Crosstalk-Resilient Beamforming for Movable Antenna Enabled Integrated Sensing and Communication

Chadi Assi; Jiacheng Yin; Maurice J. Khabbaz; Ning Wei; Yue Xiu; Zeyuan Zhang; Zheng Dong

REVIEW 5 major objections 4 minor 12 references

Crosstalk-Resilient Beamforming for Movable Antenna Enabled Integrated Sensing and Communication

T0 review · 5 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Crosstalk-aware movable-antenna beamforming lowers the angle-estimation Cramér-Rao bound in integrated sensing and communication.

desk verdict 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. read the letter →

arxiv 2509.03273 v1 pith:5BGM6LCL submitted 2025-09-03 eess.SP

Zeyuan Zhang , Yue Xiu , Zheng Dong , Jiacheng Yin , Maurice J. Khabbaz , Chadi Assi , Ning Wei This is my paper · ORCID

classification eess.SP

keywords integratedsensingandcommunicationmovableantennacrosstalkCramér-RaoboundjointbeamformingpositionoptimizationdeepreinforcementlearningTD3

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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

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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: 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.

What 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.

Soft 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.

The 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.

Who 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.

My 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.

Referee Report

5 major / 4 minor

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.

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 (5)

[Section II-B, Eqs. (7)-(8)] 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 III-A3, Eq. (16)] 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 III-A3, Eq. (18)] 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 IV, Table I and Eq. (13b)] 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 III-B and Section IV, Figs. 2-4] 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.

minor comments (4)

[Section V (Conclusion)] The word 'propsoed' should be 'proposed'.
[Appendix, Eq. (24a)] 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.
[Fig. 4 caption and Section IV] 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 III-A2] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the CRB is derived from the likelihood in the Appendix, and the TD3 reward is deliberately the CRB objective itself, not an input disguised as a prediction.

full rationale

The central derivation is self-contained and non-circular. The CRB formula in Eqs. (12)/(28) is obtained by forming the Fisher information matrix in the Appendix from the likelihood of the sensing observation, and the only model ingredient imported from prior work is the crosstalk coefficient model c_mn = η d_mn^{-ι} e^{-j(ν d_mn+ξ)} from reference [7], an external source not authored by the present authors. The reward in Eq. (16) is deliberately set equal to the CRB numerator plus a SINR penalty; choosing the reward to be the quantity being minimized is the definition of an optimization objective, not a hidden equivalence between input and output. No fitted parameter is later renamed as a prediction: the simulations compare policies trained on the same CRB objective, with the proposed policy additionally given the true crosstalk matrix in its reward. That is a difference in the information available to the agent, not a derivation loop. The self-citations [2] and [3] provide background on movable-antenna hardware and related MA-ISAC beamforming; they do not carry the CRB derivation, the TD3 construction, or the numerical conclusions. One non-circular reproducibility concern is that Eq. (7) leaves the diagonal of the coupling matrix undefined for m = n, and the minimum separation D0 in constraint (13b) is not listed in Table I; these affect the quantitative values in Figs. 3–4 but do not make the derivation circular.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central numerical claim rests on parameters imported from [7], an unspecified diagonal convention for the crosstalk matrix, and a set of standard domain assumptions (far-field, single-path target, Gaussian clutter, perfect CSI). None of these are derived in the paper, and the paper does not test sensitivity to them.

free parameters (3)

Crosstalk model parameters η, ι, ν, ξ = η=3.5e-5, ι=1.9, ν=600.4, ξ=252.8
Taken from [7] (Section IV); the central numerical results are specific to these values and no robustness sweep is provided.
Minimum antenna separation D0 = not specified
Constraint (13b) and the position parameterization in Eq. (18) rely on D0, but Table I does not list its value, so the feasible region is not fully defined.
SINR penalty factor υ = 0.1
Controls how strongly SINR violations are penalized in the reward (Eq. 17, Table I); different values could change the constraint satisfaction behavior.

assumptions (4)

domain assumption The crosstalk coupling between two antennas depends only on their separation through c_mn = η d^{-ι} e^{-j(ν d+ξ)}.
Imported from [7] for uniform linear arrays and assumed to hold for arbitrary movable-antenna positions, including the diagonal behavior which is left undefined (Eq. 7).
domain assumption Far-field propagation and single-path sensing channel.
Eq. (3) uses a single-path steering vector for the target, stated as 'for proof of concept' (Section II-A).
domain assumption Clutter echoes are zero-mean Gaussian noise with power σ_c^2.
Assumed in the Appendix following [11], combined into effective noise variance σ_n^2 = σ_s^2 + σ_c^2.
domain assumption Perfect knowledge of crosstalk matrix, channel gains, and angles at the agent.
State space in Eq. (14) includes ρ and θ, and the reward uses C(p_t); the paper does not model CSI estimation error or crosstalk uncertainty.

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Cite this review

Pith. "Pith review of Crosstalk-Resilient Beamforming for Movable Antenna Enabled Integrated Sensing and Communication." pith.science (2026). https://pith.science/paper/5BGM6LCL

@misc{pith2026250903273,
  author       = {Pith},
  title        = {Pith review of: Crosstalk-Resilient Beamforming for Movable Antenna Enabled Integrated Sensing and Communication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5BGM6LCL}},
  note         = {Machine review of arXiv:2509.03273}
}

read the original abstract

This paper investigates a movable antenna (MA) enabled integrated sensing and communication (ISAC) system under the influence of antenna crosstalk. First, it generalizes the antenna crosstalk model from the conventional fixed-position antenna (FPA) system to the MA scenario. Then, a Cramer-Rao bound (CRB) minimization problem driven by joint beamforming and antenna position design is presented. Specifically, to address this highly non-convex flexible beamforming problem, we deploy a deep reinforcement learning (DRL) approach to train a flexible beamforming agent. To ensure stability during training, a Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm is adopted to balance exploration with reward maximization for efficient and reliable learning. Numerical results demonstrate that the proposed crosstalk-resilient (CR) algorithm enhances the overall ISAC performance compared to other benchmark schemes.

Figures

Figures reproduced from arXiv: 2509.03273 by the authors.

**Figure 3.** Average CRB performance versus SNR. 8 10 12 14 16 18 20 -75 -70 -65 -60 -55 -50 -45 -40 -35 CRB (dB) FPA+RBF FPA+TD3 MA+TD3 CR-MA+TD3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Average CRB performance versus the different region of the array. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Review history (2 revisions) →

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Reference graph

Works this paper leans on

12 extracted references · 9 canonical work pages

[7]

Wolosinski, H

G. Wolosinski, H. Tataria, and V. Fusco, ``Closed form characterization of mutual coupling in uniform linear arrays,'' in 2020 14th European Conference on Antennas and Propagation (EuCAP), 2020, pp. 1--5

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work page 2025
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arXiv 2025
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H. Qin, W. Chen, Q. Wu, Z. Zhang, Z. Li, and N. Cheng, ``Cramér-rao bound minimization for movable antenna-assisted multiuser integrated sensing and communications,'' IEEE Wireless Commun. Lett., vol. 13, no. 12, pp. 3404--3408, 2024

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Hausmair, P

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2024

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [7]

Wolosinski, H

G. Wolosinski, H. Tataria, and V. Fusco, ``Closed form characterization of mutual coupling in uniform linear arrays,'' in 2020 14th European Conference on Antennas and Propagation (EuCAP), 2020, pp. 1--5

work page 2020

[2] [1]

X. Zhu, J. Liu, L. Lu, T. Zhang, T. Qiu, C. Wang, and Y. Liu, ``Enabling intelligent connectivity: A survey of secure ISAC in 6G networks,'' IEEE Communications Surveys & Tutorials, 2024

work page 2024

[3] [2]

Y. Xiu, S. Yang, W. Lyu, P. Lep Yeoh, Y. Li, and Y. Ai, ``Movable antenna enabled ISAC beamforming design for low-altitude airborne vehicles,'' IEEE Wireless Commun. Lett., vol. 14, no. 5, pp. 1311--1315, 2025

work page 2025

[4] [3]

Y. Xiu, Y. Zhao, R. Yang, D. Niyato, J. Jin, Q. Wang, G. Liu, and N. Wei, ``Movable antenna-aided cooperative ISAC network with time synchronization error and imperfect CSI,'' 2025. [Online]. Available: https://arxiv.org/abs/2501.15410

arXiv 2025

[5] [4]

H. Qin, W. Chen, Q. Wu, Z. Zhang, Z. Li, and N. Cheng, ``Cramér-rao bound minimization for movable antenna-assisted multiuser integrated sensing and communications,'' IEEE Wireless Commun. Lett., vol. 13, no. 12, pp. 3404--3408, 2024

work page 2024

[6] [5]

Hausmair, P

K. Hausmair, P. N. Landin, U. Gustavsson, C. Fager, and T. Eriksson, ``Digital predistortion for multi-antenna transmitters affected by antenna crosstalk,'' IEEE Trans. Microwave Theory Tech., vol. 66, no. 3, pp. 1524--1535, 2018

work page 2018

[7] [6]

S. S. A. Yuan, X. Chen, C. Huang, and W. E. I. Sha, ``Effects of mutual coupling on degree of freedom and antenna efficiency in holographic MIMO communications,'' IEEE Open Journal of Antennas and Propagation, vol. 4, pp. 237--244, 2023

work page 2023

[8] [8]

H.-S. Lui, H. T. Hui, and M. S. Leong, ``A note on the mutual-coupling problems in transmitting and receiving antenna arrays,'' IEEE Antennas Propag. Mag., vol. 51, no. 5, pp. 171--176, 2009

work page 2009