{"id":"6ff8170b-e540-4c90-b103-c532e8298e41","arxiv_id":"2509.03273","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A crosstalk-aware movable antenna ISAC design that jointly optimizes antenna positions and beamforming with TD3 reinforcement learning lowers the Cramer-Rao bound for angle estimation compared with fixed arrays and crosstalk-ignorant baselines.","lead":"Movable antenna systems can adjust their element positions, but antenna crosstalk changes as antennas move. This paper uses deep reinforcement learning to jointly choose antenna positions and beamforming so that radar angle estimation error stays low while user communication quality holds.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Crosstalk matrix C(p) in Eq. (7) is undefined for m=n, yet every CRB, reward, and simulation uses the full matrix; the central numerical claim is not reproducible without a stated diagonal convention.","rationale":"The reader's weakest_assumption correctly identifies the undefined diagonal. I checked the CRB derivation and it is algebraically sound: the Schur complement in the Appendix yields Eq. (28), and the conjugate convention for α_s does not change the CRB. I also considered whether the SINR expression omits sensing-signal interference; with k' ranging over all K+N columns of F in Eqs. (9)–(10) the model is complete, so I do not press that. The stress-test therefore lands on the crosstalk matrix definition. Because C(p) enters every numerical result through g_s(p), the missing diagonal is load-bearing for the claimed quantitative gains, but it is fixable and does not invalidate the conceptual approach. The verdict stays CONDITIONAL; the paper should state the diagonal convention, D0, and ideally add error bars before acceptance.","tokens_in":7962,"tokens_out":19858,"duration_ms":192178,"concrete_test":"Run the Section IV comparison with all parameters fixed except the diagonal of C(p): set c_mm=1 for one run and c_mm=0 for a second, using the same D0 (which must also be reported). If the difference in the CR-MA+TD3-to-MA+TD3 gap in Fig. 3 changes by more than about 1 dB, or the ordering of schemes changes, the headline result depends on the unspecified diagonal; if the gap is invariant, the concern is only a documentation error.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (7) defines c_mn = η d_mn^{-ι} e^{-j(ν d_mn+ξ)} for all m,n, with d_mn=|p_m-p_n|. For m=n this gives 0^{-ι}, which is infinite/undefined, so the diagonal of C(p) in Eq. (8) is not specified. The CRB in Eq. (12)/(28), the reward in Eq. (16), and every curve in Figs. 3–4 depend on the full effective channel g_s(p)=C^H(p)a_s(p); a different diagonal convention (C_mm=1 vs C_mm=0, or omitting the diagonal) changes the array gain, the CRB values, and potentially the reported gains over FPA+TD3 and MA+TD3. The same issue affects the missing D0 in constraint (13b), which does not appear in Table I. This is not a mathematical error in the FIM derivation—the CRB algebra in the Appendix is internally consistent—but it makes the quantitative claim 'CR-MA+TD3 outperforms all alternatives' underdetermined as written. The fix is a one-line convention, not a new method, which is why the paper is conditionally acceptable rather than rejectable.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a monostatic movable-antenna integrated sensing and communication (MA-ISAC) downlink with N=16 movable transmit antennas, K single-antenna users, one sensing target, and distance-dependent antenna crosstalk modeled by a coupling matrix C(p). It derives a Cramér-Rao bound (CRB) for target angle estimation under crosstalk (Eq. (12), Appendix), formulates a joint precoder-and-antenna-position CRB minimization subject to antenna separation, positioning, SINR, and power constraints (Eq. (13)), and proposes a Twin Delayed Deep Deterministic Policy Gradient (TD3) solution with a Markov decision process formulation, a custom action parameterization, and Ornstein-Uhlenbeck exploration noise. Numerical results compare FPA+RBF, FPA+TD3, crosstalk-ignorant MA+TD3, and the proposed crosstalk-resilient CR-MA+TD3 in terms of CRB versus SNR and versus array region size, concluding that the proposed scheme outperforms all alternatives.","tokens_in":8221,"tokens_out":7675,"duration_ms":68831,"significance":"If the modeling conventions are fixed and the simulations are reproducible, the paper makes a worthwhile contribution by extending crosstalk-aware beamforming to movable-antenna ISAC and by demonstrating that jointly learning antenna positions and precoders can reduce the sensing CRB. The CRB derivation in the Appendix follows standard Slepian-Bangs / complex Fisher-information algebra and is internally consistent. The effective crosstalk-involved channel g_s(p)=C^H(p)a_s(p) is a natural generalization of the fixed-array coupling model of [7], and the TD3 formulation with OU noise and a recursive position parameterization is a reasonable approach to the strongly nonconvex problem. The paper does not provide machine-checked proofs or code, but the analytical derivation is amenable to verification once the undefined quantities are specified. The main value currently lies in the problem formulation and the proposed DRL pipeline; the quantitative claims are not yet reproducible from the manuscript as written.","major_comments":[{"comment":"The crosstalk coefficient c_mn = η d_mn^{-ι} e^{-j(ν d_mn+ξ)} is undefined on the diagonal: for m=n, d_mn=0 gives 0^{-ι}. Yet the full matrix C(p) enters the effective channel g_s(p)=C^H(p)a_s(p), and therefore every CRB value in Eqs. (12), (28), the reward in Eq. (16), and all curves in Figs. 3-4 depend on the diagonal convention. Please state explicitly whether c_mm=1, c_mm=0, or some other self-coupling value is used, and confirm that the simulations use the stated convention. This is a one-line modeling convention, but without it the reported numerical gains are not reproducible.","section":"Section II-B, Eqs. (7)-(8)"},{"comment":"The reward R_t in Eq. (16) equals the positive bracket in the CRB expression (12), i.e., ˙g_s^H F F^H ˙g_s − |g_s^H F F^H ˙g_s|^2/(g_s^H F F^H g_s), plus the non-positive SINR penalty cSINR_t. Since TD3 maximizes cumulative reward, maximizing this R_t would maximize CRB_θs, directly contradicting the minimization objective (13a). Unless the algorithm actually minimizes the return, a negative sign is missing (e.g., R_t = −[bracket] + cSINR_t, or R_t = −CRB_θs up to constants). Please clarify and correct Eq. (16).","section":"Section III-A3, Eq. (16)"},{"comment":"The recursive position parameterization double-counts Δ_1. With p_1 = p_min + Δ_1 and p_n = p_1 + (n−1)D0 + Σ_{k=1}^n Δ_k for n≥2, the term Δ_1 appears both in p_1 and in the sum, so p_N = p_min + Δ_1 + (N−1)D0 + Σ_{k=1}^N Δ_k. Consequently the stated constraint Σ_{n=1}^N Δ_n ≤ Δ_max = p_max − (N−1)D0 does not enforce p_N ≤ p_max, and the claimed equivalence with constraints (13b)-(13c) is not correct as written. The intended recurrence likely has the sum starting at k=2; please fix the formula and restate the correct maximum-displacement constraint.","section":"Section III-A3, Eq. (18)"},{"comment":"The minimum antenna separation D0 appears in constraint (13b) and in the parameterization (18), but D0 is not listed in Table I or anywhere in the simulation setup. The numerical CRB results and the achievable antenna positions cannot be reconstructed without D0. Please add D0 to the table, and consider listing the crosstalk model parameters η, ι, ν, ξ there as well rather than only in the text.","section":"Section IV, Table I and Eq. (13b)"},{"comment":"The TD3 implementation details are not specified: hidden-layer sizes and activations for the actor and critic networks, learning rates, batch size, replay buffer capacity, target update frequency, and the delayed-update ratio are all omitted. In addition, Figs. 3-4 show single curves with no error bars or multiple-seed statistics, while Fig. 2 reports one training run. Because deep RL is stochastic and the convergence claim depends on the training configuration, please report mean±standard deviation over at least several random seeds and provide the full hyperparameter list.","section":"Section III-B and Section IV, Figs. 2-4"}],"minor_comments":[{"comment":"The word 'propsoed' should be 'proposed'.","section":"Section V (Conclusion)"},{"comment":"The mean observation is written as α_s^* S^H F^H g_s(p), whereas the signal model in Eq. (11) uses α_s without conjugation. The final CRB is unaffected in magnitude, but please state the conjugation convention or align the notation for consistency.","section":"Appendix, Eq. (24a)"},{"comment":"The horizontal axis of Fig. 4 is described only as 'the different region of the array'; please specify whether it is p_max−p_min, the region size in wavelengths, or the maximum aperture, and state the corresponding values of D0 and pmax for each plotted point.","section":"Fig. 4 caption and Section IV"},{"comment":"The custom activation layer for the beamforming action is described verbally ('N×K unit modulus phase achieved by tanh and K power control coefficients achieved by softmax'). A short equation or pseudo-code for the mapping from action logits to the feasible precoder F_t would improve reproducibility.","section":"Section III-A2"}],"recommendation":"major_revision","confidential_remarks":"The paper is, in its present form, an early preprint with several missing conventions rather than a completed journal submission. The central CRB derivation is sound, so the appropriate route is a major revision rather than rejection. The crosstalk-diagonal and reward-sign issues are the most urgent because they directly affect the validity of the reported performance gains; the D0 and TD3-detail omissions are also load-bearing for reproducibility. I saw no evidence of circularity or of attempts to obscure limitations; the missing items appear to be editorial omissions that can be fixed within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the core idea is reasonable and the CRB math in the appendix is internally consistent, but the paper as written has a one-line hole that undermines every numerical curve until fixed. The crosstalk matrix C(p) in Eq. (7) defines c_mn = η d_mn^{-ι} e^{-j(ν d_mn+ξ)} for all m,n. For m=n, d_mn=0, so the diagonal is undefined. The effective channel g_s(p)=C^H(p)a_s(p) appears in the CRB, the reward, and all simulations. Without a stated diagonal convention (e.g., C_mm=1), the array gain, CRB values, and reported gains over the baselines are all underdetermined. This is not a deep flaw—it is a missing modeling convention—but it is load-bearing.\n\nWhat the paper does well: it is the first, as far as I can tell, to treat antenna crosstalk as position-dependent in a movable-antenna ISAC system, and it correctly recognizes that antenna movement changes the coupling pattern. The CRB derivation follows standard estimation theory, and the FIM algebra in the appendix checks out. The TD3 formulation is a straightforward application of a known DRL algorithm to a new objective, which is fine for an engineering paper. The numerical study is internally consistent under the assumed crosstalk parameters, and the convergence plot in Fig. 2 is a nice sanity check.\n\nSoft spots, in proportion: (1) the missing diagonal convention, as above; (2) the minimum separation D0 in constraint (13b) never appears in Table I, so the geometry is not fully specified; (3) TD3 network architecture, learning rates, batch size, and exploration noise schedule are omitted—only the OU noise decay is given; (4) no error bars or multiple-seed reporting for a DRL method, which is noticeably weak given the stochasticity. None of these are fatal to the approach, but they are all needed to reproduce the claimed 5–10 dB gains. The baseline set is also narrow (FPA+RBF is a weak strawman), though MA+TD3 is a reasonable reference point.\n\nThe citation pattern is honest and the related work is properly positioned. The paper does not oversell its novelty—it claims an incremental but useful extension and delivers exactly that, pending the diagonal fix.\n\nWho this is for: researchers working on movable-antenna ISAC or DRL-based beamforming. They will get a clear problem formulation and a working template for CRB-based reward design. It deserves a serious referee, but the referee should insist on a stated diagonal convention and full simulation details before the quantitative claims are accepted.\n\nMy recommendation: send it to peer review, but expect minor-to-moderate revision. The central idea is sound; the presentation needs to close the reproducibility gaps.","headline":"Sensible MA-ISAC crosstalk extension with a checkable CRB derivation, but an undefined crosstalk-matrix diagonal and missing simulation details keep the quantitative claims from being reproducible as written.","tokens_in":8786,"tokens_out":2121,"would_cite":false,"duration_ms":20950,"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":"Crosstalk-aware movable-antenna beamforming lowers the angle-estimation Cramér-Rao bound in integrated sensing and communication.","keywords":["integrated sensing and communication","movable antenna","antenna crosstalk","Cramér-Rao bound","joint beamforming","antenna position optimization","deep reinforcement learning","TD3"],"falsifier":"Recompute the CRB curves in Figs. 3 and 4 with the diagonal of the coupling matrix set explicitly, for example $C_{mm}=1$ for all $m$, while keeping every other parameter unchanged; if the reported advantage of the crosstalk-resilient movable-antenna scheme over the crosstalk-ignoring movable-antenna scheme shrinks or reverses, the central claim does not survive. A direct measurement of the coupling matrix of a small movable array would settle which diagonal convention is physically correct.","tokens_in":7772,"feed_emoji":"📡","tokens_out":12760,"duration_ms":99502,"temperature":0.7,"pith_summary":"This paper asks whether movable antennas can improve integrated sensing and communication when the antennas themselves are coupled by crosstalk. It generalizes a standard closed-form crosstalk model from fixed arrays to movable arrays, derives the Cramér-Rao bound (CRB) for estimating a target angle with the crosstalk matrix included, and then trains a deep reinforcement-learning agent to jointly choose the antenna positions and the transmit beamforming. The central claim is that this crosstalk-aware joint design achieves a lower angle-estimation CRB than fixed-array baselines and than movable-antenna designs that ignore crosstalk. If the claim holds, the extra mechanical degrees of freedom of movable antennas can be used to absorb, rather than merely suffer, the mutual-coupling penalty in compact arrays.","feed_headline":"Crosstalk-aware movable antennas sharpen target-angle sensing in ISAC","feed_subtitle":"In integrated sensing and communication, moving antennas and adapting their precoding together beats fixed arrays even with crosstalk.","key_machinery":"The load-bearing object is the effective crosstalk-involved steering response $g_s(p)=C^H(p)a_s(p)$, built from the coupling matrix $[C(p)]_{mn}=c_{mn}$ with $c_{mn}=\\eta d_{mn}^{-\\iota}e^{-j(\\nu d_{mn}+\\xi)}$ and $d_{mn}=|p_m-p_n|$. It converts the crosstalk matrix into a modified channel that appears everywhere in the CRB, the reward, and the SINR constraints. The second piece of machinery is the TD3 algorithm, an off-policy actor-critic method with twin Q-networks, delayed policy updates, and clipped target smoothing, which is used to search the joint space of precoders and antenna positions. The reward is essentially the part of the CRB denominator that depends on the design variables, plus a SINR-violation penalty; maximizing it is equivalent to lowering the CRB while keeping communication quality.","core_discovery":"The paper's central discovery is an analytical and algorithmic recipe for making antenna crosstalk work against itself. The sensing channel is rewritten through an effective crosstalk-involved response $g_s(p)=C^H(p)a_s(p)$, where $C(p)$ is the coupling matrix whose entries depend on inter-antenna distances. The target-angle Cramér-Rao bound then takes the form $$\\mathrm{CRB}_{\\theta_s} = \\frac{\\$sigma_n^{2}$}{2L|\\alpha_s|^2}\\left[\\dot{g}_s^H(p)FF^H\\dot{g}_s(p)-\\frac{|g_s^H(p)FF^H\\dot{g}_s(p)|^2}{g_s^H(p)FF^H g_s(p)}\\right],$$ and the paper proposes to minimize this quantity over the precoding matrix $F$ and the antenna positions $p$, subject to minimum antenna separation, feasible region, per-user SINR, and total power constraints. Because that optimization is highly non-convex, the proposed solution is a Twin Delayed Deep Deterministic Policy Gradient (TD3) agent whose action is the joint beamforming and position update and whose reward is the negative of this CRB plus a penalty for SINR violations. Numerical results in the paper show the crosstalk-resilient TD3 scheme outperforming fixed half-wavelength ULA configurations and a movable-antenna TD3 scheme that ignores crosstalk.","pith_inferences":["The same substitution $g_s(p)=C^H(p)a_s(p)$ should carry over to multi-target and clutter-aware CRB derivations, so the machinery is not obviously limited to a single point target.","Because the state already includes angles and channel gains, the TD3 agent could be extended to tracking by feeding it target-angle estimates from previous frames; the reward would then be a time-averaged CRB rather than an instantaneous one.","A clean experiment would add a fourth baseline: a fixed-position array optimized by the same crosstalk-aware TD3 agent. That would isolate how much of the gain comes from mobility itself versus from crosstalk awareness in the reward.","The distance-only dependence of the coupling model suggests the matrix $C(p)$ could be learned from measured S-parameters during training, turning the parametric model into a data-driven prior and making the agent robust to model mismatch."],"forward_implications":["A movable-antenna ISAC base station that jointly optimizes positions and precoding with crosstalk in the reward achieves a lower angle-estimation CRB than a fixed half-wavelength ULA with random or TD3-optimized beamforming.","The sensing gain grows with the size of the movable region: the paper reports the CRB falling from about $-63.8$ dB at a $7.5\\lambda$ region to below $-70.9$ dB at a $20\\lambda$ region, showing that extra mechanical freedom directly buys estimation accuracy.","The TD3 training converges steadily around 200 episodes and stays near its final reward thereafter, indicating that a single actor-critic agent can handle the joint continuous optimization without an alternating closed-form solution.","Specializing the coupling matrix to the identity recovers the standard no-crosstalk MA-ISAC CRB, so the derived bound is a strict generalization of earlier analyses.","The penalty formulation means communication QoS is not sacrificed for sensing: the agent balances the inverse CRB against per-user SINR constraints inside the reward."],"supporting_citations":[{"why":"Supplies the closed-form mutual-coupling model $c_{mn}=\\eta d_{mn}^{-\\iota}e^{-j(\\nu d_{mn}+\\xi)}$ that the paper generalizes to movable antennas.","marker":"[7]"},{"why":"Provides the crosstalk signal model $x_n[l]=\\sum_m c_{mn}u_m[l]$ that defines the coupling matrix in Eq. (6).","marker":"[9]"},{"why":"Establishes the CRB-minimization formulation for movable-antenna ISAC that this paper extends with crosstalk.","marker":"[4]"},{"why":"Supplies the movable-antenna channel and position-control model (flexible wires and stepper motors) used in Eqs. (1)-(3).","marker":"[2]"},{"why":"Defines the Twin Delayed Deep Deterministic Policy Gradient algorithm used to train the joint beamforming and positioning agent.","marker":"[10]"},{"why":"Justifies treating clutter echoes as Gaussian noise and provides the Fisher-information derivation structure used for the CRB in the appendix.","marker":"[11]"}],"fun_headline_variants":["Crosstalk-resilient movable antennas sharpen ISAC sensing","Joint MA positions and beamforming beat fixed arrays under crosstalk","TD3 solves non-convex crosstalk-aware ISAC beamforming","Reinforcement learning optimizes movable antenna ISAC against crosstalk","Turning crosstalk into an ally for movable antenna ISAC"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The results rest on the assumption that crosstalk between two antennas follows the distance-based formula in Eq. (7), but that formula has no defined value when the two antennas are at the same point, and the paper never states what value it uses for those diagonal entries; changing that unstated value will change the reported gains.","fun_headline_variants_meta":{"raw":{"variants":["Crosstalk-resilient movable antennas sharpen ISAC sensing","Joint MA positions and beamforming beat fixed arrays under crosstalk","TD3 solves non-convex crosstalk-aware ISAC beamforming","Reinforcement learning optimizes movable antenna ISAC against crosstalk","Turning crosstalk into an ally for movable antenna ISAC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00038,"raw_usage":{"total_tokens":2045,"prompt_tokens":996,"completion_tokens":1049,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":612,"completion_tokens_details":{"reasoning_tokens":958}},"tokens_in":612,"tokens_out":1049,"duration_ms":8829,"temperature":1.0,"reasoning_tokens":958,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:31:37.552189+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the CRB curves in Figs. 3 and 4 with the diagonal of the coupling matrix set explicitly, for example $C_{mm}=1$ for all $m$, while keeping every other parameter unchanged; if the reported advantage of the crosstalk-resilient movable-antenna scheme over the crosstalk-ignoring movable-antenna scheme shrinks or reverses, the central claim does not survive. A direct measurement of the coupling matrix of a small movable array would settle which diagonal convention is physically correct.","supporting_citations":[{"cited_title":"Wolosinski, H","cited_arxiv_id":null,"evidence_quote":"Supplies the closed-form mutual-coupling model $c_{mn}=\\eta d_{mn}^{-\\iota}e^{-j(\\nu d_{mn}+\\xi)}$ that the paper generalizes to movable antennas."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the crosstalk signal model $x_n[l]=\\sum_m c_{mn}u_m[l]$ that defines the coupling matrix in Eq. (6)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the CRB-minimization formulation for movable-antenna ISAC that this paper extends with crosstalk."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the movable-antenna channel and position-control model (flexible wires and stepper motors) used in Eqs. (1)-(3)."},{"cited_title":"Boyer, ``Performance bounds and angular resolution limit for the moving colocated MIMO radar,'' IEEE Trans","cited_arxiv_id":null,"evidence_quote":"Justifies treating clutter echoes as Gaussian noise and provides the Fisher-information derivation structure used for the CRB in the appendix."}],"review_version":2}