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arxiv: 2605.20535 · v1 · pith:YZD65X4Knew · submitted 2026-05-19 · 💻 cs.IT · eess.SP· math.IT

Rotatable Coupler Antenna Enhanced Wireless Network: Modeling and Coupler Rotation Optimization

Xiaodan Shao , Chuangye Shan , Weihua Zhuang , Xuemin Shen This is my paper

Pith reviewed 2026-05-21 06:07 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords rotatable coupler antennamechanical beamformingmutual couplingrotation optimizationSNR maximizationconditional-gradient algorithmpoint-to-point communicationpassive couplers
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The pith

Rotatable coupler antennas use one active antenna and multiple 3D-rotating passive couplers to achieve mechanical beamforming that maximizes user SNR.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a rotatable coupler antenna (RCA) consisting of one fixed active antenna and several low-cost passive couplers that independently rotate in three-dimensional space. It develops a channel model from multi-port circuit theory that expresses mutual coupling coefficients directly as functions of those rotations. The authors then pose and solve a nonconvex optimization problem that chooses the rotation angles to maximize received signal-to-noise ratio at a single-antenna user, subject to practical rotation limits. They introduce a spherical-cap conditional-gradient algorithm initialized by the cross-entropy method to find good rotation solutions. Simulations indicate that the resulting system outperforms benchmark schemes while using substantially fewer active antennas and RF chains.

Core claim

By modeling mutual coupling as a continuous function of 3D coupler rotations and optimizing those rotations, a single active antenna plus passive couplers can perform mechanical beamforming that raises received SNR without additional RF chains for the couplers.

What carries the argument

The multi-port circuit model that writes mutual coupling coefficients as explicit functions of the 3D coupler rotation angles, which converts the beamforming task into a constrained nonconvex optimization solved by a spherical-cap conditional-gradient algorithm with cross-entropy initialization.

If this is right

  • The RCA system can significantly improve communication performance compared with benchmark schemes.
  • The system requires substantially fewer active antennas and RF chains than conventional arrays.
  • The spherical-cap conditional-gradient algorithm with cross-entropy initialization produces high-quality rotation solutions under practical constraints.
  • Spectrum and energy efficient wireless links become feasible at lower hardware cost through mechanical reconfiguration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same rotation-optimization approach could be applied to multi-user downlink scenarios where coupler angles are chosen to shape channels toward several receivers simultaneously.
  • In large-scale base stations this mechanical degree of freedom might reduce total power draw by keeping most elements passive and RF-chain-free.
  • Practical systems would need to balance SNR gains against the energy and latency cost of physically rotating the couplers.
  • The modeling technique may extend to other mechanically reconfigurable antennas where physical motion supplements electronic phase shifters.

Load-bearing premise

The multi-port circuit model accurately captures the mutual coupling coefficients as a continuous function of the 3D coupler rotations, and the spherical-cap conditional-gradient algorithm with cross-entropy initialization reliably finds high-quality rotation solutions under the stated practical constraints.

What would settle it

A hardware test that measures actual received SNR when couplers are rotated according to the computed solution versus when they are held fixed; absence of substantial SNR gain or clear failure of the algorithm to converge would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2605.20535 by Chuangye Shan, Weihua Zhuang, Xiaodan Shao, Xuemin Shen.

Figure 1
Figure 1. Figure 1: Proposed rotatable coupler antenna-aided point-to-point communication system. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Hardware implementation of the proposed RCA. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the physical non-intersection constraint [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Convergence behavior of the proposed algorithm. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: The normalized beampatterns (dB) of the proposed [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Optimized coupler rotations around the active antenna. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Achievable rates of the proposed RCA versus the [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Achievable rates of different schemes versus the [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

Flexible coupler antenna systems have recently received significant research interest due to their capability to intelligently reconfigure wireless channels by controlling coupler positions and/or rotations and dynamically exploiting mutual coupling. In this paper, we investigate a new type of flexible coupler antenna, termed rotatable coupler antenna (RCA), for enabling spectrum and energy efficient wireless communication cost-effectively. Specifically, an RCA consists of one fixed active antenna and multiple low-cost passive couplers, each of which can independently rotate in three-dimensional (3D) space, so as to collaboratively achieve mechanical beamforming without requiring additional radio-frequency (RF) chains for the couplers. We study an RCA-enhanced point-to-point communication system, where one RCA is deployed at the transmitter to serve a single user equipped with a fixed antenna. Based on multi-port circuit theory, we establish the channel model and characterize the mutual coupling coefficients as a function of coupler rotations. We formulate a new problem to maximize the received signal-to-noise ratio (SNR) at the user by optimizing the 3D rotations of all couplers, subject to practical coupler rotation constraints. To tackle this nonconvex problem, we develop a spherical-cap conditional-gradient-based algorithm with cross-entropy-method initialization. Simulation results demonstrate that the proposed RCA system can significantly improve communication performance in comparison with benchmark schemes, while requiring substantially fewer active antennas and RF chains.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper proposes a rotatable coupler antenna (RCA) system consisting of one fixed active antenna and multiple low-cost passive couplers that rotate independently in 3D space to achieve mechanical beamforming. Based on multi-port circuit theory, the authors derive a channel model that expresses mutual coupling coefficients as continuous functions of the coupler rotation angles. They formulate a non-convex optimization problem to maximize the received SNR at a single-antenna user subject to practical rotation constraints, and develop a spherical-cap conditional-gradient algorithm initialized via the cross-entropy method. Simulation results are used to claim substantial performance gains over benchmark schemes while using fewer active antennas and RF chains.

Significance. If the multi-port circuit model accurately represents the rotation-dependent mutual coupling and the proposed algorithm consistently identifies high-quality rotation configurations, the work offers a hardware-efficient approach to beamforming that reduces the number of required RF chains. The modeling rests on standard circuit-theoretic tools and the optimization operates on the appropriate manifold, which are positive attributes. The simulation-based evidence for SNR improvement is the central empirical support; its strength depends on the fidelity of the underlying channel model and the robustness of the reported gains across varied scenarios.

major comments (2)
  1. [§III] §III (Channel Modeling): the derivation of the mutual-coupling matrix as a continuous function of the three rotation angles per coupler relies on a specific multi-port impedance formulation; it is not shown whether this expression remains accurate when coupler spacing approaches the wavelength or when near-field effects become non-negligible, which directly affects the reliability of the subsequent SNR gains reported in simulations.
  2. [§V] §V (Proposed Algorithm): while the spherical-cap conditional-gradient procedure with CEM initialization is described, no convergence analysis or comparison against alternative manifold optimizers (e.g., Riemannian gradient descent) is provided; this leaves open whether the claimed high-quality solutions are reliably attained or merely artifacts of the chosen initialization under the tested rotation constraints.
minor comments (3)
  1. [Abstract] The abstract and introduction would benefit from a brief statement of the key modeling assumptions (e.g., far-field approximation, lossless couplers) to help readers assess applicability.
  2. [Simulation Results] In the simulation section, the parameter values for coupler spacing, operating frequency, and rotation constraint bounds should be tabulated for reproducibility.
  3. [§II] Notation for the rotation angles (e.g., α, β, γ) is introduced without an accompanying diagram showing the 3D coordinate system relative to the coupler geometry.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and the recommendation of minor revision. We address each major comment below and will update the manuscript to incorporate clarifications and additional analysis where appropriate.

read point-by-point responses

  1. Referee: [§III] §III (Channel Modeling): the derivation of the mutual-coupling matrix as a continuous function of the three rotation angles per coupler relies on a specific multi-port impedance formulation; it is not shown whether this expression remains accurate when coupler spacing approaches the wavelength or when near-field effects become non-negligible, which directly affects the reliability of the subsequent SNR gains reported in simulations.

    Authors: We agree that the validity range of the model merits explicit discussion. The multi-port circuit formulation in Section III is derived under the standard far-field assumption with inter-coupler spacing greater than λ/2, where higher-order near-field terms can be neglected. In the revision we will add a dedicated paragraph in §III stating these modeling assumptions, citing relevant electromagnetic references, and include a brief sensitivity study in the simulations section that compares the circuit-model SNR predictions against full-wave results for spacings approaching λ/2. This will directly address the reliability of the reported gains. revision: yes

  2. Referee: [§V] §V (Proposed Algorithm): while the spherical-cap conditional-gradient procedure with CEM initialization is described, no convergence analysis or comparison against alternative manifold optimizers (e.g., Riemannian gradient descent) is provided; this leaves open whether the claimed high-quality solutions are reliably attained or merely artifacts of the chosen initialization under the tested rotation constraints.

    Authors: We acknowledge the value of convergence analysis and comparative benchmarks. In the revised manuscript we will insert a short convergence subsection in §V that invokes the established convergence guarantees of conditional-gradient methods on compact manifolds. We will also add a simulation figure comparing the proposed spherical-cap conditional-gradient algorithm (with CEM initialization) against Riemannian gradient descent in terms of achieved SNR and iteration count under identical rotation constraints, thereby confirming that the reported high-quality solutions are robust rather than initialization-dependent. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation rests on standard circuit theory and manifold optimization

full rationale

The paper establishes the channel model and mutual-coupling function directly from multi-port circuit theory as a continuous map of 3D rotation angles to the impedance matrix. The optimization objective (maximize received SNR) is defined from this model without fitting parameters to the evaluation data. The spherical-cap conditional-gradient algorithm with cross-entropy initialization is presented as a standard technique for the non-convex manifold-constrained problem. No load-bearing step reduces by construction to a fitted input, self-citation, or renamed empirical pattern; the central claim is supported by independent modeling and algorithmic choices rather than circular re-use of the same quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of multi-port circuit theory to rotating passive couplers and on the existence of a tractable non-convex optimization landscape. No free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Multi-port circuit theory accurately models the mutual coupling coefficients between the active antenna and the rotatable passive couplers as a function of their 3D orientations.
    Invoked when the authors state they characterize mutual coupling coefficients as a function of coupler rotations.

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Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [1]

    Next generation advanced transceiver technolo- gies for 6G and beyond,

    C. You, Y . Cai, Y . Liu, M. Di Renzo, T. M. Duman, A. Yener, and A. Lee Swindlehurst, “Next generation advanced transceiver technolo- gies for 6G and beyond,”IEEE J. Sel. Areas Commun., vol. 43, no. 3, pp. 582–627, Mar. 2025

    work page 2025

  2. [2]

    On the road to 6G: Visions, requirements, key technologies, and testbeds,

    C.-X. Wang, X. You, X. Gaoet al., “On the road to 6G: Visions, requirements, key technologies, and testbeds,”IEEE Commun. Surv. Tutor ., vol. 25, no. 2, pp. 905–974, Secondquart. 2023

    work page 2023

  3. [3]

    Scalable cell-free massive MIMO systems,

    E. Bj ¨ornson and L. Sanguinetti, “Scalable cell-free massive MIMO systems,”IEEE Trans. Commun., vol. 68, no. 7, pp. 4247–4261, Jul. 2020

    work page 2020

  4. [4]

    Robust and secure wireless communications via intelligent reflecting surfaces,

    X. Yu, D. Xu, Y . Sun, D. W. K. Ng, and R. Schober, “Robust and secure wireless communications via intelligent reflecting surfaces,”IEEE J. Sel. Areas Commun., vol. 38, no. 11, pp. 2637–2652, Nov. 2020

    work page 2020

  5. [5]

    A tutorial on extremely large-scale MIMO for 6G: Fundamentals, signal processing, and applications,

    Z. Wanget al., “A tutorial on extremely large-scale MIMO for 6G: Fundamentals, signal processing, and applications,”IEEE Commun. Surv. Tutorials., vol. 26, no. 3, pp. 1560–1605, thirdquart. 2024

    work page 2024

  6. [6]

    Target sensing with intelligent reflecting surface: Architecture and performance,

    X. Shao, C. You, W. Ma, X. Chen, and R. Zhang, “Target sensing with intelligent reflecting surface: Architecture and performance,”IEEE J. Sel. Areas Commun., vol. 40, no. 7, pp. 2070–2084, Jul. 2022

    work page 2070

  7. [7]

    Atomic norm minimization-based DoA estimation for IRS-assisted sensing systems,

    R. Li, S. Sun, and M. Tao, “Atomic norm minimization-based DoA estimation for IRS-assisted sensing systems,”IEEE Wireless Commun. Lett., vol. 13, no. 10, pp. 2672–2676, Oct. 2024

    work page 2024

  8. [8]

    Secure intelligent reflecting surface-aided integrated sensing and communica- tion,

    M. Hua, Q. Wu, W. Chen, O. A. Dobre, and A. L. Swindlehurst, “Secure intelligent reflecting surface-aided integrated sensing and communica- tion,”IEEE Trans. Wireless Commun., vol. 23, no. 1, pp. 575–591, Jan. 2024

    work page 2024

  9. [9]

    Terahertz massive MIMO with holographic reconfigurable intelligent surfaces,

    Z. Wan, Z. Gao, F. Gao, M. D. Renzo, and M.-S. Alouini, “Terahertz massive MIMO with holographic reconfigurable intelligent surfaces,” IEEE Trans. Commun., vol. 69, no. 7, pp. 4732–4750, Jul. 2021

    work page 2021

  10. [10]

    Near-field MIMO communications for 6G: Fundamentals, challenges, potentials, and future directions,

    M. Cui, Z. Wu, Y . Lu, X. Wei, and L. Dai, “Near-field MIMO communications for 6G: Fundamentals, challenges, potentials, and future directions,”IEEE Commun. Mag., vol. 61, no. 1, pp. 40–46, Jan. 2023

    work page 2023

  11. [11]

    Massive MIMO for next generation wireless systems,

    E. G. Larsson, O. Edfors, F. Tufvesson, and T. L. Marzetta, “Massive MIMO for next generation wireless systems,”IEEE Commun. Mag., vol. 52, no. 2, pp. 186–195, Feb. 2014

    work page 2014

  12. [12]

    Coupler position optimiza- tion and channel estimation for flexible coupler antenna aided multiuser communication,

    X. Shao, C. Shan, W. Zhuang, and X. Shen, “Coupler position optimiza- tion and channel estimation for flexible coupler antenna aided multiuser communication,”arXiv preprint arXiv:2602.11319, 2026

    work page arXiv 2026

  13. [13]

    Flexi- ble coupler antenna enhanced wireless communication: Modeling and coupler position optimization,

    X. Shao, C. Shan, Y . Du, J. Li, R. Zhang, and C.-X. Wang, “Flexi- ble coupler antenna enhanced wireless communication: Modeling and coupler position optimization,”IEEE Trans. Wireless Commun., 2026

    work page 2026

  14. [14]

    Flexible coupler antenna for wireless networks: Opportunities and challenges,

    X. Shao, C. Shan, W. Zhuang, and X. Shen, “Flexible coupler antenna for wireless networks: Opportunities and challenges,”IEEE Commun. Mag., 2026

    work page 2026

  15. [15]

    Flexible coupler antenna enhanced low- altitude wireless communication,

    X. Shao, Y . Du, and R. Zhang, “Flexible coupler antenna enhanced low- altitude wireless communication,”IEEE J. Sel. Top. Signal Process., 2026

    work page 2026

  16. [16]

    Flexible coupler array with reconfigurable pattern: Mechanical beamforming and digital agent,

    X. Shao, Y . Zhang, N. Cheng, W. Zhuang, and X. Shen, “Flexible coupler array with reconfigurable pattern: Mechanical beamforming and digital agent,”IEEE Trans. Commun., 2026

    work page 2026

  17. [17]

    Flexible coupler antenna enhanced wireless communication via joint optimization of coupler positions and tunable loads,

    Y . Du, X. Shao, D. Zhao, Z.-H. Cheng, , Y .-H. Liu, B.-Z. Wang, and R. Zhang, “Flexible coupler antenna enhanced wireless communication via joint optimization of coupler positions and tunable loads,”submitted to IEEE Trans. Wireless Commun., 2026

    work page 2026

  18. [18]

    Characteristics and channel capacity studies of a novel 6G non-stationary massive MIMO channel model considering mutual coupling,

    Y . Yang, C.-X. Wang, J. Huang, and J. Thompson, “Characteristics and channel capacity studies of a novel 6G non-stationary massive MIMO channel model considering mutual coupling,”IEEE J. Sel. Areas Commun., vol. 42, no. 6, pp. 1519–1533, Jun. 2024

    work page 2024

  19. [19]

    Mutual coupling-aware channel estimation and beamforming for RIS-assisted communications,

    P. Zheng, S. Tarboush, H. Sarieddeen, and T. Y . Al-Naffouri, “Mutual coupling-aware channel estimation and beamforming for RIS-assisted communications,” 2025, early access

    work page 2025

  20. [20]

    A review on rf micro-electro-mechanical- systems (mems) switch for radio frequency applications,

    Kurmendra and R. Kumar, “A review on rf micro-electro-mechanical- systems (mems) switch for radio frequency applications,”Microsystem Technologies, vol. 27, no. 7, pp. 2525–2542, 2021

    work page 2021

  21. [21]

    6D movable antenna based on user distribution: Modeling and optimization,

    X. Shao, Q. Jiang, and R. Zhang, “6D movable antenna based on user distribution: Modeling and optimization,”IEEE Trans. Wireless Commun., vol. 24, no. 1, pp. 355–370, Jan. 2025

    work page 2025

  22. [22]

    6D movable antenna enhanced wireless network via discrete position and rotation optimiza- tion,

    X. Shao, R. Zhang, Q. Jiang, and R. Schober, “6D movable antenna enhanced wireless network via discrete position and rotation optimiza- tion,”IEEE J. Sel. Areas Commun., vol. 43, no. 3, pp. 674–687, Mar. 2025

    work page 2025

  23. [23]

    6DMA enhanced wireless network with flexible antenna position and rotation: Opportunities and challenges,

    X. Shao and R. Zhang, “6DMA enhanced wireless network with flexible antenna position and rotation: Opportunities and challenges,”IEEE Commun. Mag., vol. 63, no. 4, pp. 121–128, Apr. 2025

    work page 2025

  24. [24]

    Distributed channel estimation and optimization for 6D movable antenna: Unveiling directional sparsity,

    X. Shao, R. Zhang, Q. Jiang, J. Park, T. Q. S. Quek, and R. Schober, “Distributed channel estimation and optimization for 6D movable antenna: Unveiling directional sparsity,”IEEE J. Sel. Topics Signal Process., vol. 19, no. 2, pp. 349–365, Mar. 2025

    work page 2025

  25. [25]

    AI signal processing paradigm for movable antenna: From spatial position optimization to electromagnetic reconfigurability,

    Y . Li, Z. Wan, C. Sunet al., “Ai signal processing paradigm for movable antenna: From spatial position optimization to electromagnetic reconfigurability,”arXiv preprint arXiv:2510.19209, 2025

    work page arXiv 2025

  26. [26]

    UA V-enabled passive 6D movable antennas: Joint deployment and beamforming optimization,

    C. Liu, W. Mei, P. Wang, Y . Meng, B. Ning, and Z. Chen, “UA V-enabled passive 6D movable antennas: Joint deployment and beamforming optimization,”arXiv preprint arXiv:2412.11150, 2024

    work page arXiv 2024

  27. [27]

    6D movable holographic surface assisted integrated data and energy transfer: A sensing enhanced approach,

    Z. Wang, Y . Zhao, G. Hu, Y . Zheng, and K. Yang, “6D movable holographic surface assisted integrated data and energy transfer: A sensing enhanced approach,”arXiv preprint arXiv:2510.21137, 2025

    work page arXiv 2025

  28. [28]

    Passive six-dimensional movable antenna (6dma)- assisted multiuser communication,

    H. Wanget al., “Passive six-dimensional movable antenna (6dma)- assisted multiuser communication,”IEEE Wireless Commun. Lett., vol. 14, no. 4, pp. 1014–1018, Apr. 2025

    work page 2025

  29. [29]

    6DMA-aided cell-free massive MIMO communication,

    X. Shiet al., “6DMA-aided cell-free massive MIMO communication,” IEEE Wireless Commun. Lett., vol. 14, no. 5, pp. 1361–1365, May 2025

    work page 2025

  30. [30]

    Aerial 6D movable antenna-enabled cell-free networks,

    W. Wanget al., “Aerial 6D movable antenna-enabled cell-free networks,” IEEE Trans. V eh. Technol., vol. 75, no. 3, pp. 5268–5273, Mar. 2026

    work page 2026

  31. [31]

    Wireless communi- cation with flexible reflector: Joint placement and rotation optimization for coverage enhancement,

    H. Lu, Z. Yu, Y . Zeng, S. Ma, S. Jin, and R. Zhang, “Wireless communi- cation with flexible reflector: Joint placement and rotation optimization for coverage enhancement,”IEEE Trans. Wireless Commun., vol. 24, no. 10, pp. 8252–8266, Oct. 2025

    work page 2025

  32. [32]

    Hybrid near-far field 6D movable antenna design exploiting directional sparsity and deep learning,

    X. Shaoet al., “Hybrid near-far field 6D movable antenna design exploiting directional sparsity and deep learning,”IEEE Trans. Wireless Commun., 2025, early access

    work page 2025

  33. [33]

    Rate maximization for downlink pinching-antenna systems,

    Y . Xu, Z. Ding, and G. K. Karagiannidis, “Rate maximization for downlink pinching-antenna systems,”IEEE Wireless Commun. Lett., vol. 14, no. 5, pp. 1431–1435, May 2025

    work page 2025

  34. [34]

    A tutorial on six-dimensional mov- able antenna for 6G networks: Synergizing positionable and rotatable antennas,

    X. Shao, W. Mei, C. Youet al., “A tutorial on six-dimensional mov- able antenna for 6G networks: Synergizing positionable and rotatable antennas,”IEEE Commun. Surv. Tutor ., 2025, early access

    work page 2025

  35. [35]

    Statistical channel-based low-complexity rotation and position optimization for 6d movable antennas enabled wireless com- munication,

    Q. Jianget al., “Statistical channel-based low-complexity rotation and position optimization for 6d movable antennas enabled wireless com- munication,”IEEE Trans. Wireless Commun., vol. 25, pp. 8874–8889, 2026. 14

    work page 2026

  36. [36]

    Exploiting six-dimensional mov- able antenna for wireless sensing,

    X. Shao, R. Zhang, and R. Schober, “Exploiting six-dimensional mov- able antenna for wireless sensing,”IEEE Wireless Commun. Lett., vol. 14, no. 2, pp. 265–269, Feb. 2025

    work page 2025

  37. [37]

    A tutorial on movable antennas for wireless networks,

    L. Zhuet al., “A tutorial on movable antennas for wireless networks,” IEEE Commun. Surv. Tutor ., vol. 28, pp. 3002–3054, 2026

    work page 2026

  38. [38]

    Polarforming antenna enhanced sensing and communication: Modeling and optimization,

    X. Shao, R. Zhang, H. Zhou, Q. Jiang, C. Zhou, W. Zhuang, and X. Shen, “Polarforming antenna enhanced sensing and communication: Modeling and optimization,”IEEE J. Sel. Areas Commun., 2025, early access

    work page 2025

  39. [39]

    A low-power piezoelectric MEMS motor using standing wave,

    T. Yang, Y . Chen, X. Li, K. Zhang, J. He, and W. Su, “A low-power piezoelectric MEMS motor using standing wave,”Sensors and Actuators A: Physical, vol. 387, p. 116367, 2025

    work page 2025

  40. [40]

    C. A. Balanis,Antenna Theory: Analysis and Design. John wiley & sons, 2016

    work page 2016

  41. [41]

    Differ- ential evolution-based end-fire realized gain optimization of active and parasitic arrays,

    R. Konstantinou, I. Kanbaz, O. Yurduseven, and M. Matthaiou, “Differ- ential evolution-based end-fire realized gain optimization of active and parasitic arrays,”IEEE Access, vol. 13, pp. 9857–9867, 2025

    work page 2025

  42. [42]

    Spherical designs for approximations on spherical caps,

    C. Li and X. Chen, “Spherical designs for approximations on spherical caps,”SIAM J. Numer . Anal., vol. 62, no. 6, pp. 2506–2528, 2024

    work page 2024

  43. [43]

    Projection-like retractions on matrix mani- folds,

    P.-A. Absil and J. Malick, “Projection-like retractions on matrix mani- folds,”SIAM J. Optim., vol. 22, no. 1, pp. 135–158, 2012

    work page 2012

  44. [44]

    Spherical fibonacci point sets for illumination integrals,

    R. Marques, C. Bouville, M. Ribardiere, L. P. Santos, and K. Bouatouch, “Spherical fibonacci point sets for illumination integrals,” inComputer Graphics F orum, vol. 32, no. 8. Wiley Online Library, 2013, pp. 134– 143

    work page 2013

  45. [45]

    The cross-entropy method for combinatorial and continuous optimization,

    R. Y . Rubinstein, “The cross-entropy method for combinatorial and continuous optimization,”Methodol. Comput. Appl. Probab., vol. 1, pp. 127–190, 1999

    work page 1999

  46. [46]

    Mutual impedance of nonplanar-skew sinusoidal dipoles,

    J. Richmond and N. Geary, “Mutual impedance of nonplanar-skew sinusoidal dipoles,”IEEE Trans. Antennas Propag., vol. 23, no. 3, pp. 412–414, May 1975

    work page 1975