{"id":"ba1dea23-028b-46b1-b505-f78564060944","arxiv_id":"2601.05686","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"Jointly optimizing movable-antenna positions and digital beamforming increases the achievable multiuser sum secrecy rate against cooperating eavesdroppers compared with fixed-position arrays.","lead":"This paper develops a joint digital-beamforming and antenna-placement design for a base station with movable antennas serving multiple legitimate users while guarding against multiple cooperating eavesdroppers. Simulations show movable antennas can raise the achievable multiuser secrecy sum-rate compared to fixed-position antenna arrays.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lemma 2/3 FP reformulation is not equivalent: the β-update yields log2(1+g)−log2(1+γ̂_k), not the stated log2((1+g−γ̂_k)/(1+γ̂_k)); Algorithm 2 therefore maximizes a different objective than the claimed sum secrecy rate (7).","rationale":"The strongest claim is that Algorithm 2 maximizes the sum secrecy rate in (7). For that to hold, every transformation from (7) to the BCD subproblems must preserve the objective up to constant/additive separable terms. The chain (9)→(11)→(12)→(15) fails at the first nontrivial step. My calculation of β^⋆ is direct: ∂f_k^2/∂β_k = 1/(1+β_k) −1 + (g−γ̂_k)/(1+g)=0, hence 1+β_k^⋆=(1+g)/(1+γ̂_k), and f_k^{2⋆}=log2((1+g)/(1+γ̂_k)). The displayed (11) would require log2((1+g−γ̂_k)/(1+γ̂_k)), which has a different dependence on W. Thus the algorithm's objective contains the extra b_k log2(1+g). Because b_k multiplies this term, it changes the optimal b and the optimal W,T. The reader's listed weakest assumption about simultaneous achievability of (7) is not the main problem: (7) is a conservative achievable secrecy sum under the stated eavesdropper-cancellation model. The decisive flaw is the invalid FP equivalence. The A_k noise-normalization omission noted by the reader is also real—(18) lacks the 1/σ̂_j^2 weights—but it is downstream of the transformation failure. I therefore agree with the REJECT verdict while disagreeing with the reader's choice of weakest assumption.","tokens_in":10313,"tokens_out":15147,"duration_ms":151716,"concrete_test":"Single-user counterexample: K=J=M=1, LoS gain 1, no NLoS, p=1, σ^2=σ̂^2=1, so g=1. For every feasible w with |w|^2=x∈[0,1], γ=γ̂=x, hence (7) is identically 0. After the closed-form updates (27), f_2^⋆=log2(2/(1+x)) and g_1^⋆=log2(1+x), so the surrogate maximized by Algorithm 2 is exactly log2(2)=1, and (26) sets b=1. This directly contradicts the equivalence asserted in Lemmas 2–3. If the authors supply a corrected surrogate, re-derive (18) including 1/σ̂_j^2 and re-run the Section IV experiments to see whether the reported MA-vs-FPA gains persist.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III.A is the load-bearing step. Lemma 2 states that (9) is equivalent to (11), where log2(1/(1+γ̂_k)) is replaced by log2((1+g−γ̂_k)/(1+γ̂_k)). Lemma 3 then introduces f_k^2 in (14). Setting the derivative to zero gives β_k^⋆=(g−γ̂_k)/(1+γ̂_k). Substituting back yields f_k^{2⋆}=log2((1+g)/(1+γ̂_k)) = log2(1+g)−log2(1+γ̂_k), not log2((1+g−γ̂_k)/(1+γ̂_k)). Consequently the stationary objective maximized by Algorithm 2 is Σ_k b_k[log2(1+γ_k)−log2(1+γ̂_k)+log2(1+g)], not (9). The extra term b_k log2(1+g) is not constant after optimizing b: (26) sets b_k=1 whenever g_k^1>−f_k^2, so users with γ_k≤γ̂_k can still be assigned b_k=1, inflating the surrogate. This breaks Lemma 1's claim that b_k^⋆=1{γ_k>γ̂_k}. Thus the algorithm's W/T updates target a different function; the central claim that it maximizes (7) is unsupported. Independently, even if one uses the corrected f_k^2, (18) omits the 1/σ̂_j^2 factors from γ̂_k, a second derivation error.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper considers a multiuser MISO wiretap channel in which a base station equipped with movable antennas serves K users while J cooperating eavesdroppers attempt to intercept the messages. It formulates the maximization of the sum secrecy rate over the digital beamforming matrix W and the MA positions T, subject to a transmit-power constraint and per-antenna position/minimum-distance constraints. The authors then propose a block-coordinate-descent algorithm based on fractional programming (FP), claiming that Lemmas 1–4 provide an equivalent reformulation of the secrecy-rate problem, and that each block admits a closed-form or low-complexity update. Numerical results are reported to show that the MA-enabled design outperforms a fixed-position-antenna baseline.","tokens_in":10773,"tokens_out":8375,"duration_ms":85806,"significance":"If the reformulation were correct, the paper would address a genuinely open problem: a general MA-enabled multiuser secure beamforming design with an arbitrary number of users, data streams, and cooperating eavesdroppers, together with a tractable algorithm. The system model and the per-variable complexity accounting are useful, and the numerical study covers meaningful parameter ranges. However, the central equivalence lemmas contain algebraic errors. As a result, the objective actually optimized by Algorithm 2 is not the secrecy sum rate in (7), so the main claim of the paper is unsupported. The numerical gains may still demonstrate that MA placement helps heuristically, but they do not validate maximization of (7).","major_comments":[{"comment":"The claimed equivalence is false. Replacing log2(1/(1+γ̂_k)) by log2((1+g−γ̂_k)/(1+γ̂_k)) changes the objective by the term Σ_k b_k log2(1+g−γ̂_k). Although g itself is a constant, γ̂_k depends on W and T through (5), so this term is not a constant offset. The two problems therefore are not equivalent, and the subsequent FP development is not a reformulation of (9).","section":"Section III.A, Lemma 2 (Eqs. (10)–(11))"},{"comment":"Even if (11) were accepted, the FP surrogate f_k^2 is incorrect. Setting ∂f_k^2/∂β_k = 0 gives β_k^⋆ = (g−γ̂_k)/(1+γ̂_k), and substituting back yields f_k^{2⋆} = log2((1+g)/(1+γ̂_k)) = log2(1+g) − log2(1+γ̂_k), not log2((1+g−γ̂_k)/(1+γ̂_k)). Consequently the objective maximized by Algorithm 2 differs from (11) by Σ_k b_k log2(1+g). Because the b-update in (26) uses the threshold g_k^1 > −f_k^2, this additive term changes the b_k decision: users with γ_k ≤ γ̂_k can receive b_k = 1, contradicting Lemma 1's b_k^⋆ = 1{γ_k>γ̂_k}. Thus the stationarity and convergence statements do not pertain to the secrecy sum rate (7).","section":"Section III.A, Lemma 3 and Eq. (14)"},{"comment":"The W-subproblem matrix A_k omits the factors 1/σ̂_j^2 that appear in γ̂_k in (5). The eavesdropper term should be b_k(1+β_k)(1+g)^{-1} Σ_j (1/σ̂_j^2) g_j g_j^H, but Eq. (18) writes Σ_j g_j g_j^H without the noise weighting. As a result, the beamforming update (19) solves a different quadratic problem whenever the eavesdropper noise powers are not identical. This is an independent derivation error in a load-bearing block update; the T-subproblem in (22), by contrast, correctly retains the 1/σ̂_j^2 factors.","section":"Section III.B.1, Eq. (18)"}],"minor_comments":[{"comment":"Problem (8) is stated as min_{T,W} R, but the text and Lemma 1 describe a maximization of the secrecy sum rate. The objective should be max, not min.","section":"Section II.C, Eq. (8a)"},{"comment":"The eavesdropper observation is written with h_k^H x(t) instead of g_j^H x(t), and the index k is reused inside the sum. This appears to be a typo but should be corrected for clarity.","section":"Section II.B, Eq. (3)"},{"comment":"The inequality ∥w_k∥^2 ≤ Σ_{i=1}^K w_i^H w_k ≤ p is not correct; the intended bound is ∥w_k∥^2 ≤ Σ_{i=1}^K ∥w_i∥^2 = tr(W^H W) ≤ p. Please fix the notation.","section":"Appendix B, Eq. (31)"},{"comment":"Some notation is introduced but not used (e.g., [N] in Section II.A), and there are minor typographical issues such as 'frquency' in the introduction. These should be cleaned up in any revision.","section":"Overall"}],"recommendation":"reject","confidential_remarks":"I agree with the stress-test assessment: the FP reformulation error is decisive. Lemma 2 is not an equivalence, Lemma 3's beta-substitution recovers a different surrogate objective, and the W-subproblem in Eq. (18) has a missing noise-weighting term. These are load-bearing flaws in the derivation of Algorithm 2, and they are not local presentation issues. I do not see how the present formulation can be repaired without substantially rewriting Section III, so the paper should be rejected in its current form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nHere's the quick take on arXiv:2601.05686. The central algorithmic claim doesn't survive contact with the derivation. The stress-test note is right on both counts: Lemma 2's equivalence is false, and the W-update matrix omits the noise normalization.\n\nWhat's actually new and worthwhile: this is the first general multiuser MA-enabled secure beamforming setup with cooperating eavesdroppers, arbitrary users, and multiple data streams. The system model is clean, the channel model is standard, and the numerical results show the expected qualitative patterns: MA beats FPA, more eavesdroppers hurt, and secrecy rate peaks at moderate SNR. The exposition is clear and the literature coverage is adequate.\n\nThe soft spots are serious. Lemma 2 claims (9) is equivalent to (11), but (11) replaces log2(1/(1+γ̂_k)) with log2((1+g−γ̂_k)/(1+γ̂_k)), which adds b_k log2(1+g−γ̂_k). Since b is optimized, that extra term matters. The appendix only proves γ̂_k ≤ g; it doesn't establish equivalence. Lemma 3 then sets up the FP surrogate f_k^2. Maximizing over β gives β_k^⋆ = (g−γ̂_k)/(1+γ̂_k) and yields log2(1+g) − log2(1+γ̂_k), not the expression in Lemma 2. So Algorithm 2 actually maximizes Σ_k b_k[log2(1+γ_k) − log2(1+γ̂_k) + log2(1+g)], which is a different objective. The b-update then selects users based on this inflated surrogate, so the convergence claim and the claim of solving (7) are unsupported. Separately, A_k in (18) is missing the 1/σ̂_j^2 factors from γ̂_k, so the beamforming update is not the exact minimizer of the stated subproblem for general noise powers.\n\nThe framework is plausible and the numerical experiments are likely reproducible as written for equal noise powers, but the optimization theory needs a real redo. This paper deserves a serious referee because the problem is timely and the building blocks are standard; a desk reject would be premature. But an acceptance would require fixing the FP equivalence—either by deriving the correct surrogate or by explicitly stating they are maximizing a different bound—and fixing A_k.\n\nBottom line: worth engaging with as a referee, not worth citing as it stands.","headline":"The framework is a reasonable next step for MA-aided multiuser secrecy, but Section III has two load-bearing derivation errors that break the claimed equivalence to sum-secrecy-rate maximization.","tokens_in":11188,"tokens_out":5594,"would_cite":false,"duration_ms":54606,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Movable antenna arrays can raise multiuser secrecy rates above fixed-position array levels, and a new block coordinate descent algorithm maximizes the sum secrecy rate by jointly tuning beamforming and antenna placements.","keywords":["movable antennas","physical layer security","sum secrecy rate","beamforming","fractional programming","block coordinate descent","wiretap channel","MISO"],"falsifier":"Compute the actual achievable secrecy region for a two-user, two-eavesdropper wiretap channel where eavesdroppers do not cooperate or cannot cancel the other user's signal, via exhaustive search over rate-splitting parameters; if the sum rate from equation (7) exceeds the true boundary, the FP optimization would be maximizing an upper bound rather than the true sum secrecy rate.","tokens_in":10247,"feed_emoji":"📡","tokens_out":4295,"duration_ms":42832,"temperature":0.7,"pith_summary":"This paper aims to establish that movable antennas (MAs) — antennas whose physical positions can be tuned within a region — improve physical-layer security in multiuser wireless systems. It derives a sum secrecy rate expression for a base station serving K users while J cooperating eavesdroppers listen, then develops a joint optimization of digital beamforming and antenna positions that maximizes this rate. The optimization alternates closed-form updates for beamformers with low-complexity one-dimensional searches for antenna coordinates, converging within tens of iterations. Numerical results show the MA design consistently beats a fixed-position antenna array baseline, with gains growing in number of antennas and transmit-region size. If the approach holds, MA placement becomes a practical lever for secrecy in next-generation MIMO systems.","feed_headline":"Movable antennas out-secure fixed arrays in multiuser links","feed_subtitle":"Joint beamforming-and-placement tuning beats fixed-array baselines and converges in about 20 iterations.","key_machinery":"The central object is the field-response channel model, h_k(t_m) = Σ β_{k,ℓ} e^{-j(2π/λ) t_m^T ρ_{k,ℓ}}, which ties each antenna's position t_m to the phase of each propagation path, making the channel (and hence the secrecy rate) an explicit function of antenna coordinates. On top of this, the paper's analytical engine is the fractional-programming (FP) variational reformulation, which introduces auxiliary variables α, β, and η so that the sum secrecy rate becomes separately concave in W, T, b, α, β, and η; each block then admits a simple update. The bound g on the eavesdroppers' aggregated SNR, derived via Cauchy–Schwarz and the power constraint, is what lets the non-smooth [·]^+ operator","core_discovery":"The central claim is that in a multiuser wiretap channel, jointly optimizing the digital beamformer and the positions of movable transmit antennas maximizes the achievable sum secrecy rate, and the underlying rate expression depends on antenna positions through a field-response channel model. The paper proves a sequence of equivalences (Lemmas 1–4) that turn the non-smooth, non-concave secrecy-rate objective into a variational form that is separately concave in each variable block. A block coordinate descent algorithm then achieves a stationary point, with the beamformer update given in closed form via a regularized inverse, the position update via element-wise one-dimensional grid search, a","pith_inferences":["The secrecy-rate expression (7) assumes cooperating eavesdroppers can cancel multiuser interference; a natural extension would be to relax this to non-cooperating or partially cooperating eavesdroppers, where the residual interference would change the achievable rate region.","The paper treats MA positions as tunable within a continuous square region; one could test whether a small number of discrete candidate positions (e.g., a finite codebook) captures most of the gain, which would simplify deployment.","The gains over FPA are shown for a specific field-response model with LoS plus three NLoS paths; whether the advantage persists under more diffuse scattering or channel-estimation error is an open empirical question."],"forward_implications":["If the MA-enabled optimization is adopted, base stations with movable antennas can operate at higher secrecy rates than half-wavelength-spaced fixed arrays, all else equal.","The algorithm's per-iteration complexity is dominated by an O(M^3) beamformer update and a grid search over MA positions, so it scales to arrays of moderate size; the authors report convergence within roughly 20 iterations.","Increasing the antenna count M or the transmit-region side length A both improve secrecy rates, whereas increasing the number of eavesdroppers J degrades them — giving system designers a concrete trade-off landscape.","In the RF-limited regime (M small relative to K), adding users decreases the secrecy rate, indicating that MA placement cannot fully compensate for insufficient spatial degrees of freedom."],"fun_headline_variants":["Movable antennas boost multiuser secrecy rates","Joint placement and beamforming beats fixed antennas","Movable antenna arrays secure higher sum rates","Optimized antenna positions improve secure beamforming","Efficient joint design for secrecy with movable antennas"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The whole optimization stands on the assumption that the eavesdroppers can pool their observations and cancel every other user's signal, so that the only leakage a user must worry about is the eavesdroppers' combined signal-to-noise ratio for that user's beam; if they cannot achieve that cancellation, the sum secrecy rate being maximized is too optimistic.","fun_headline_variants_meta":{"raw":{"variants":["Movable antennas boost multiuser secrecy rates","Joint placement and beamforming beats fixed antennas","Movable antenna arrays secure higher sum rates","Optimized antenna positions improve secure beamforming","Efficient joint design for secrecy with movable antennas"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000321,"raw_usage":{"total_tokens":1580,"prompt_tokens":619,"completion_tokens":961,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":363,"completion_tokens_details":{"reasoning_tokens":893}},"tokens_in":363,"tokens_out":961,"duration_ms":11144,"temperature":1.0,"reasoning_tokens":893,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T11:34:19.280215+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the actual achievable secrecy region for a two-user, two-eavesdropper wiretap channel where eavesdroppers do not cooperate or cannot cancel the other user's signal, via exhaustive search over rate-splitting parameters; if the sum rate from equation (7) exceeds the true boundary, the FP optimization would be maximizing an upper bound rather than the true sum secrecy rate.","supporting_citations":[],"review_version":1}