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REVIEW 3 major objections 5 minor 33 references

Joint Radiation Power, Antenna Position, and Beamforming Optimization for Pinching-Antenna Systems with Motion Power Consumption

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper proposes the first pinching-antenna system design that treats antenna radiation power as an adjustable variable, jointly optimizing it with antenna positions and transmit beamforming to minimize average power consumption under…

desk verdict A solid, useful PASS optimization paper with a physical-realizability gap in the new radiation-power variables and overstated convergence claims; worth refereeing after revision. read the letter →

arxiv 2507.02348 v1 pith:C5Y657BE submitted 2025-07-03 eess.SP cs.SYeess.SY

Yiming Xu , Dongfang Xu , Xianghao Yu , Shenghui Song , Zhiguo Ding , Robert Schober This is my paper · ORCID
classification eess.SPcs.SYeess.SY
keywords pinching-antennasystemsradiationpoweroptimizationantennapositionbeamformingmotionconsumptionADMMblockcoordinatedescentquality-of-serviceconstraints
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

Pinching-antenna systems place lightweight antennas along dielectric waveguides, so both large-scale path loss and fine-grained channel phase can be reshaped by moving antennas. Previous PASS designs fixed each antenna's radiation power and ignored the energy needed to move the antennas, so this paper asks whether jointly choosing antenna positions, radiation power ratios, and beamforming can lower total average power while meeting per-user signal-to-interference-plus-noise requirements. It claims the first PASS formulation in which radiation power is an adjustable optimization variable, and it solves that problem for both continuous and discrete antenna motion, using an ADMM-based algorithm for the continuous case and a block-coordinate-descent method for the discrete mixed-integer problem. Simulations show that the optimized designs consume less average power than equal-radiation, motion-unaware, and conventional MIMO baselines, and that PASS becomes increasingly attractive as the service area grows.

What carries the argument

The central objects are the radiation power vector $\alpha_m$, the in-waveguide phase matrix $G_m$, the free-space channel $h_k$, and their product $h_k^H G A$ inside each user's SINR. The continuous-movement solution rests on variable splitting: auxiliary variables $\theta$ and $t_k$ rewrite the position-dependent exponential channel as equality constraints, which an ADMM augmented Lagrangian then handles by alternating minimization, with a descent-lemma upper bound giving a closed-form phase update and successive convex approximation giving convex position subproblems. The discrete-movement solution rests on a binary position-selection matrix $Z$, a bilinear transformation lemma that converts the coupling $Z A W$ into a linear-matrix-inequality plus a trace constraint, and a penalty-SCA outer loop for the binary constraint. Together these pieces turn a severely coupled nonconvex problem into a sequence of convex subproblems.

What would settle it

Re-run the joint optimization with the radiation ratios $\alpha_{m,n}$ tied to the PA-waveguide spacings through the physical model cited in the paper, and compare the resulting average power with the equal-radiation baseline; if the power advantage disappears, the radiation-power gain is an artifact of assuming free $\alpha$.

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Extended reading notes

Core claim

The paper's central claim is that a downlink multi-user pinching-antenna system can minimize the average of transmit power and antenna-motion power by jointly optimizing the positions $x_{m,n}$ of the antennas along each waveguide, the radiation power ratios $\alpha_{m,n}$, and the transmit beamformers $w_k$, subject to SINR, radiated-power, minimum-spacing, and movement-distance constraints. The coupling is formalized through the effective channel $h_k^H G A$, in which position-dependent in-waveguide phases and radiation ratios enter multiplicatively, and positions influence both the magnitude and phase of the free-space channel. For continuous movement, variable splitting introduces auxiliary phase and effective-channel variables, and an ADMM framework alternatingly solves SOCP, fractional-programming, and successive-convex-approximation subproblems; for discrete movement, the position choice is encoded as a binary selection matrix and solved with a block-coordinate-descent method using a bilinear transformation and a penalty on the binary constraint. The paper states that both algorithms converge to a stationary point, and its simulations show average-power reductions relative to baselines that fix radiation power or ignore motion cost.

Load-bearing premise

The optimization treats each antenna's radiation power ratio $\alpha_{m,n}$ as a free variable chosen independently of the antenna's position, even though the physical device sets that ratio by the gap between the antenna and the waveguide, a quantity the model does not constrain.

Editorial extensions

If this is right

  • Both proposed algorithms converge to a stationary point of their respective problems, so a system designer can reliably alternate between movement, radiation, and beamforming updates.
  • Total power is genuinely minimized over both transmission and movement, so optimizing transmit power alone, as earlier PASS designs do, is suboptimal when antenna motion costs energy.
  • Adjustable radiation power provides an extra degree of freedom that lowers average power relative to equal-radiation designs.
  • Discrete placement with roughly one thousand candidate positions per waveguide approaches the continuous-design performance, giving a concrete resolution target for actuator hardware.
  • PASS keeps average power largely insensitive to service-area growth compared with conventional MIMO, reflecting a path-loss advantage from in-waveguide propagation.

Reading between the lines

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

  • An editorial inference: the physical radiation models cited in the paper tie $\alpha$ to the spacing between a pinching antenna and the waveguide, so a fully physical implementation would couple $\alpha$ and the antenna positions; enforcing that coupling might reduce the reported radiation-power gains.
  • An editorial inference: the motion-power model is linear in traveled distance, so adding speed-dependent or acceleration-dependent terms, or a multi-frame repositioning budget, would change the optimal trade-off and can be tested within the same ADMM/BCD structure.
  • An editorial inference: the variable-splitting ADMM technique should transfer to other channels where antenna positions affect both magnitude and phase, such as near-field movable-antenna systems, where the same nonconvex coupling arises.
  • An editorial inference: the discrete-to-continuous gap plotted against the number of candidate positions suggests that a closed-form quantization-error bound for the discrete design could be derived from the problem's Lipschitz constants, turning the thousand-position heuristic into a design rule.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper considers a downlink multi-user pinching-antenna system (PASS) and formulates a joint optimization of transmit beamforming, radiation power ratios alpha_{m,n}, and antenna positions to minimize the total average power (transmission plus PA motion) subject to per-user SINR constraints, minimum antenna spacing, movement range, and per-waveguide radiation-power constraints. For continuous antenna movement, the problem is transformed by variable splitting into an ADMM form with SOCP/QCQP subproblems, including a closed-form phase update in (60). For discrete movement, the problem is cast as an MINLP and solved by a BCD/penalty/SCA method. Numerical comparisons are provided against a conventional MIMO baseline, an equal-radiation-power PASS baseline, and a motion-unaware baseline.

Significance. If the two issues below are resolved, this would be a timely and useful contribution to PASS design: it appears to be the first treatment that explicitly includes PA motion power and treats radiation power as an optimization variable; the algorithmic decomposition is nontrivial; the closed-form theta update in (60) is supported by a valid Lipschitz-surrogate argument; and the simulations use independent baselines rather than fitting parameters to the model. However, the physical achievability of the optimized radiation ratios and the rigorous convergence of both algorithms are not established, so the current version overstates both the attainable gains and the theoretical guarantees.

major comments (3)
  1. [Section II-A, Eq. (2); problem (16), C2; Section I, refs. [11], [12]] The radiation power ratios alpha_{m,n} are treated as independent free variables subject only to the per-waveguide power constraint C2. The paper cites [11] and [12] for a physical model in which alpha_{m,n} is determined by the spacing between the PA and the waveguide, and [12] derives a closed-form spacing only for equal radiation powers. No spacing or gap variable is introduced in the system model, and no achievable-region characterization is given for the mapping from spacing to alpha at the optimized positions. Since the performance gains attributed to radiation-power optimization in Figures 3-6, and the corresponding discussion in Section V.B, are obtained over the potentially enlarged set {||alpha_m||_2^2 <= 1}, the claimed improvement over the fixed-radiation baseline may be an artifact of unphysical solutions. Please close this gap by introducing the spacing variables and their constraints, or by proving or quoting an achievable range for alpha and verifying that the optimized solutions lie in it.
  2. [Section III, convergence paragraph after Algorithm 1; Algorithm 1, line 9; Eqs. (42)-(49)] The claim that Algorithm 1 converges to a stationary point of problem (16) via the ADMM theory of [21] is not supported. The cited theory assumes fixed penalty parameters, whereas Algorithm 1 multiplies rho_1 and rho_2 by epsilon > 1 at every outer iteration (line 9), so the quadratic penalty terms in the augmented Lagrangian can increase even when the primal variables improve. In addition, the alpha-update in (42)-(49) maximizes the sum of per-user SINRs; it is not a minimization of the augmented Lagrangian of (26), and no monotonicity result is proved for this heuristic update. The SCA surrogates in (39), (59), and (72) individually give upper bounds on the corresponding subproblem objectives, but the paragraph does not establish that their alternating application, together with the heuristic alpha-update and the increasing penalty parameters, yields a non-increasing augmented Lagrangian. Please either keep the penalty parameters fixed and use a proper block-minimization step for alpha, or provide a dedicated convergence proof for the modified scheme; in either case, report the final residuals of constraints C6 and C7 to support the claim that a feasible point is reached.
  3. [Section IV.B, after Algorithm 2; Algorithm 2; Eq. (105)] The statement that Algorithm 2 is guaranteed to converge to a stationary point of problem (84) within polynomial time, by the results of [32], is not justified. The alpha-update in (105) maximizes a sum-SINR objective rather than minimizing the block objective f5 of problem (84), so the block successive minimization conditions of [32] are not met. Moreover, the penalty method introduced in (100) is described without explaining whether zeta is increased during the iterations or how the final binary constraint violation is controlled; the stopping criterion in Algorithm 2 checks only the relative change of the surrogate objective rf5, not feasibility of the original constraints. Please provide a formal convergence analysis for the actual updates used, or soften the claim to empirical convergence and report the final violations of the binary constraints.
minor comments (5)
  1. [Section II-A, Eq. (10)] The notation A = diag[alpha_1,...,alpha_M] in R^{MN x M} is nonstandard; since each alpha_m is an N x 1 vector, A should be described as the block-diagonal matrix with N x 1 blocks alpha_m, rather than a standard diagonal matrix, to avoid confusion.
  2. [Section III-B, Eq. (34)] The notation ||W||_2^2 in constraint C8 is ambiguous; this should be the squared Frobenius norm ||W||_F^2, since ||W||_2 usually denotes the spectral norm.
  3. [Section IV.A, after Eq. (84)] The sentence 'Compared to problem (16) ... problem (73)' contains a typo: the reference should be to the newly formulated problem (84), not problem (73).
  4. [Section V.C, Fig. 4] The text reports power-consumption increments of 56.6% and 89.1% while the y-axis of Fig. 4 is labeled in dBm; percentage changes computed from dBm values are not physically meaningful, so these increments should be computed and reported in linear power units.
  5. [Fig. 5 caption] The caption says 'antenna spacing of discrete antenna positions' while the x-axis label and the text refer to the number of available discrete positions on each waveguide; the caption should be aligned with the actual quantity plotted.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the optimized radiation-power design is self-contained given the stated model; the main risk is physical realizability of alpha, not circular reasoning.

full rationale

Walking the derivation chain from the system model in Section II through problem (16) and Algorithms 1-2, the central claim (lower average power consumption from joint optimization) is not equivalent to an input by construction. The radiation power ratios alpha_m, antenna positions X, and beamformers w_k are optimization variables, not fitted parameters, and the algorithms solve the problem as defined. Baseline 2 fixes alpha_{m,n}=sqrt(1/N), so the reported improvement from radiation power optimization is a feasible-set-inclusion consequence of constraint C2; this is a direct implication of the model, not a hidden reuse of the conclusion. The paper does cite the authors' own prior work for the PASS channel and radiation-power modeling context ([5], [10], [11], [12]) and for the motion-energy formula ([18]), but those citations supply modeling assumptions rather than the paper's results, and no uniqueness theorem or forced-choice argument is imported from them. The genuine concern flagged by the weakest assumption is a modeling gap, not circularity: in eq. (2) and constraint C2, alpha is treated as an arbitrary vector with ||alpha_m||_2^2 <= 1, while the cited [12] model in Section I ties radiation power ratios to the spacing between PAs and waveguides and derives a closed-form spacing only for equal radiation powers. The paper never introduces that spacing mapping or verifies that every alpha satisfying C2 is physically realizable at the optimized positions, so the numerical gains over the equal-power baseline may be unattainable in practice. This is a correctness and physical-validity risk located in Section II-A (eq. (2)) and Section II-C (C2), not a circular reduction of the derivation to its own inputs. Accordingly, the circularity score is 1.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central optimization relies on modeling assumptions about lossless waveguides, LoS spherical-wave channels, and freely adjustable radiation power. The most fragile is the free-radiation-power assumption, which conflicts with the physical model cited in [12]. No data fitting is used; the penalty parameters and simulation constants are chosen by hand but are not part of the scientific claim. No new physical entities are introduced.

assumptions (5)
  • domain assumption In-waveguide propagation is lossless, so the only in-waveguide effect is phase delay.
    Invoked in Section II-A before equation (2); simplifies the channel model and is cited from reference [10].
  • domain assumption The free-space channel is dominated by a strong LoS spherical wave with known user positions, giving h_{m,n} = beta * exp(-j 2 pi r / lambda_c) / r.
    Section II-A, equation (7); this channel model is the basis of the SINR expression and the subsequent optimizations.
  • ad hoc to paper Radiation power ratios alpha_{m,n} are free variables independent of PA-waveguide spacing, subject only to the sum-power constraint C2.
    Section II-A, constraint C2; this contradicts the physical model in [12] where alpha depends on spacing, and the realizability of arbitrary alpha at the optimized positions is not discussed.
  • domain assumption Motion power consumption is linear in distance: E = P * |Delta x| / v, with constant motor power P and speed v.
    Section II-B, equation (15), borrowed from movable-antenna literature [18] and used in the objective function.
  • ad hoc to paper The ADMM with increasing penalty parameters and a heuristic alpha-update converges to a stationary point of the original problem (16).
    Section III-F claims this via reference [21], but standard ADMM convergence requires fixed penalties and exact minimization of the augmented Lagrangian; the alpha update in (49) maximizes SINR, not the Lagrangian.

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Pith. "Pith review of Joint Radiation Power, Antenna Position, and Beamforming Optimization for Pinching-Antenna Systems with Motion Power Consumption." pith.science (2026). https://pith.science/paper/C5Y657BE

@misc{pith2026250702348,
  author       = {Pith},
  title        = {Pith review of: Joint Radiation Power, Antenna Position, and Beamforming Optimization for Pinching-Antenna Systems with Motion Power Consumption},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C5Y657BE}},
  note         = {Machine review of arXiv:2507.02348}
}
read the original abstract

Pinching-antenna systems (PASS) have been recently proposed to improve the performance of wireless networks by reconfiguring both the large-scale and small-scale channel conditions. However, existing studies ignore the physical constraints of antenna placement and assume fixed antenna radiation power. To fill this research gap, this paper investigates the design of PASS taking into account the motion power consumption of pinching-antennas (PAs) and the impact of adjustable antenna radiation power. To that end, we minimize the average power consumption for a given quality-of-service (QoS) requirement, by jointly optimizing the antenna positions, antenna radiation power ratios, and transmit beamforming. To the best of the authors' knowledge, this is the first work to consider radiation power optimization in PASS, which provides an additional degree of freedom (DoF) for system design. The cases with both continuous and discrete antenna placement are considered, where the main challenge lies in the fact that the antenna positions affect both the magnitude and phase of the channel coefficients of PASS, making system optimization very challenging. To tackle the resulting unique obstacles, an alternating direction method of multipliers (ADMM)-based framework is proposed to solve the problem for continuous antenna movement, while its discrete counterpart is formulated as a mixed integer nonlinear programming (MINLP) problem and solved by the block coordinate descent (BCD) method. Simulation results validate the performance enhancement achieved by incorporating PA movement power assumption and adjustable radiation power into PASS design, while also demonstrating the efficiency of the proposed optimization framework. The benefits of PASS over conventional multiple-input multiple-output (MIMO) systems in mitigating the large-scale path loss and inter-user interference is also revealed.

Figures

Figures reproduced from arXiv: 2507.02348 by the authors.

Figure 1
Figure 1. Illustration of a PASS-enabled downlink multi-user [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Convergence behavior of the proposed algorithms for [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Average power consumption (dBm) versus SINR require [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (2 more)
Figure 6
Figure 6. Figure 6: Average power consumption (dBm) versus antenna move [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 5
Figure 5. Figure 5: Average power consumption (dBm) versus antenna spac [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

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Works this paper leans on

33 extracted references · 21 canonical work pages

  1. [12]

    Pinchi ng-antenna systems (PASS): Power radiation model and optimal beamform ing de- sign,

    X. Xu, X. Mu, Z. Wang, Y . Liu, and A. Nallanathan, “Pinchi ng-antenna systems (PASS): Power radiation model and optimal beamform ing de- sign,” arXiv preprint arXiv:2505.00218 , 2025

    arXiv 2025

  2. [11]

    Modeling a nd beamforming optimization for pinching-antenna systems,

    Z. Wang, C. Ouyang, X. Mu, Y . Liu, and Z. Ding, “Modeling a nd beamforming optimization for pinching-antenna systems,” arXiv preprint arXiv:2502.05917, 2025

    arXiv 2025

  3. [21]

    Distributed optimization and statistical learning via the alternating direction method of multipliers,

    S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al. , “Distributed optimization and statistical learning via the alternating direction method of multipliers,” F oundations and Trends® in Machine learning , vol. 3, no. 1, pp. 1–122, 2011

    2011

  4. [32]

    A unified converg ence analysis of block successive minimization methods for nonsmooth opt imization,

    M. Razaviyayn, M. Hong, and Z.-Q. Luo, “A unified converg ence analysis of block successive minimization methods for nonsmooth opt imization,” SIAM Journal on Optimization , vol. 23, no. 2, pp. 1126–1153, 2013

    work page 2013

  5. [1]

    An overview of massive MIMO: Benefits and challenges,

    L. Lu, G. Y . Li, A. L. Swindlehurst, A. Ashikhmin, and R. Zh ang, “An overview of massive MIMO: Benefits and challenges,” IEEE J. Select. Topics Signal Process. , vol. 8, no. 5, pp. 742–758, 2014

    work page 2014

  6. [2]

    Smart and reconfigurable wireless communications: From IRS model ing to algorithm design,

    X. Y u, V . Jamali, D. Xu, D. W. K. Ng, and R. Schober, “Smart and reconfigurable wireless communications: From IRS model ing to algorithm design,” IEEE Wireless Commun. , vol. 28, no. 6, pp. 118–125, 2021

    work page 2021

  7. [3]

    A tutorial on movable antennas for wi reless networks,

    L. Zhu, W. Ma, W. Mei, Y . Zeng, Q. Wu, B. Ning, Z. Xiao, X. Sha o, J. Zhang, and R. Zhang, “A tutorial on movable antennas for wi reless networks,” IEEE Commun. Surv. Tutor ., (Early Access) , 2025

    work page 2025

  8. [4]

    Fl uid antenna systems,

    K.-K. Wong, A. Shojaeifard, K.-F. Tong, and Y . Zhang, “Fl uid antenna systems,” IEEE Trans. Wireless Commun. , vol. 20, no. 3, pp. 1950–1962, 2021

    work page 1950

Show all 33 references
  1. [5]

    Flexible-ante nna systems: A pinching-antenna perspective,

    Z. Ding, R. Schober, and H. Vincent Poor, “Flexible-ante nna systems: A pinching-antenna perspective,” IEEE Trans. Commun. , (Early Access) , 2025

    2025

  2. [6]

    Pinch ing an- tenna systems (PASS): Architecture designs, opportunitie s, and outlook,

    Y . Liu, Z. Wang, X. Mu, C. Ouyang, X. Xu, and Z. Ding, “Pinch ing an- tenna systems (PASS): Architecture designs, opportunitie s, and outlook,” arXiv preprint arXiv:2501.18409 , 2025

    2025 arXiv

  3. [7]

    Pinching antenna: Using a di electric waveguide as an antenna,

    H. O. Y . Suzuki and K. Kawai, “Pinching antenna: Using a di electric waveguide as an antenna,” NTT DOCOMO Technical J , 2022

    2022

  4. [8]

    Joint transmit a nd pinching beamforming for PASS: Optimization-based or learning-bas ed?

    X. Xu, X. Mu, Y . Liu, and A. Nallanathan, “Joint transmit a nd pinching beamforming for PASS: Optimization-based or learning-bas ed?” arXiv preprint arXiv:2502.08637, 2025

    2025 arXiv

  5. [9]

    Rate maximizati on for down- link pinching-antenna systems,

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

    2025

  6. [10]

    Antenna activation fo r NOMA as- sisted pinching-antenna systems,

    K. Wang, Z. Ding, and R. Schober, “Antenna activation fo r NOMA as- sisted pinching-antenna systems,” IEEE Wireless Commun. Lett. , vol. 14, no. 5, pp. 1526–1530, 2025

    2025

  7. [13]

    Joint antenna position and t ransmit power optimization for pinching antenna-assisted ISAC systems,

    Y . Qin, Y . Fu, and H. Zhang, “Joint antenna position and t ransmit power optimization for pinching antenna-assisted ISAC systems, ” arXiv preprint arXiv:2503.12872, 2025

    2025 arXiv

  8. [14]

    Pin ching- antenna systems (PASS)-enabled secure wireless communica tions,

    G. Zhu, X. Mu, L. Guo, S. Xu, Y . Liu, and N. Al-Dhahir, “Pin ching- antenna systems (PASS)-enabled secure wireless communica tions,” arXiv preprint arXiv:2504.13670, 2025

    2025

  9. [15]

    Mechanica l power modeling and energy efficiency maximization for movable ant enna sys- tems,

    X. Wei, W. Mei, X. Huang, Z. Chen, and B. Ning, “Mechanica l power modeling and energy efficiency maximization for movable ant enna sys- tems,” arXiv preprint arXiv:2505.05914 , 2025

    2025 arXiv

  10. [16]

    Design and synthesis of antenna array with m ovable elements along semicircular paths,

    S. Basbug, “Design and synthesis of antenna array with m ovable elements along semicircular paths,” IEEE Antennas Wireless Propag. Lett. , vol. 16, pp. 3059–3062, 2017

    2017

  11. [17]

    Microwave engineering,

    D. M. Pozar, “Microwave engineering,” F ourth Editions, University of Massachusetts at Amherst, John Wiley & Sons, Inc , pp. 26–30, 2012

    2012

  12. [18]

    G lobally optimal movable antenna-enhanced multi-user communicati on: Discrete antenna positioning, motion power consumption, and imperf ect csi,

    Y . Wu, D. Xu, D. W. K. Ng, W. Gerstacker, and R. Schober, “G lobally optimal movable antenna-enhanced multi-user communicati on: Discrete antenna positioning, motion power consumption, and imperf ect csi,” arXiv preprint arXiv:2408.15435, 2024

    2024 arXiv

  13. [19]

    Movable-antenna en hanced multiuser communication via antenna position optimizatio n,

    L. Zhu, W. Ma, B. Ning, and R. Zhang, “Movable-antenna en hanced multiuser communication via antenna position optimizatio n,” IEEE Trans. Wireless Commun., vol. 23, no. 7, pp. 7214–7229, 2024

    2024

  14. [20]

    A tutorial on fluid antenna system for 6 G networks: Encompassing communication theory, optimizati on methods and hardware designs,

    W. K. New, K.-K. Wong, H. Xu, C. Wang, F. R. Ghadi, J. Zhang , J. Rao, R. Murch, P . Ramírez-Espinosa, D. Morales-Jimenez, C.-B. Chae, and K.-F. Tong, “A tutorial on fluid antenna system for 6 G networks: Encompassing communication theory, optimizati on methods and hardware des...

    2024

  15. [22]

    Multiplica tive noise removal using variable splitting and constrained optimiza tion,

    J. M. Bioucas-Dias and M. A. T. Figueiredo, “Multiplica tive noise removal using variable splitting and constrained optimiza tion,” IEEE Trans. Image Process. , vol. 19, no. 7, pp. 1720–1730, 2010

    2010

  16. [23]

    Boyd and L

    S. Boyd and L. V andenberghe, Convex Optimization . Cambridge University Press, 2004

    2004

  17. [24]

    CVX: Matlab software for discipli ned convex programming, version 2.2,

    M. Grant and S. Boyd, “CVX: Matlab software for discipli ned convex programming, version 2.2,” Jan. 2020

    2020

  18. [25]

    SNR/CRB- constrained joint beamforming and reflection designs for RIS-ISAC syste ms,

    R. Liu, M. Li, Q. Liu, and A. Lee Swindlehurst, “SNR/CRB- constrained joint beamforming and reflection designs for RIS-ISAC syste ms,” IEEE Trans. Wireless Commun. , vol. 23, no. 7, pp. 7456–7470, 2024

    2024

  19. [26]

    Fractional programming for communic ation sys- tems—part I: Power control and beamforming,

    K. Shen and W. Y u, “Fractional programming for communic ation sys- tems—part I: Power control and beamforming,” IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2616–2630, 2018

    2018

  20. [27]

    Majorization-minim ization algo- rithms in signal processing, communications, and machine l earning,

    Y . Sun, P . Babu, and D. P . Palomar, “Majorization-minim ization algo- rithms in signal processing, communications, and machine l earning,” IEEE Trans. Signal Process. , vol. 65, no. 3, pp. 794–816, 2017

    2017

  21. [28]

    Nonlinear programming,

    D. P . Bertsekas, “Nonlinear programming,” J. Oper . Res. Soc. , vol. 48, no. 3, pp. 334–334, 1997

    1997

  22. [29]

    Ben-Tal and A

    A. Ben-Tal and A. Nemirovski, Lectures on modern convex optimization: analysis, algorithms, and engineering applications . SIAM, 2001

    2001

  23. [30]

    Res olution- aware beam scanning for joint detection and communication i n isac systems,

    Y . Xu, D. Xu, Z. Xie, Z. Jiang, S. Song, and D. W. K. Ng, “Res olution- aware beam scanning for joint detection and communication i n isac systems,” Sci. China Inf. Sci. , vol. 68, no. 5, p. 150305, 2025

    2025

  24. [31]

    Joint o ptimization of source precoding and relay beamforming in wireless mimo r elay networks,

    U. Rashid, H. D. Tuan, H. H. Kha, and H. H. Nguyen, “Joint o ptimization of source precoding and relay beamforming in wireless mimo r elay networks,” IEEE Trans. Commun. , vol. 62, no. 2, pp. 488–499, 2014

    2014

  25. [33]

    [Online]

    Faulhaber, Stepper Motors, Series DM0620 , vol. [Online]. Available: https://www.faulhaber.com/fileadmin/Import/Media/EN_TI_STEPPER_M OTORS.pdf, 2022

    2022

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