Yunpu Zhang , Shiqi Gong , Heng Liu , Guangchi Zhang This is my paper · ORCID

classification eess.SP

keywords physicallayersecuritymixednear-fieldandfar-fieldextremelylarge-scalearrayinsecure-transmissionregionenergy-spreadeffectpowerallocationsuccessiveconvexapproximationFresnelintegrals

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 considers a security setup in which a base station equipped with an extremely large array serves legitimate users in the far field while eavesdroppers sit in the near field. It claims that, because a far-field beam spreads its energy across the near-field region, a near-field eavesdropper can intercept the signal intended for a far-field user even when the eavesdropper is not at the same angle as that user. For one user and one eavesdropper, the paper gives a closed-form description of the insecure-transmission region and shows it is much larger than the region predicted by conventional far-field analysis. It then shows that with two users the signal destined for the second user acts as useful interference at the eavesdropper, shrinking the insecure region and improving the sum-secrecy-rate, and it provides an algorithm for power allocation in the general multi-user case. If the analysis is right, far-field-only security models are optimistic for extremely large arrays.

What carries the argument

The load-bearing object is the mixed-field correlation function $\eta(\theta_q; \theta_p, r_p) = |\mathbf{b}^H(\theta_p, r_p)\mathbf{a}(\theta_q)|$, the absolute inner product between a near-field steering vector and a far-field steering vector. Lemma 2 approximates this correlation by $G(\beta_1,\beta_2)$, an expression built from Fresnel integrals, with $\beta_1$ capturing the angular difference and $\beta_2$ the Eve's location; this converts the secure-transmission condition $\eta^2 < r_E^2/r_B^2$ into the angular interval of Proposition 1. The effective Rayleigh distance $Z$ supplies the distance boundary that separates the near-field region, where the eavesdropper sits, from the far-field region, where the legitimate users sit.

What would settle it

Compute the exact correlation $\eta = |\mathbf{b}^H(\theta_E,r_E)\mathbf{a}(\theta_B)|$ by direct summation of the $N$ antenna terms for the parameters in Example 1 ($N=256$, $f=30$ GHz, Eve at $(0\ \text{rad}, 10\ \text{m})$), and compare the boundary where $\eta = r_E/r_B$ with the boundary predicted by Proposition 1; a substantial mismatch in the angular interval would falsify the claimed expansion.

Watch

Extended reading notes

Core claim

The central claim is that in a mixed near-field/far-field system the insecure-transmission region of a far-field Bob takes the form of an angular interval around the Eve's angle, combined with the condition that the Bob lies beyond the effective Rayleigh distance. For a fixed Eve at $(\theta_E, r_E)$, a Bob at angle $\theta_B$ and distance $r_B$ is insecure when the mixed-field correlation $\eta = |\mathbf{b}^H(\theta_E, r_E)\mathbf{a}(\theta_B)|$ satisfies $\eta \ge r_E/r_B$, which Proposition 1 converts into the interval given by the two roots of the Fresnel-integral approximation $G(\beta_1,\beta_2) = r_E/r_B$. This region is significantly larger than in far-field-only systems, where insecurity essentially requires Bob and Eve to share the same spatial angle. The two-Bob extension shows that the interference from another Bob at the Eve can make the inequality harder to satisfy, thereby reducing the insecure region.

Load-bearing premise

Everything rests on the unproved approximation that the overlap between a near-field beam and a far-field beam is accurately given by the Fresnel-integral formula $G(\beta_1,\beta_2)$; if that formula is off for the distances and angles considered, the size and even the existence of the expanded insecure region could change.

Editorial extensions

If this is right

In a mixed-field system with one Bob and one Eve, a far-field Bob whose angle differs from the Eve's by up to a threshold (which grows with the Eve's proximity and the Bob's distance) cannot achieve secure transmission, so far-field-only security analyses underestimate the threat.
The insecure angular region shrinks when the Eve moves away from the boresight or farther from the base station, and it expands when the Bob is more distant, because the energy-spread effect is stronger in those regimes.
With two Bobs, the interference that Bob 2 causes at the Eve can be exploited: allocating power to Bob 2 weakens the Eve's ability to intercept Bob 1, and in the high-SNR regime the closed-form power allocation is proportional to the two Bob-to-Eve correlation magnitudes.
For the general multi-Bob, multi-Eve case, the proposed SCA-based power-allocation algorithm achieves a higher sum-secrecy-rate than a scheme designed with the simplified far-field channel model, and some links that would be deemed insecure in isolation can become useful jammers.

Reading between the lines

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

A direct extension the paper leaves implicit is that the same energy-spread mechanism should apply to any near-field receiver, not only eavesdroppers; the secure-region expansion is one consequence of a general channel-model mismatch in extremely large arrays.
One testable design consequence is that a scheduler could deliberately place or select 'jamming' users close to the Eve's angle to shrink the insecure region of a target user, turning the paper's two-Bob insight into a multi-user scheduling rule.
The analysis assumes perfect Eve channel state information at the base station; a natural extension would be to robustify the power allocation against Eve location uncertainty, where the Fresnel-integral approximation could again be used to bound the worst-case insecure region.

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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

Short version: this is a real extension, not a repackaging. The mixed-field PLS scenario—far-field Bobs, near-field Eves under an XL-array—hasn't been treated before, and the central qualitative claim is well motivated and supported: a far-field beam spreads energy into the near field, so Eves at other angles can intercept, making the insecure region larger than a pure far-field analysis predicts. The paper earns credit for isolating that effect, writing the secrecy rate under a low-complexity MRT/hybrid architecture, and giving closed-form insecure-region conditions for one-Bob and two-Bob cases. The SCA power allocation for the general case is standard but competently done, and the numerical comparison against a far-field-model benchmark makes the practical point clearly.

The soft spot is where the reader and the stress-test note point: Lemma 2. The mixed-field correlation G(β1,β2) is asserted with 'proof omitted' and cited to the authors' own prior work. Proposition 1 and the claimed exact angular boundary in (22) are built directly on inverting G. Appendix A only inverts the function; it does not derive it. If G is off in the parameter range used (Eve at 5–10 m, 256 antennas, β2 not large), the boundary width and the size of the insecure region change. The paper's own USW-based numerics (Fig. 3) show the expanded region exists qualitatively, but they don't validate the specific closed-form curve as a contribution. That is a legitimate referee-level concern, not a manufactured one. The fix is cheap: either include the derivation of G (or a proper reference with proof) or add a figure comparing the closed-form boundary against exact USW correlation over a dense grid.

The two-Bob section has smaller soft spots: the secure-transmission condition assumes far-field beam orthogonality when angles differ (fine in massive arrays, but it is an approximation), and the closed-form power allocation in Proposition 3 uses high-SNR plus strong-Eve-correlation assumptions. These are acknowledged as approximations and are less load-bearing than Lemma 2.

Bottom line: the central claim is likely right, but the quantitative characterization is not yet fully supported. This paper deserves a serious referee and a request for revision rather than a desk reject. The authors are clearly capable; the missing derivation is the kind of thing that can be added. I would bring it to the reading group if near-field PLS is on anyone's radar, and I'd cite it once the Lemma 2 issue is resolved.

Referee Report

3 major / 5 minor

Summary. The paper considers a downlink physical-layer security system in which an XL-array base station serves far-field legitimate users (Bobs) while near-field eavesdroppers (Eves) are located close to the array. The authors formulate a sum-secrecy-rate maximization problem over power allocation, analyze two special cases (one-Bob-one-Eve and two-Bob-one-Eve), characterize the Bob's insecure-transmission region in closed form, and propose an SCA-based algorithm for the general case. The central claim is that the insecure-transmission region of a far-field Bob is significantly expanded relative to conventional far-field PLS because a far-field beam causes energy spread in the near-field, so Eves at nearby angles and short distances can intercept the signal even when they are not at the same angle as the Bob. Numerical results in Section V compare the proposed mixed-field design with far-field-model-based benchmarks and show rate gains.

Significance. If the theoretical characterization is correct, the paper delivers a practically important warning: far-field-only security analyses that ignore near-field energy spreading may substantially underestimate the insecurity region. The closed-form one-Bob result and the two-Bob insight that cross-user interference can be exploited to degrade Eve's reception are potentially useful for system design. The paper is generally clearly written and the numerical experiments are informative, but the central result depends on an unproved Fresnel approximation (Lemma 2) cited to the authors' prior work, and two other theoretical steps contain gaps. With those points resolved or validated, the contribution would be a solid addition to the XL-array and PLS literatures.

major comments (3)

[Section III-A, Lemma 2 and Appendix A] The mixed-field correlation approximation in (19)-(20), stated with 'Proof omitted,' is the load-bearing premise for Proposition 1 and the closed-form angular boundaries in (22). The Fresnel-integral expression G(beta1, beta2) is used to invert G(beta1, beta2)=Lambda, and any approximation error in the parameter regime (N=256, r_E=5-10 m, beta2 approximately 2.9) could change the size, shape, and even existence of the predicted insecure region. Please provide a proof of Lemma 2 in the appendix or, failing that, a numerical comparison of G(beta1, beta2) with the exact USW correlation |b^H(theta_E,r_E)a(theta_B)| from (3) over the full parameter ranges used in Figures 3 and 4, including the boundary curves beta1=beta1^(+-)(Lambda). The current reliance on [9] and [35] is not sufficient for a result that is claimed as a new closed-form characterization.
[Section III-B, Lemma 3 and Appendix B] In deriving the secure-transmission condition (27), the proof sets |a^H(theta_B,1)a(theta_B,2)|^2 = 0 whenever theta_B,1 differs from theta_B,2. For a finite array of N=256 elements this is only an asymptotic idealization; the actual cross-correlation has non-negligible sidelobes for small angular separations. Since Lemma 3 and Proposition 2 rely on this exact zero, the claimed narrowing of the insecure region from Bob-2-to-Eve interference is not quantitatively justified. Please either restate the condition with the exact finite-N cross-correlation term or provide a bound showing that the neglected term is negligible for the angular separations and array sizes considered in the examples.
[Section IV, Lemma 4] The proof that Problems (P2) and (P4) have the same optimal solution is incomplete and arguably incorrect as written. The argument that 'we can always increase its value in the objective to zero by setting PB,k=0' considers only the k-th term and ignores the coupling through interference: reducing PB,k changes every RB,i and RE,i in (16) by modifying the interference-plus-noise terms at the other Bobs and at the Eves. Thus the equivalence statement is not established. Please provide a correct proof or reformulate the problem so that the relaxation in (P4) is provably tight at optimality.

minor comments (5)

[Section III-A, Eq. (17)] Equation (17) as printed contains a typo: the numerator inside the logarithm is written as 1 + (mu/r_B^2)(1/r_B^2 - |b^H a|^2/r_E^2), which is dimensionally inconsistent; it should be 1 + mu/r_B^2 - (mu/r_E^2)|b^H a|^2 (equivalently the ratio (1+mu/r_B^2)/(1+mu/r_E^2|b^H a|^2)). The subsequent condition in Lemma 1 uses the correct form, but the displayed equation should be fixed.
[Section III-A, Proposition 1] The distance condition in (21) is written as r_B > Z with Z called 'the effective Rayleigh distance,' but Section II defines an angle-dependent effective Rayleigh distance Z(theta). Please specify whether Z is evaluated at theta_B, theta_E, or a fixed reference angle; the radial boundary of the insecure region depends on this choice.
[Equation (16) and throughout] In (16), the cross-correlation term is typed as |a^H(theta_B,k)a^H(theta_B,i)|^2; the second vector should be a(theta_B,i), not a^H(theta_B,i). This is a minor typographical error but it appears in a load-bearing expression.
[Appendix C, Eqs. (47)-(51)] The definitions of g_i,j and g_E,j in Appendix C are written inconsistently with the main text: (47)-(48) define g_i,j = |h^H_B,i w_B,j| and g_E,j = |h^H_E w_B,j|, but the earlier signal model uses h^H_B,i as a channel row vector and w_B,j as the analog beam. Please unify the notation and define these quantities after (16) or in a table.
[Figures 5 and 6] There are several typos in the figure captions and text, including 'sheme' in Fig. 6 and 'technque' in Remark 6. Also, the caption of Fig. 3(c) says 'multipath USWs,' while the text describes a Rician factor of 10 dB; please reconcile the terminology.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity found; the derivation chain is self-contained apart from a non-circular self-cited approximation.

full rationale

I walked the derivation chain of arXiv:2504.19555 and found no step in which a claimed prediction reduces by construction to a fitted input, a self-referential definition, or a self-citation that itself assumes the target result. Lemma 1 is a direct algebraic reformulation of the secrecy-rate expression, so the secure-transmission condition is not smuggled in. Lemma 2 is the closest candidate for a circularity concern: it approximates the mixed-field correlation function |b^H(theta_E,r_E) a(theta_B)| by Fresnel integrals G(beta1,beta2), with the proof omitted and cited to the authors' own prior works [9] and [35] ('Proof: The proof is similar to that in [Theorem 1 [9]] and hence is omitted for brevity'). This is a load-bearing analytical tool for Proposition 1, and the self-citation is notable. However, it is not circular under the review rules: Lemma 2 is a parameter-free mathematical approximation whose stated modeling assumptions (near-field USW, far-field UPW) do not include the paper's target conclusion about insecure-transmission regions; it is externally checkable by direct computation of the exact correlation; and the paper independently validates the qualitative phenomenon with exact-USW simulation in Fig. 3 without relying on Lemma 2 to generate those points. Proposition 1 then follows by substituting G into Lemma 1's condition and inverting beta1; this is algebra, not a self-fulfilling prediction. Proposition 2 and Proposition 3 similarly follow from the same channel model and from standard high-SNR approximations, with no parameter fitted to the results being 'predicted.' The SCA algorithm in Section IV is a standard convexification with no hidden reuse of benchmark outputs. Numerical results are Monte-Carlo evaluations rather than fits. The omitted proof of Lemma 2 is a rigor/verifiability concern that belongs in correctness assessment, not a circularity finding, because the cited result is independent evidence rather than an assumption equivalent to the conclusion. I therefore report no significant circularity.

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

The paper introduces no fitted parameters and no new physical entities. The analysis relies on standard channel models and a correlation approximation borrowed from the authors' prior work [9], [35], plus several domain simplifications such as LoS-only channels, orthogonal beams, and independent Eves.

assumptions (6)

domain assumption The LoS path has much stronger power than NLoS paths, so channels are approximated by their LoS components.
Section III, paragraph before Case I: 'the LoS path has much stronger power than the NLoS paths', enabling the analytical tractability of the closed-form results.
domain assumption The BS has perfect CSI of all Bobs and Eves.
Section II-A2, footnote 1: CSI acquired via existing far-field and near-field channel estimation and beam training methods, citing [15], [25]-[27].
domain assumption Eves operate independently without cooperation in intercepting signals.
Section II-A2: 'Similar to [30]-[32], we consider that the M Eves operate independently without cooperation...', giving RE,k = max_{m} RE,m,k.
ad hoc to paper Far-field steering vectors for distinct angles are exactly orthogonal.
Appendix B, proof of Lemma 3: 'When theta_B,1 != theta_B,2, the Bob 2 to Bob 1 interference is negligible, i.e., |a^H(theta_B,1)a(theta_B,2)|^2 = 0.' This is approximate for finite N.
domain assumption The correlation between a near-field steering vector and a far-field steering vector is accurately approximated by the Fresnel-integral function G(beta1, beta2).
Lemma 2: 'The mixed-field correlation function eta(theta_q; theta_p, r_p) can be approximated as [35]... Proof: The proof is similar to that in [Theorem 1 [9]] and hence is omitted for brevity.' This is central to Proposition 1.
domain assumption High-SNR conditions and negligible noise at the Eve are assumed for the closed-form power allocation in Proposition 3.
Proposition 3 and Appendix C: solutions are derived under 'high-SNR regimes' and when 'the noise power at Eve can be neglected'.

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Cite this review

Pith. "Pith review of Physical-Layer Security in Mixed Near-Field and Far-Field Communication Systems." pith.science (2026). https://pith.science/paper/744PK5UC

@misc{pith2026250419555,
  author       = {Pith},
  title        = {Pith review of: Physical-Layer Security in Mixed Near-Field and Far-Field Communication Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/744PK5UC}},
  note         = {Machine review of arXiv:2504.19555}
}

read the original abstract

Extremely large-scale arrays (XL-arrays) have emerged as a promising technology to improve the spectrum efficiency and spatial resolution of future wireless systems. Different from existing works that mostly considered physical layer security (PLS) in either the far-field or near-field, we consider in this paper a new and practical scenario, where legitimate users (Bobs) are located in the far-field of a base station (BS) while eavesdroppers (Eves) are located in the near-field for intercepting confidential information at short distance, referred to as the mixed near-field and far-field PLS. Specifically, we formulate an optimization problem to maximize the sum-secrecy-rate of all Bobs by optimizing the power allocation of the BS, subject to the constraint on the total BS transmit power. To shed useful insights, we first consider a one-Bob-one-Eve system and characterize the insecure-transmission region of the Bob in closed form. Interestingly, we show that the insecure-transmission region is significantly \emph{expanded} as compared to that in conventional far-field PLS systems, due to the energy-spread effect in the mixed-field scenario. Then, we further extend the analysis to a two-Bob-one-Eve system. It is revealed that as compared to the one-Bob system, the interferences from the other Bob can be effectively used to weaken the capability of Eve for intercepting signals of target Bobs, thus leading to enhanced secrecy rates. Furthermore, we propose an efficient algorithm to obtain a high-quality solution to the formulated non-convex problem by leveraging the successive convex approximation (SCA) technique. Finally, numerical results demonstrate that our proposed algorithm achieves a higher sum-secrecy-rate than the benchmark scheme where the power allocation is designed based on the (simplified) far-field channel model.

Figures

Figures reproduced from arXiv: 2504.19555 by the authors.

**Figure 1.** The considered mixed-field PLS system. Notations: Lowercase and uppercase boldface letters are used to represent vectors and matrices, such as a and A. For vectors and matrices, the superscripts (·) H and (·) T stand for the transpose and Hermitian transpose, respectively. Additionally, calligraphic letters (e.g., A) denote discrete and finite sets. The notations |·|, k·k, and k·kF refer to the absolute value of a s… view at source ↗

**Figure 2.** Illustrations of function G(β1, β2) v.s. β1 and β2. As shown in (18), the secure-transmission condition of Bob is jointly affected by the path-loss ratio and the mixedfield channel-beam correlation, both of which are affected by the locations of Bob and Eve. Specifically, a larger angular difference between Bob and Eve (i.e., lower channel-beam correlation) and a larger path-loss ratio generally lead to less inform… view at source ↗

**Figure 3.** Insecure-transmission region of the Bob in the mixed [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Secrecy rate of Bob in the one-Bob-one-Eve system. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Illustration of the power allocation designs based o [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: Sum-secrecy-rate v.s. system parameters. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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Reference graph

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

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