Movable-Antenna-Enhanced Physical-Layer Service Integration: Performance Analysis and Optimization

Boyu Ning; Jun Fang; Weidong Mei; Xin Wei; Xuanlin Shen; Zhi Chen

REVIEW 3 major objections 4 minor 17 references

Movable-Antenna-Enhanced Physical-Layer Service Integration: Performance Analysis and Optimization

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Movable antennas let one base station run secrecy and multicast at full array gain, which fixed-position antennas cannot match.

desk verdict First MA + PHY-SI paper with a genuinely thought-provoking LoS dominance result, but the main theorem only holds for even N — stated for all N and simulated for odd N. read the letter →

arxiv 2507.03449 v2 pith:L7XJCNY2 submitted 2025-07-04 cs.IT eess.SPmath.IT

Xuanlin Shen , Xin Wei , Weidong Mei , Zhi Chen , Jun Fang , Boyu Ning This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords movableantennasphysical-layerserviceintegrationsecrecyrateregionmulticastbeamformingsemidefiniterelaxationdiscretesamplingline-of-sightchannelsantennapositionoptimization

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

Physical-layer service integration sends a public (multicast) message and a confidential message at the same time from one transmitter; conventionally, fixed-position antennas limit how well these two services can coexist. This paper asks whether movable antennas, antennas that can be repositioned inside a small square region, can expand the achievable set of (multicast rate, secrecy rate) pairs. It establishes that under line-of-sight channels with an arbitrarily large movement region, there is an antenna layout that gives the confidential beam full array gain at the intended user, zero gain at the other user, and the multicast beam full array gain at both users simultaneously. From that, it proves that this layout dominates every other antenna position in both rates. The paper also develops a two-layer optimization algorithm, semidefinite relaxation for beamforming and discrete sampling for antenna positions, and shows numerically that the secrecy rate region is much larger with movable antennas than with fixed-position antennas.

What carries the argument

The load-bearing identity is the beam-gain formula for a uniform linear array, $g_{i,k}(T) = \frac{1}{N}\frac{1-\cos(2\pi N r_{i,k}d)}{1-\cos(2\pi r_{i,k}d)}$, where $r_{i,k}$ is the difference of inter-antenna phase increments toward user $k$ for beam $i$. The whole dominance argument reduces to choosing one integer spacing $d$ such that, modulo $2\pi$, each $2\pi r_{i,k}d$ takes the required value: near $0$ for the three beams that should add constructively, and near $\pi$ for the confidential beam at the non-intended user so the numerator vanishes when $N$ is even. Lemma 1 obtains such a $d$ from a Diophantine approximation result, using the fact that the $r_{i,k}$ values are, with probability one, irrational and not rationally related. On the algorithmic side, the inner layer uses semidefinite relaxation with a Charnes-Cooper transformation, a change of variables that convexifies the fractional objective, to solve the beamforming problem for a fixed antenna layout, and the outer layer performs a sequential discrete sampling over candidate positions.

What would settle it

Take an odd number of movable antennas ($N=3$) and apply the equal-spacing construction of Lemma 1 with $2\pi r_{c,2}d \approx \pi \pmod{2\pi}$: the confidential beam gain at user 2 becomes $1/N$, not $0$, so the claimed simultaneous full gain and perfect null is not achieved by this construction, and Theorem 1's universal dominance over all antenna positions would need a different geometry to survive. Alternatively, deliberately choose user directions that make the $r_{i,k}$ values rationally dependent and search exhaustively over a finite grid: if any antenna layout yields a higher secrecy rate at the same multicast rate than the Lemma-1 layout, the asymptotic dominance claim fails for that finite region.

Watch

Extended reading notes

Core claim

The paper's central claim is Theorem 1: in a line-of-sight channel with an arbitrarily large movement region, there exists an antenna position vector $T^\star$ such that the achievable multicast rate and secrecy rate both satisfy $R_0(T^\star) \ge R_0(T)$ and $R_c(T^\star) \ge R_c(T)$ for every other position vector $T$. The construction behind it places the $N$ movable antennas in a uniform line and chooses the spacing $d$ so that the confidential beam adds constructively at user 1 and destructively at user 2, while the multicast beam adds constructively at both users; for an even number of antennas this yields beam gains $g_{c,1}=g_{0,1}=g_{0,2}=N$ and $g_{c,2}=0$. Thus one antenna geometry simultaneously serves two service types at the maximum possible array gain, something a fixed array cannot generically do. The paper further shows that a single movable antenna can lose to simple time-sharing because one position cannot serve both services well, whereas multiple movable antennas restore the advantage of simultaneous transmission.

Load-bearing premise

The result stands on the assumption that a single antenna spacing can be chosen to make the confidential beam add up at user 1, cancel at user 2, and the multicast beam add up at both users at the same time; the proof requires the relevant direction-dependent constants to be irrational and not rational multiples of each other, the movement region to be large enough to contain the required spacing, and, in the printed construction, an even number of antennas to make the cancellation exact.

Editorial extensions

If this is right

In line-of-sight scenarios with a large enough movement region, movable antennas can achieve full array gain for multicast at both users and, at the same time, a perfect spatial null for the confidential message at the non-intended user; no fixed-position array can match both.
The secrecy rate region of the movable-antenna system contains the fixed-position-antenna region and also beats the time-sharing benchmark, reversing the single-antenna case where time-sharing can win.
The proposed two-layer algorithm reaches these gains with worst-case complexity $O(N^{7.5}M^2)$, where $M$ is the number of sampling points per dimension; the inner SDR step has the same complexity order as conventional fixed-position-antenna PHY-SI.
Increasing the number of antennas $N$ or the movement region size $A$ enlarges the secrecy-multicast rate region, with the gain saturating once the region is large enough.
Coarse sampling (e.g., 25 points per dimension) already outperforms the fixed-position benchmark, so the theoretical full-array-gain result does not require fine-grained continuous positioning.

Reading between the lines

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

The one-spacing-fits-all construction is essentially spatial interference alignment: a single degree of freedom, the inter-antenna spacing, simultaneously aligns three beams constructively and one beam destructively. This suggests the same Diophantine machinery could extend to more than two users or multiple eavesdroppers by allocating more antennas to satisfy more simultaneous phase conditions.
The single-MA-versus-time-sharing failure points to a threshold effect: for each channel realization there may be a minimum number of antennas beyond which movable-antenna PHY-SI always beats time-sharing; finding that threshold as a function of channel statistics would be a natural next step, but the paper does not compute it.
Because the theory needs an arbitrarily large region while the numerical gains saturate at a few wavelengths, a practical conjecture is that a finite region of about $8\lambda$ already captures most of the asymptotic benefit; verifying this with an exhaustive search over all feasible layouts would test how much the asymptotic assumption matters.
The reliance on direction-dependent phase constants being irrational and not rationally related means special geometries, such as users placed symmetrically so that two $r_{i,k}$ values are rational multiples of each other, may break the construction; one could deliberately construct such a geometry and check whether a different antenna layout still dominates fixed positions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The paper is the first to apply movable antennas to physical-layer service integration, and it has one result that actually made me stop: in a LoS channel, with an arbitrarily large movement region and even N, there is an antenna placement that nulls the confidential signal at user 2 while giving full gain to user 1 and full multicast gain to both users. That is a neat extension of the null-steering idea in the MA literature, and it goes beyond the existing secrecy-only or multicast-only MA papers.

What works well: the single-MA power allocation derivation is clean and correct as far as I checked. The point that a single moving antenna can make PHY-SI worse than time sharing, because the optimal position differs for the two messages and you can't share positions, is a genuinely new observation. The SDR-plus-discrete-sampling algorithm is reasonable for a letter, and the numerical comparisons to FPA and PSO are consistent.

Now the soft spots. The main theorem is stated for any N and any LoS geometry, but the proof does not cover odd N. Condition (14) puts 2π r_c,2 d near π modulo 2π, and simultaneously requires 2π N r_c,2 d near 0 modulo 2π. These are compatible only when N is even; for odd N the confidential gain at user 2 tends to 1/N, not 0. Since the simulations include N=3 and N=5, this is not an edge case for the numerics. The theorem also depends on the r_i,k being rationally independent, which the authors mention in the proof as 'with probability one' but omit from the statement. And Lemma 1 calls d a positive integer when it is a physical spacing in meters; the Diophantine approximation presumably applies to normalized frequency differences, so the statement as written has a unit inconsistency. None of those are fatal if the theorem is restated with the right hypotheses, but as written Theorem 1 is too strong.

Minor issues: the rank-count argument for the SDR says rank^2(Z*)+rank^2(Γ*) ≤ 3 and concludes both are rank one. That conclusion isn't forced by the bound alone; you need to handle the possibility of a rank-zero solution. Also no code or error bars, which is common for a letter but worth noting.

Bottom line: this is a worthwhile contribution to the MA/PHY-SI subfield, and the central idea deserves to see the light after a careful revision. A referee should demand that the odd-N case be either proven, fixed with a different construction, or explicitly excluded from the theorem. I would send it to review.

Referee Report

3 major / 4 minor

Summary. The manuscript studies a downlink MISO physical-layer service integration (PHY-SI) system in which a base station equipped with N movable antennas transmits a multicast message to two users and a confidential message to user 1, with user 2 acting as a potential eavesdropper. The aim is to maximize the secrecy rate subject to a multicast rate constraint, a power constraint, and antenna-position constraints. In the single-MA case, the authors derive a closed-form optimal power allocation and compare the resulting rate region with time-sharing, concluding that PHY-SI may lose to time-sharing with one MA. In the LoS case, Lemma 1 constructs an APV and array-response beamformers for an arbitrarily large movement region, and Theorem 1 claims that this APV dominates every other APV in both multicast and secrecy rates. The general problem is then addressed by a two-layer algorithm: an SDR-based inner beamforming solver and a discrete-sampling outer APV search. Numerical results compare the proposed scheme with FPA and PSO benchmarks and study the effects of sampling resolution, region size, and number of antennas.

Significance. If the analytical claims are fully established, the paper makes a useful conceptual contribution: movable antennas can simultaneously configure a multicast beam toward both users and a null toward the eavesdropper, which is a genuinely different capability from single-service MA designs. The LoS dominance argument is parameter-free and does not rely on fitted data, and the single-MA power-allocation derivation in Eqs. (5)-(6) is algebraically sound. The numerical study is informative and includes a PSO benchmark, which strengthens the empirical comparison. However, the proof of Lemma 1 contains a coordinate inconsistency and an unproven parity condition, and the SDR rank-one argument in Section IV-A rests on a miscounted constraint number. These gaps affect the two main theoretical claims, so the paper needs substantial revision before the results can be accepted.

major comments (3)

[Section III-B, Eq. (13)] The definition of r_{i,k} in Eq. (13) is inconsistent with the array response in Eq. (8) when the antennas are placed at t_n = [(n-1)d, 0]^T. Substituting this position into Eq. (8) gives a phase difference proportional to (sin θ_k cos φ_k - sin θ_i cos φ_i), with no term involving (cos θ_k - cos θ_i). Since the Diophantine conditions in Eq. (14) are imposed on the printed r_{i,k}, the proof of Eq. (12) does not currently follow from the actual beam gains. The authors should correct the definition of r_{i,k} and re-derive the limiting gains in Eq. (13).
[Lemma 1, Eq. (14), and Theorem 1] The null-steering construction in Lemma 1 requires 2π r_{c,2} d → π (mod 2π) and 2π N r_{c,2} d → 0 (mod 2π). These two congruences are compatible only when N is even: if r_{c,2} d ≡ 1/2 mod 1, then N r_{c,2} d ≡ N/2 mod 1, which is 0 only for even N. For odd N the limiting confidential beam gain at user 2 is 1/N rather than 0, so Eq. (12) is not achieved by the stated construction. Theorem 1 is therefore unproven for odd N, even though the numerical section includes N=3 and N=5. The theorem should be restricted to even N, or a different construction valid for all N must be supplied.
[Section IV-A, after Eq. (22)] The rank bound is stated as rank^2(Z*) + rank^2(Γ*) ≤ 3, where '3' is claimed to be the number of linear equalities and inequalities in problem (22). Problem (22) actually contains four affine constraints: the Charnes-Cooper equality, the two multicast-rate inequalities, and the trace constraint. The standard rank result would therefore give rank^2(Z*) + rank^2(Γ*) ≤ 4, which permits, for example, rank(Z*) = 2 and rank(Γ*) = 0 and does not force both matrices to be rank-one. Consequently, the claimed global optimality of the SDR-based inner solution is not established by the cited argument; either a corrected proof of rank-one recovery or a reformulation of the inner solver as a heuristic is needed.

minor comments (4)

[Lemma 1 proof] The proof calls d a positive integer, but d also acts as a physical antenna spacing in the phase term 2π r_{i,k} d; the authors should state that d is an integer multiple of the wavelength, or otherwise normalize the spacing variable.
[Lemma 1 and Theorem 1] The proof uses the assumption that all r_{i,k} are irrational and rationally independent, but Lemma 1 and Theorem 1 are stated without this qualification. The statements should either include the generic-geometry assumption or prove the result for all angle tuples.
[Section III-A, Eq. (5)] The optimal power allocation in Eq. (5) gives P_c^* = (P|h_2(t)|^2 - τ_{ms} σ^2) / ((τ_{ms}+1)|h_2(t)|^2), which is nonnegative only when P|h_2(t)|^2 ≥ τ_{ms} σ^2; the authors should state this feasibility condition explicitly.
[Lemma 1 statement] The notation θ_0 ≠ θ_c ≠ θ_k is ambiguous; pairwise distinctness of θ_0, θ_c, θ_1, and θ_2 should be written explicitly.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the central MA secrecy-rate gain is a parameter-free construction, and the cited self-works are auxiliary optimization tools.

full rationale

I find no circular step in the paper's derivation chain. The central analytical claim (Theorem 1) is supported by Lemma 1, which constructs an APV T* with equal antenna spacing d and invokes an external Diophantine approximation result [16] to satisfy the conditions in (14). This is a constructive existence argument, not a fitted parameter or a renamed input. Theorem 1 then compares rates between T* and an arbitrary T by re-normalizing the power allocation in (17); the inequalities follow algebraically from the gains in (12) and are not equivalent to the conclusion by construction. The optimization part uses SDR with a rank-one recovery argument cited from the authors' prior work [2] and a discrete sampling method cited from [17], but these citations supply standard tools and are not used to manufacture the claimed MA-over-FPA gain; the numerical section benchmarks against FPA, PSO, and time-sharing. One non-circular correctness caveat is worth flagging: Lemma 1's conditions (14) are mutually inconsistent for odd N, because 2π r_{c,2}d approaching π (mod 2π) forces 2π N r_{c,2}d to approach Nπ, which is not 0 (mod 2π) unless N is even. This is a proof gap affecting the stated coverage of odd N (including the numerical N=3 and N=5 cases), but it is a correctness issue rather than a self-referential or definitional circularity. Overall, the minor self-citations are not load-bearing for the central performance claim, so the circularity score is low.

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

No constants are fitted to data in this paper. The theoretical results are parameter-free constructions; simulation settings (P, noise, L=7, A, M) are standard choices, not tuning to force the conclusion. The physical assumptions are itemized above.

assumptions (6)

domain assumption The field-response MA channel model of [5] accurately describes h_k(T) with L=7 i.i.d. complex Gaussian paths and uniformly random AoDs.
Used in Sections II and V to define all channel vectors; the claimed MA gains are model-dependent.
domain assumption Perfect CSI for every MA position is available at the BS, using the technique in [5].
Stated in Section II before (P1); the joint optimization assumes channel knowledge as a function of T.
domain assumption Antenna movement delay is much smaller than the channel coherence time.
Stated in Section II to justify optimizing T as a static variable.
domain assumption For the LoS analysis, the r_{i,k} values are irrational and linearly independent over Q with probability one, so the simultaneous Diophantine approximation from [16] applies.
Invoked in Lemma 1 proof to assert existence of d satisfying (14).
domain assumption The antenna movement region can be relaxed to be arbitrarily large for the LoS dominance result.
Footnote 1 in Section III-B discloses this asymptotic relaxation, mirroring massive-MIMO analysis.
standard math The SDR rank bound for the Charnes-Cooper reformulation (22) guarantees rank-one optimal Z* and Gamma*.
Used in Section IV-A to retrieve w0 and wc from the relaxed problem; sourced from [2].

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Cite this review

Pith. "Pith review of Movable-Antenna-Enhanced Physical-Layer Service Integration: Performance Analysis and Optimization." pith.science (2026). https://pith.science/paper/L7XJCNY2

@misc{pith2026250703449,
  author       = {Pith},
  title        = {Pith review of: Movable-Antenna-Enhanced Physical-Layer Service Integration: Performance Analysis and Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L7XJCNY2}},
  note         = {Machine review of arXiv:2507.03449}
}

read the original abstract

Movable antennas (MAs) have drawn increasing attention in wireless communications due to their capability to create favorable channel conditions via local movement within a confined region. In this letter, we investigate its application in physical-layer service integration (PHY-SI), where a multi-MA base station (BS) simultaneously transmits both confidential and multicast messages to two users. The multicast message is intended for both users, while the confidential message is intended only for one user and must remain perfectly secure from the other. Our goal is to jointly optimize the secrecy and multicast beamforming, as well as the MAs' positions at the BS to maximize the secrecy rate for one user while satisfying the multicast rate requirement for both users. To gain insights, we first conduct performance analysis of this MA-enhanced PHY-SI system in two special cases, revealing its unique characteristics compared to conventional PHY-SI with fixed-position antennas (FPAs). To address the secrecy rate maximization problem, we propose a two-layer optimization framework that integrates the semidefinite relaxation (SDR) technique and a discrete sampling algorithm. Numerical results demonstrate that MAs can greatly enhance the achievable secrecy rate region for PHY-SI compared to FPAs.

Figures

Figures reproduced from arXiv: 2507.03449 by the authors.

**Figure 1.** MA-enhanced MISO PHY-SI system. respectively. However, to the best of our knowledge, there is no existing work focusing on the application of MAs in PHYSI, where the MA position optimization needs to cater to both secrecy and multicast transmission, as well as their mutual interference. To fill in this gap, in this letter, we investigate an MAenhanced PHY-SI system as shown in [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗

**Figure 2.** Comparison between PHY-SI and time sharing for a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Achievable secrecy rate region versus (a) the number [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Physical layer service integr ation in wireless networks: Signal processing challenges,

R. Schaefer and H. Boche, “Physical layer service integr ation in wireless networks: Signal processing challenges,” IEEE Signal Process. Mag. , vol. 31, no.3, pp.147-156, Apr. 2014

work page 2014

[2] [2]

On artiﬁcial-no ise-aided transmit design for multiuser MISO systems with integrated services,

W. Mei, Z. Chen, L. Li, J. Fang, and S. Li, “On artiﬁcial-no ise-aided transmit design for multiuser MISO systems with integrated services,” IEEE Trans. V eh. Technol., vol. 66, no. 9, pp. 8179-8195, Sep. 2017

work page 2017

[3] [3]

Joint power allocation and passive beamf orming design for IRS-assisted physical-layer service integration,

B. Ning et al., “Joint power allocation and passive beamf orming design for IRS-assisted physical-layer service integration,” IEEE Trans. Wireless Commun., vol. 20, no. 11, pp. 7286-7301, Nov. 2021

work page 2021

[4] [4]

Movable antennas for wireless communi- cation: Opportunities and challenges,

L. Zhu, W. Ma and R. Zhang, “Movable antennas for wireless communi- cation: Opportunities and challenges,” IEEE Commun. Mag. , vol. 62, no. 6, pp. 114-120, June 2024

work page 2024

[5] [5]

A tutorial on movable antennas for wirele ss networks,

L. Zhu, et al., “A tutorial on movable antennas for wirele ss networks,” IEEE Commun. Surveys Tuts. , 2025, early access

work page 2025

[6] [6]

Movable-antenna array enhanc ed beam- forming: Achieving full array gain with null steering,

L. Zhu, W. Ma and R. Zhang, “Movable-antenna array enhanc ed beam- forming: Achieving full array gain with null steering,” IEEE Commun. Lett., vol. 27, no. 12, pp. 3340-3344, Dec. 2023

work page 2023

[7] [7]

Flexible beam cover age optimization for movable-antenna array,

D. Wang, W. Mei, B. Ning, and Z. Chen, “Flexible beam cover age optimization for movable-antenna array,” Proc. IEEE Global Commun. Conf., Cape Town, South Africa, 2024, pp. 4914-4919

work page 2024

[8] [8]

CSI-Free position optimization for mova ble antenna communication systems: A derivative-free optimization ap proach,

X. Zeng et al., “CSI-Free position optimization for mova ble antenna communication systems: A derivative-free optimization ap proach,” IEEE Wireless Commun. Lett. , vol. 14, no. 1, pp. 53-57, Jan. 2025

work page 2025