{"id":"94d2d8c0-75dc-425b-9a6b-ed84ff0a6b1b","arxiv_id":"2501.01217","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Movable antennas placed on both transmit and receive sides of an ISAC base station, with jointly optimized positions and beamformers, improve sensing SINR by roughly 57% over fixed antenna baselines in simulation.","lead":"A team of wireless engineers proposes a movable antenna design for base stations that jointly senses targets and serves users, and shows in simulation that it improves sensing quality by over 50% compared with fixed antennas. The result matters because it suggests 6G base stations could achieve radar-like sensing with fewer antennas and less power.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Appendix A's rank-one proof is unsupported: subtracting two rank-one matrices from a positive definite matrix can drop rank by 2, so Eq. (56) may fail and the SDR beamformer extraction is not justified.","rationale":"The reader's weakest-assumption identification is correct, and I agree with it. The paper's central claim is numerical: MAs deliver over 50% higher sensing SINR and can match FPA at roughly 7 dB lower transmit power. That claim is only as trustworthy as the algorithm used to generate it. The transmit-beamforming step is the core of the alternating algorithm: it supplies the beamformers that the MA-position updates and the next receive-beamforming update depend on. If the SDR returns a higher-rank X_n, the simple SVD extraction is invalid, and the subsequent iterations solve subproblems for a transmit beamformer that may be infeasible. The Appendix A proof is therefore not a cosmetic gap. The specific flaw is Eq. (56): for any Hermitian A≻0 and rank-one Hermitian H1,H2, rank(A−H1−H2) ≥ N−2, not N−1; a concrete example is A=I_3, H1=e1e1^H, H2=e2e2^H, giving rank 1, which is less than N−1=2. The 'randomness' of channel eigenvalues cannot rule this out. Although standard SDR tightness results exist for related MISO downlink problems, they typically require additional structure such as active SINR constraints or a specific number of users and are not established here. The paper also provides no code and no Monte Carlo description, so the numerical headline cannot currently be independently checked; however, that is secondary to the analytical gap. I would keep the CONDITIONAL verdict: the contribution is plausible and the simulation trends are internally consistent, but the algorithm's correctness is not established. A corrected rank-one proof or a randomization-based recovery procedure is needed before the numerical claims can be fully trusted.","tokens_in":25935,"tokens_out":7151,"duration_ms":75842,"concrete_test":"Solve P3.1 (or P3.2) with CVX/SDPT3 for 100 random channel realizations using the paper's channel model, e.g., N=4, K=2, L=2, M=3. After rounding eigenvalues below 1e-6 relative to trace to zero, count how many optimal X_k have rank > 1. If any optimal X_k has rank 2, the rank-one claim is false and the SVD extraction cannot be used without a randomization step; if all have numerical rank 1, the conclusion may still be true even though the proof in Eq. (56) is invalid, and a corrected proof should be supplied.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing concern is the rank-one tightness proof in Appendix A. In Eq. (56), the authors assert N−1 ≤ rank(Z_k) ≤ N for Z_k = A − ζ\\tilde H_d − \\barλ_k \\hat H_k, where A≻0 and \\tilde H_d, \\hat H_k are rank-one. This does not follow from any stated property: by Weyl's inequality, subtracting two rank-one PSD matrices from a positive definite Hermitian matrix can reduce the rank by two, so only rank(Z_k) ≥ N−2 is guaranteed. The appeal to 'the maximum eigenvalues of \\tilde H_d and \\hat H_k are different' is irrelevant to rank loss, and PSD-ness of Z_k does not prevent two eigenvalues from vanishing. Since (56) is the only input to the Sylvester inequality step (57) used to conclude rank(X_k) ≤ 1, the SDR relaxation is not proved tight. If a returned X_k has rank 2, the SVD extraction of w_n from W_n^* = X_n/ℓ is not feasible, and the transmit beamformer passed to the MA-position updates (P4.1, P5.1) may violate the SINR constraints. The headline numbers—the 57.54% gain at 25 dBm and the 18 dBm versus 25 dBm matching claim—depend on this beamformer being exact, and no Gaussian randomization fallback is described.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies an integrated sensing and communication (ISAC) system in which both the base-station transmitter and receiver are equipped with movable antennas (MAs) whose two-dimensional positions can be optimized. The authors formulate the problem of maximizing the sensing SINR subject to per-user communication SINR constraints and a transmit power constraint, and they propose an alternating optimization (AO) algorithm. The algorithm alternates between closed-form receive beamforming, transmit beamforming obtained via the Charnes-Cooper transform and semidefinite relaxation (SDR), and successive convex approximation (SCA) based updates of the transmit and receive antenna positions. Simulation results are reported showing that the proposed scheme outperforms fixed-position-antenna (FPA) and single-sided MA baselines, including a claimed 57.54% sensing SINR improvement over FPA at 25 dBm and an ability to match FPA's 25 dBm performance using only 18 dBm transmit power.","tokens_in":26225,"tokens_out":3021,"duration_ms":32282,"significance":"If the results hold, the paper makes a useful contribution to the emerging MA-ISAC literature: it extends MA position optimization to both ends of an ISAC link, includes clutter sensing, and provides a complete AO/SCA-style algorithm with complexity analysis. The work is independently grounded in the sense that the reported gains are evaluated against external FPA and single-sided MA baselines, and no fitted constants or self-referential derivations appear in the core numerical claims. The main risk is the unsupported SDR tightness proof, which is load-bearing for the transmit beamforming extraction and therefore for the headline simulation numbers.","major_comments":[{"comment":"The proof of Theorem 1 asserts that Z_k = A - zeta * Htilde_d - bar_lambda_k * Hhat_k satisfies rank(Z_k) >= N - 1 after subtracting two rank-one positive semidefinite matrices from A ≻ 0. This does not follow from any stated property: by Weyl's inequality or simple rank subadditivity, subtracting two rank-one matrices can reduce the rank by up to two, so only rank(Z_k) >= N - 2 is guaranteed in general. The observation that the maximum eigenvalues of Htilde_d and Hhat_k are different does not prevent two eigenvalues of A from being reduced to zero after both subtractions, and positive semidefiniteness of Z_k does not change that. Since Eq. (56) is the only input to the Sylvester inequality step (57) used to conclude rank(X_k) <= 1, the rank-one tightness of the SDR is not proved. If a returned X_k has rank 2, the SVD extraction of w_n from W_n^* = X_n / ell is not feasible, and the transmit beamformer subsequently used in the position updates (P4.1, P5.1) may violate the SINR constraints. No Gaussian randomization or other rank-recovery fallback is described. I ask the authors to either supply a rigorous proof of (56), or re-frame Theorem 1 as a heuristic claim and add a rank-recovery procedure with numerical validation of the rank-one property.","section":"Appendix A, Eq. (56)"},{"comment":"The convergence statement is asserted rather than proved. The text says 'the convergence is ensured by the presence of an upper power bound and the non-decreasing nature of each iteration,' but it does not establish that each subproblem update (20), P3/P3.1, P4.1, and P5.1 is individually monotone in the sensing SINR, nor that the SCA surrogate updates satisfy the standard sufficient decrease conditions, nor that an upper bound on the objective exists across the feasible set. The termination criterion in Algorithm 1 therefore has no proven basis, and the claim that the algorithm 'generally achieves convergence after 20 iterations' in Fig. 2 is an empirical observation without a supporting argument. Please provide a formal convergence proof for the AO-SCA scheme, or state the specific assumptions under which monotone convergence holds.","section":"Section III-E, convergence"},{"comment":"The simulation section does not report Monte Carlo details, making the quantitative claims difficult to verify. The first paragraph of Section IV specifies K=2, L=2, locations, path counts, and user path response distributions, but the target and clutter PRVs are only said to be 'configured appropriately,' the Rician factor kappa and the exact path loss exponents are not fully tied to the displayed curves, and no number of channel realizations, seed information, or averaging procedure is given. The headline percentages (57.54% at 25 dBm in Fig. 3, 38.43%, 21.12%, 77.67% in Fig. 7) appear to be point estimates without error bars or confidence intervals. Please add a complete parameter table, specify how many independent channel realizations are averaged, and report error bars or at least the range across realizations for the main comparison curves.","section":"Section IV, simulation setup"}],"minor_comments":[{"comment":"The organization paragraph states that conclusions are presented in Section VI, but the conclusions appear in Section V; please correct the cross-reference.","section":"Section I-C"},{"comment":"The word 'T ag/Benchmark' contains a typo; it should read 'Tag/Benchmark' or 'Benchmark schemes.'","section":"Section IV, paragraph before benchmarks"},{"comment":"In the receive antenna update, the condition is written as '1 ≤ b ≠ m ≤ N,' but the receive antenna index set is of size M, not N; this should be '1 ≤ b ≠ m ≤ M.'","section":"Algorithm 1, line 6"},{"comment":"The notation paragraph uses 'R(s)' for the real part but the main text later uses the symbol ℜ; please unify the notation.","section":"Notation, Section I-C"},{"comment":"The bounds involving the Hessians use both ||·||_2 and ||·||_F in the same chain; please clarify the norm being bounded and ensure the inequalities are written consistently.","section":"Equations (34)-(35)"},{"comment":"The claim that the proposed scheme at 18 dBm matches FPA at 25 dBm is stated without a direct comparison point in the text of Fig. 3; please indicate the corresponding operating point in the figure or state it explicitly in the caption.","section":"Section V, conclusion"}],"recommendation":"major_revision","confidential_remarks":"The central concern is the rank-one tightness proof in Appendix A, which is load-bearing for the transmit beamforming extraction and hence for the quantitative claims in Section V. If the authors cannot prove the rank bound, the SDR-based solution must be replaced by or supplemented with a rank-recovery mechanism, and the simulation claims need to be re-validated. The convergence proof and the missing Monte Carlo details are secondary but still important for a journal-level acceptance. I would like the editor to ask for a revised version that addresses these three points before sending the paper back for review."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Take the conditional verdict seriously. The paper extends MA-ISAC to 2D movable antennas on both Tx and Rx and reports ~57% sensing SINR gain over FPA at 25 dBm. The extension is real relative to prior work that uses Tx-only 1D or RIS-aided MAs. What is good: the problem formulation is careful, the AO decomposition is sensible (closed-form receive MVDR, Charnes-Cooper + SDR for transmit, SCA for positions), and the simulations sweep power, antenna counts, thresholds, and moveable area consistently. The gains are plausible and the baselines are fair.\n\nThe soft spot is exactly where the stress-test lands: Appendix A's rank-one proof. Equation (56) asserts N−1 ≤ rank(Z_k) after subtracting two rank-one matrices from A ≻ 0. That does not follow; Weyl's inequality only guarantees N−2. The claim that different maximum eigenvalues matter is irrelevant to rank loss. Since (57) relies on rank(Z_k) ≥ N−1, the conclusion rank(X_k) ≤ 1 is not established. If the SDR returns rank-2 solutions, the SVD extraction of w_n is not justified, and the reported power-matching result (18 dBm vs 25 dBm) could be an artifact. The authors need either a correct proof or a Gaussian randomization fallback.\n\nConvergence is also only asserted, not proved. The SCA bounds in (32)-(33) are surrogates; monotonic increase of the true sensing SINR is not guaranteed. And the paper gives no Monte Carlo details, no error bars, and no code. The smooth curves could be a single channel draw; that is not enough to support the percentage claims. Minor typo: \"T ag/Benchmark\" in Section IV.\n\nThese are fixable in revision. The central idea is not broken, and the comparisons are externally grounded. I would send this to peer review with a clear expectation of major revision. It is a solid incremental contribution for the MA-ISAC subfield, not a breakthrough. If the authors can repair the rank proof and add statistical transparency, it would be a decent journal paper.","headline":"Solid incremental extension of MA-ISAC to dual-sided 2D movable antennas, but the rank-one SDR tightness proof has a real gap and the simulation reporting is too thin to back the headline numbers.","tokens_in":26749,"tokens_out":3417,"would_cite":false,"duration_ms":35905,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that letting base-station antennas move within a small area can raise integrated sensing-and-communication performance by over 50% while using less power.","keywords":["integrated sensing and communication","movable antenna","antenna position optimization","beamforming design","sensing SINR","successive convex approximation","semidefinite relaxation"],"falsifier":"For a random channel realization where the two rank-one matrices in Appendix A have nearly parallel principal directions, solve $P_{3.2}$ and check whether any optimal solution has rank above one; if it does, the SDR tightness argument and the SVD extraction of the transmit beamformers fail.","tokens_in":25745,"feed_emoji":"📡","tokens_out":6404,"duration_ms":55413,"temperature":0.7,"pith_summary":"This paper sets out to show that the spatial degrees of freedom of movable antennas are not just a communication asset but a sensing asset in an integrated sensing and communication (ISAC) system. It proposes a design where both the transmit and receive arrays of a bistatic base station carry antennas that can shift position within a small two-dimensional region, and it optimizes those positions together with the transmit and receive beamformers. The target is to maximize sensing SINR while keeping every user's communication SINR above a required threshold. The paper reports that this dual-sided movable-antenna design outperforms single-sided and fixed-position baselines, with gains exceeding 50% in sensing SINR and a power saving of about 7 dB for equal sensing performance. If these results hold, movable antennas become a concrete way to get better ISAC performance without more antennas, more RF chains, or more transmit power.","feed_headline":"Moving antennas beat fixed arrays in ISAC by 57%","feed_subtitle":"Jointly repositioning transmit and receive antennas lifts sensing SINR and matches fixed arrays with 7 dB less power.","key_machinery":"The central mechanism is an alternating-optimization loop that cycles through three subproblems: a closed-form MVDR receive beamformer, a transmit-beamforming problem recast through the Charnes-Cooper transform and semidefinite relaxation (with a proof that the relaxed solution is rank-one), and a position-update step that replaces the nonconvex sensing-SINR and communication-SINR functions with second-order Taylor bounds inside a successive convex approximation. The channel model that makes position a variable is the field-response model, in which each propagation path contributes a phase that depends linearly on the antenna coordinates, so moving an antenna reshapes the array response vectors. This joint treatment is what lets the algorithm exploit the added spatial degrees of freedom for both sensing gain and interference suppression.","core_discovery":"The paper claims that an ISAC base station whose transmit and receive arrays both use movable antennas, with positions optimized jointly with the beamformers, achieves a sensing SINR about 57.54% higher than an otherwise identical fixed-position array at 25 dBm, and reaches the fixed-array sensing SINR with roughly 7 dB less transmit power (18 dBm versus 25 dBm). The optimization objective is sensing SINR, constrained by per-user communication SINR thresholds, and the gains come from using the added spatial degrees of freedom both to sharpen the target response and to suppress clutter echoes. The same framework also shows that deploying movable antennas on only one side of the link already helps, with receive-side movement providing larger sensing gains than transmit-side movement in the simulated scenarios.","pith_inferences":["A natural extension is to scale the user count and clutter count; the simulations fix K=2 and L=2, so whether the 57% gain survives denser interference is untested in the paper.","If the rank-one SDR proof is generically valid only when the two rank-one channel matrices are well separated in eigenstructure, then worst-case channel alignments may require a different extraction procedure; the paper does not explore this.","The saturation of gain with movement area suggests a design rule of thumb—size the MA region to about 2.6 wavelengths—which could be tested in a prototype.","Because receive-side MAs contributed more than transmit-side MAs in every simulated sweep, a resource-constrained deployment could start with moving receive antennas only and still capture most of the benefit."],"forward_implications":["Deploying movable antennas on both the transmit and receive arrays of an ISAC base station yields a 57.54% higher sensing SINR than fixed-position antennas at the same 25 dBm transmit power.","The same dual-sided MA design reaches the sensing SINR of a fixed-antenna system at about 18 dBm instead of 25 dBm, a saving of roughly 7 dB.","Single-sided MA deployments also help, with receive-side MAs providing larger gains than transmit-side MAs in the simulated scenarios.","The benefit of enlarging the antenna movement region saturates around a 2.6-wavelength side length, so the gain does not require unbounded antenna travel.","MA-assisted ISAC maintains stable sensing performance as communication SINR thresholds rise, losing about 1 dB when both user thresholds go from -5 dB to 20 dB."],"supporting_citations":[{"why":"Supplies the field-response channel model that expresses every channel vector as a position-dependent phase superposition.","marker":"[18]"},{"why":"Establishes the MIMO capacity motivation for movable antennas that the paper extends to ISAC.","marker":"[19]"},{"why":"Provides the antenna-position-optimization approach for multiuser MIMO that the paper adapts for transmit and receive MAs.","marker":"[26]"},{"why":"Shows movable antennas improve sensing alone, the result the paper generalizes to joint sensing and communication.","marker":"[39]"},{"why":"Presents the one-dimensional Tx-MA ISAC baseline that the paper compares against with 2D MAs at both ends.","marker":"[40]"},{"why":"Supplies the MVDR closed form used for the receive beamforming update.","marker":"[47]"},{"why":"Provides the majorization-minimization and SCA machinery behind the second-order Taylor expansions for antenna positions.","marker":"[49]"},{"why":"Supports the rank-one SDR proof by justifying that the two rank-one channel matrices have distinct maximum eigenvalues.","marker":"[51]"}],"fun_headline_variants":["Movable antennas lift ISAC sensing SINR by 57%","ISAC with movable antennas cuts power 7 dB at same sensing","Jointly moving antennas boosts ISAC sensing, trims power","Movable antennas match fixed ISAC with 7 dB less transmit power","ISAC sensing gain 57% from movable antennas, power cut 7 dB"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof that the relaxed transmit-beamforming problem has rank-one solutions assumes that subtracting the two one-dimensional channel terms from the positive-definite matrix $A$ still leaves a remainder of rank at least $N-1$, but that assumption is asserted without proof.","fun_headline_variants_meta":{"raw":{"variants":["Movable antennas lift ISAC sensing SINR by 57%","ISAC with movable antennas cuts power 7 dB at same sensing","Jointly moving antennas boosts ISAC sensing, trims power","Movable antennas match fixed ISAC with 7 dB less transmit power","ISAC sensing gain 57% from movable antennas, power cut 7 dB"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000489,"raw_usage":{"total_tokens":2398,"prompt_tokens":927,"completion_tokens":1471,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":543,"completion_tokens_details":{"reasoning_tokens":1377}},"tokens_in":543,"tokens_out":1471,"duration_ms":9870,"temperature":1.0,"reasoning_tokens":1377,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:32:04.171620+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For a random channel realization where the two rank-one matrices in Appendix A have nearly parallel principal directions, solve $P_{3.2}$ and check whether any optimal solution has rank above one; if it does, the SDR tightness argument and the SVD extraction of the transmit beamformers fail.","supporting_citations":[{"cited_title":"Modeling and Performance An alysis for Movable Antenna Enabled Wireless Communications,","cited_arxiv_id":null,"evidence_quote":"Supplies the field-response channel model that expresses every channel vector as a position-dependent phase superposition."},{"cited_title":"Movable-Antenna En hanced Multiuser Communication via Antenna Position Optimizatio n,","cited_arxiv_id":null,"evidence_quote":"Provides the antenna-position-optimization approach for multiuser MIMO that the paper adapts for transmit and receive MAs."},{"cited_title":"Movable Antenna Enhanced Wi reless Sensing via Antenna Position Optimization,","cited_arxiv_id":null,"evidence_quote":"Shows movable antennas improve sensing alone, the result the paper generalizes to joint sensing and communication."},{"cited_title":"MIMO Radar WaveformOptimiza- tion With Prior Information of the Extended Target and Clutt er,","cited_arxiv_id":null,"evidence_quote":"Supplies the MVDR closed form used for the receive beamforming update."},{"cited_title":"Majorization-Minim ization Algo- rithms in Signal Processing, Communications, and Machine L earning,","cited_arxiv_id":null,"evidence_quote":"Provides the majorization-minimization and SCA machinery behind the second-order Taylor expansions for antenna positions."},{"cited_title":"Exploiting NOMA and RIS in Integrated Sensing and Communication,","cited_arxiv_id":null,"evidence_quote":"Supports the rank-one SDR proof by justifying that the two rank-one channel matrices have distinct maximum eigenvalues."}],"review_version":1}