pith. sign in

arxiv: 2605.04775 · v1 · submitted 2026-05-06 · 📡 eess.SP

Two-Timescale Design for Rotatable-Antenna Systems With Imperfect CSI: Rate Analysis and Orientation Optimization

Ziyuan Zheng , Qingqing Wu , Wen Chen This is my paper

Pith reviewed 2026-05-08 16:22 UTC · model grok-4.3

classification 📡 eess.SP
keywords rotatable antennaimperfect CSItwo-timescale designmultiuser MIMOmaximum-ratio combiningweighted zero-forcingrate analysisorientation optimization
0
0 comments X

The pith

Optimizing rotatable antenna orientations from statistical CSI alone improves uplink rates in multiuser MIMO systems despite imperfect instantaneous channel knowledge.

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

The paper sets up a two-timescale framework for uplink multiuser MIMO where each base-station antenna can rotate its boresight within a limited angular region. Orientations are chosen once from long-term statistical CSI while receive combiners are recomputed every coherence interval from LMMSE estimates. Closed-form rate expressions are obtained for maximum-ratio combining via the use-and-then-forget bound and a statistical surrogate for weighted zero-forcing; these expressions explicitly separate the effects of rotation on useful signal power, estimation-error self-interference, and multiuser interference. The analysis reveals that the rotation minimizing estimation error is not the same as the rotation maximizing rate, and that the two combiners favor different orientations because of their different ways of aggregating signals versus suppressing interference. If the framework holds, systems gain rate improvements without the overhead of adjusting antennas on every coherence interval.

Core claim

Under imperfect CSI the use-and-then-forget achievable rate for MRC and the corresponding statistical surrogate for wZF are functions of the rotatable-antenna orientations through the second-order channel statistics; maximizing these expressions over the product of spherical caps yields orientations that differ from those minimizing channel-estimation error and that differ between MRC and wZF, with the resulting non-convex problems solved by a projected-gradient algorithm whose derivatives are computed from the same statistics.

What carries the argument

The two-timescale separation that fixes rotatable-antenna orientations from statistical CSI on a large timescale while updating linear combiners from LMMSE estimates on a small timescale, together with the closed-form rate expressions that expose the influence of rotation on signal, error, and interference terms.

If this is right

  • The orientation that maximizes rate is distinct from the orientation that minimizes channel-estimation error.
  • MRC and wZF achieve their best performance at different rotation configurations because of their differing treatments of useful signal and residual interference.
  • The projected-gradient algorithm over spherical caps reliably improves the statistical rate surrogates.
  • Numerical evaluation confirms that the derived large-timescale expressions accurately track actual rates and deliver noticeable gains relative to non-optimized orientations.

Where Pith is reading between the lines

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

  • The same statistical optimization could be applied when user locations change slowly, allowing the long-term orientation to track slowly varying statistics without per-coherence updates.
  • The framework might extend to downlink transmission or to other reconfigurable antenna technologies that alter effective channel statistics in a similar way.
  • In large arrays the reduction in control signaling for antenna adjustments could translate into lower overall system overhead and energy use.
  • Further work could test whether the preferred orientations remain stable when additional hardware constraints such as mutual coupling or power limits are included.

Load-bearing premise

That statistical channel knowledge alone is enough to choose long-term antenna orientations without incurring a large performance penalty from mismatch with the actual instantaneous channel realizations.

What would settle it

A direct comparison, in simulation or hardware testbed, of the measured uplink sum rate when orientations are chosen by the proposed statistical optimization versus when they are chosen to minimize estimation error or held fixed, all under the same LMMSE estimation and combiner update rules.

Figures

Figures reproduced from arXiv: 2605.04775 by Qingqing Wu, Wen Chen, Ziyuan Zheng.

Figure 1
Figure 1. Figure 1: Illustration of the system model: a) the RA-enabled uplink multiuser view at source ↗
Figure 2
Figure 2. Figure 2: Average sum rate versus the number of BS antennas. view at source ↗
Figure 3
Figure 3. Figure 3: Average sum rate versus the number of users. view at source ↗
Figure 4
Figure 4. Figure 4: Average sum rate versus the user transmit power. view at source ↗
Figure 6
Figure 6. Figure 6: Average sum rate versus the antenna directional parameter. view at source ↗
Figure 9
Figure 9. Figure 9: Average sum rate versus the user angular separation. view at source ↗
Figure 10
Figure 10. Figure 10: Average rate versus the maximum rotation angle of single-user LoS view at source ↗
read the original abstract

This paper studies uplink multiuser MIMO with a rotatable antenna (RA) array under imperfect channel state information (CSI), where each base-station antenna can adjust its boresight direction within an angular region. To balance performance and control overhead, we propose a two-timescale design: RA orientations are optimized from statistical CSI on a large timescale, while linear receive combiners are updated per coherence block from linear minimum-mean-squared-error (LMMSE) channel estimates. Under this framework, we derive a closed-form use-and-then-forget (UatF)-based rate expression for maximum-ratio combining (MRC) and a closed-form statistical rate surrogate for weighted zero-forcing (wZF) under imperfect CSI, revealing how RA rotation influences useful signal strength, estimation-error-induced self-interference, and multiuser interference. The analysis shows that the orientation minimizing channel-estimation error differs from the rate-maximizing one, and that MRC and wZF prefer different rotation configurations due to their distinct mechanisms of signal aggregation and error-aware user separation. For the resulting non-convex rotation design problems, we develop a projected-gradient algorithm over a product of spherical caps with explicit derivatives of the required channel statistics and rate metrics. Numerical results verify the accuracy of the large-timescale surrogates and show substantial performance gains from RA optimization.

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 / 2 minor

Summary. The paper proposes a two-timescale design for uplink multiuser MIMO with rotatable-antenna (RA) arrays under imperfect CSI. RA orientations are optimized from statistical CSI on a large timescale, while MRC and wZF combiners are updated per coherence block from LMMSE estimates. Closed-form UatF rate expressions for MRC and statistical surrogates for wZF are derived, showing how rotation affects signal strength, estimation-error self-interference, and multiuser interference. The analysis claims that the orientation minimizing LMMSE error differs from the rate-maximizing orientation, and that MRC and wZF select distinct rotations due to differing signal aggregation and error-aware separation mechanisms. A projected-gradient algorithm over products of spherical caps is developed using explicit derivatives of the channel statistics, with numerical results verifying the surrogates and demonstrating performance gains.

Significance. If the derivations and numerical distinctions hold, the work provides useful analytical tools and optimization methods for RA systems that balance control overhead with performance under realistic imperfect CSI. The closed-form rate expressions and explicit gradient derivations for the non-convex problems are strengths, as is the demonstration that error-minimization and rate-maximization objectives yield different optima. This could inform practical RA deployments where statistical CSI suffices for long-term orientation design.

major comments (2)
  1. [§4] §4 (projected-gradient algorithm for non-convex rotation design): The rate-maximization problems for MRC and wZF are non-concave over the compact but non-convex feasible set of spherical caps. The algorithm is guaranteed only to reach stationary points. The headline claim that MRC and wZF prefer distinct orientations (and that these differ from the error-minimizing orientation) rests on comparing the outputs of three separate runs of this local solver. No results from multiple random initializations, basin-hopping, or global methods are reported to confirm that the observed preference ordering is not an artifact of convergence to different local stationary points.
  2. [Numerical results] Numerical results (verification of surrogates and orientation comparisons): The accuracy of the UatF bound and wZF statistical surrogate is asserted via post-hoc numerical validation, but the manuscript does not specify the number of Monte-Carlo trials, the range of SNR/user configurations tested, or whether any data points were excluded. Without these details it is difficult to assess whether the reported distinction between error-minimizing and rate-maximizing orientations, and between MRC and wZF preferences, is robust across the operating regime.
minor comments (2)
  1. [§4] Notation for the spherical-cap constraints and the projection operator could be clarified with an explicit definition or reference to a standard definition in the optimization literature.
  2. [Introduction / §3] The abstract states that the analysis 'reveals how RA rotation influences useful signal strength, estimation-error-induced self-interference, and multiuser interference'; a short qualitative discussion of these mechanisms in the introduction or §3 would help readers connect the closed-form expressions to the physical intuition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We address each major comment below and outline the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [§4] §4 (projected-gradient algorithm for non-convex rotation design): The rate-maximization problems for MRC and wZF are non-concave over the compact but non-convex feasible set of spherical caps. The algorithm is guaranteed only to reach stationary points. The headline claim that MRC and wZF prefer distinct orientations (and that these differ from the error-minimizing orientation) rests on comparing the outputs of three separate runs of this local solver. No results from multiple random initializations, basin-hopping, or global methods are reported to confirm that the observed preference ordering is not an artifact of convergence to different local stationary points.

    Authors: We agree that the optimization problems are non-convex and that the projected-gradient method is only guaranteed to find stationary points. In the revised manuscript, we will add a new subsection in Section IV and additional figures in Section V reporting results from 20 independent random initializations per problem instance (MRC, wZF, and error-minimization). These runs consistently converged to the same orientation preferences reported in the original figures, with the MRC and wZF optima remaining distinct from each other and from the error-minimizing orientation. We will also explicitly state that the reported solutions are representative stationary points verified through multi-start initialization, while noting the inherent limitations of local methods on non-convex sets. revision: partial

  2. Referee: [Numerical results] Numerical results (verification of surrogates and orientation comparisons): The accuracy of the UatF bound and wZF statistical surrogate is asserted via post-hoc numerical validation, but the manuscript does not specify the number of Monte-Carlo trials, the range of SNR/user configurations tested, or whether any data points were excluded. Without these details it is difficult to assess whether the reported distinction between error-minimizing and rate-maximizing orientations, and between MRC and wZF preferences, is robust across the operating regime.

    Authors: We acknowledge that the simulation details were insufficiently specified. In the revised manuscript, we will add a dedicated paragraph in Section V-A detailing the Monte-Carlo setup: 10,000 independent channel realizations per data point, SNR range from 0 dB to 30 dB in 5 dB steps, user counts K = 4, 6, 8, and antenna counts M = 16, 32. No data points were excluded. The surrogate verification and orientation comparisons were performed over this full grid, and the distinctions between error-minimizing and rate-maximizing orientations (as well as between MRC and wZF) held consistently across all tested regimes. revision: yes

Circularity Check

0 steps flagged

Derivation chain is self-contained; no circular reductions

full rationale

The paper derives closed-form UatF rate expressions for MRC and statistical surrogates for wZF directly from LMMSE channel estimation and standard bounding techniques, without fitting parameters to the target metrics. Separate non-convex programs are then defined for error minimization versus rate maximization under MRC and wZF, each with its own explicit objective involving channel statistics. The projected-gradient solver is a generic numerical method applied to these distinct objectives over spherical caps; the reported preference differences arise from the differing mathematical forms rather than any input-output equivalence by construction. No load-bearing self-citation or ansatz smuggling is present in the provided abstract or described chain, and all steps remain externally verifiable against standard massive-MIMO literature.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review performed from abstract only; ledger populated from standard MIMO assumptions implied by the text.

axioms (2)
  • domain assumption LMMSE channel estimation model and use-and-then-forget bounding apply under imperfect CSI
    Invoked to obtain the closed-form MRC rate and wZF surrogate
  • domain assumption Statistical CSI is stationary over the large timescale
    Required for optimizing orientations independently of instantaneous realizations

pith-pipeline@v0.9.0 · 5542 in / 1434 out tokens · 42518 ms · 2026-05-08T16:22:18.556787+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

31 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    An overview of MIMO communications–A key to gigabit wireless,

    A. J. Paulraj et al., “An overview of MIMO communications–A key to gigabit wireless,”Proc. IEEE, vol. 92, no. 2, pp. 198–218, Feb. 2004

    2004

  2. [2]

    Shifting the MIMO paradigm,

    D. Gesbert et al., “Shifting the MIMO paradigm,”IEEE Signal Process. Mag., vol. 24, no. 5, pp. 36–46, Sep. 2007

    2007

  3. [3]

    An overview of massive MIMO: Benefits and challenges,

    L. Lu et al., “An overview of massive MIMO: Benefits and challenges,” IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp. 742–758, Oct. 2014

    2014

  4. [4]

    An overview of signal processing techniques for millimeter wave MIMO systems,

    R. W. Heath et al., “An overview of signal processing techniques for millimeter wave MIMO systems,”IEEE J. Sel. Topics Signal Process., vol. 10, no. 3, pp. 436–453, Apr. 2016

    2016

  5. [5]

    Noncooperative cellular wireless with unlimited num- bers of base station antennas,

    T. L. Marzetta, “Noncooperative cellular wireless with unlimited num- bers of base station antennas,”IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3590–3600, Nov. 2010

    2010

  6. [6]

    A survey on reconfigurable and movable antennas for wireless communications and sensing,

    W. Ma et al., “A survey on reconfigurable and movable antennas for wireless communications and sensing,”IEEE Commun. Surv. Tut., vol. 28, pp. 4842–4882, 2026

    2026

  7. [7]

    Towards smart and reconfigurable environment: Intelligent reflecting surface aided wireless network,

    Q. Wu and R. Zhang, “Towards smart and reconfigurable environment: Intelligent reflecting surface aided wireless network,”IEEE Commun. Mag., vol. 58, no. 1, pp. 106–112, Jan. 2020

    2020

  8. [8]

    Intelligent reflecting surface-aided wireless communica- tions: A tutorial,

    Q. Wu et al., “Intelligent reflecting surface-aided wireless communica- tions: A tutorial,”IEEE Trans. Commun., vol. 69, no. 5, pp. 3313–3351, May 2021

    2021

  9. [9]

    Movable-antenna enhanced multiuser communication via antenna position optimization,

    L. Zhu et al., “Movable-antenna enhanced multiuser communication via antenna position optimization,”IEEE Trans. Wireless Commun., vol. 23, no. 7, pp. 7214–7229, Jul. 2024

    2024

  10. [10]

    Fluid antenna systems,

    K.-K. Wong et al., “Fluid antenna systems,”IEEE Trans. Wireless Commun., vol. 20, no. 3, pp. 1950–1962, Mar. 2021

    1950

  11. [11]

    Integrating movable antennas and intelligent reflecting surfaces (MA-IRS): Fundamentals, practical solutions, and ISAC,

    Q. Wu et al., “Integrating movable antennas and intelligent reflecting surfaces (MA-IRS): Fundamentals, practical solutions, and ISAC,”IEEE Wireless Commun., vol. 33, no. 1, pp. 155–163, Feb. 2026

    2026

  12. [12]

    Joint transmitter and receiver design for movable antenna enhanced multicast communications,

    Y . Gao et al., “Joint transmitter and receiver design for movable antenna enhanced multicast communications,”IEEE Trans. Wireless Commun., vol. 23, no. 12, pp. 18186–18200, Dec. 2024

    2024

  13. [13]

    Throughput maximization for movable antenna systems with movement delay consideration,

    H. Wang et al., “Throughput maximization for movable antenna systems with movement delay consideration,”IEEE Trans. on Wireless Commun., vol. 25, pp. 883–899, 2026

    2026

  14. [14]

    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

    2025

  15. [15]

    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

    2025

  16. [16]

    Rotatable Antenna Enabled Spectrum Sharing: Joint Antenna Orientation and Beamforming Design,

    X. Peng et al., “Rotatable Antenna Enabled Spectrum Sharing: Joint Antenna Orientation and Beamforming Design,”IEEE Trans. Wireless Commun., vol. 25, pp. 15660-15674, 2026,

    2026

  17. [17]

    Cell-Free MIMO with Rotatable Antennas: When Macro-Diversity Meets Antenna Directivity

    X. Peng et al., “Cell-free MIMO with rotatable antennas: When macro-diversity meets antenna directivity,”arXiv preprint: 2601.16543, https://arxiv.org/abs/2601.16543, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  18. [18]

    Low-altitude ISAC with rotatable active and passive arrays,

    Z. Zheng et al., “Low-altitude ISAC with rotatable active and passive ar- rays”,arXiv preprint:2512.20987, 2025, http://arxiv.org/abs/2512.20987

    work page arXiv 2025

  19. [19]

    Rotatable antenna enabled wireless communication and sensing: Opportunities and challenges,

    B. Zheng et al., “Rotatable antenna enabled wireless communication and sensing: Opportunities and challenges,”IEEE Wireless Commun., early access, doi: 10.1109/MWC.2025.3611919

    work page doi:10.1109/mwc.2025.3611919 2025

  20. [20]

    Compressed sensing based channel estimation for movable antenna communications,

    W. Ma, L. Zhu, and R. Zhang, “Compressed sensing based channel estimation for movable antenna communications,”IEEE Commun. Lett., vol. 27, no. 10, pp. 2747–2751, Oct. 2023

    2023

  21. [21]

    Wireless communication with cross-linked rotatable antenna array: Architecture design and rotation optimization,

    A. Zheng et al., “Wireless communication with cross-linked rotatable antenna array: Architecture design and rotation optimization,”arXiv preprint: 2601.04862, 2026, http://arxiv.org/abs/2601.04862

    work page arXiv 2026

  22. [22]

    Fluid antenna-assisted MIMO transmission exploiting statistical CSI,

    Y . Ye et al., “Fluid antenna-assisted MIMO transmission exploiting statistical CSI,”IEEE Commun. Lett., vol. 28, no. 1, pp. 223–227, Jan. 2024

    2024

  23. [23]

    Intelligent reflecting surface enhanced wireless net- works: Two-timescale beamforming optimization,

    M.-M. Zhao et al., “Intelligent reflecting surface enhanced wireless net- works: Two-timescale beamforming optimization,”IEEE Trans. Wireless Commun., vol. 20, no. 1, pp. 2–17, Jan. 2021

    2021

  24. [24]

    Two-timescale design for movable antenna-enabled multiuser MIMO systems,

    Z. Zheng et al., “Two-timescale design for movable antenna-enabled multiuser MIMO systems,”IEEE Trans. Commun., vol. 73, no. 11, pp. 10554–10571, Nov. 2025

    2025

  25. [25]

    Channel estimation for multicell multiuser massive MIMO uplink over Rician fading channels,

    L. Wu et al., “Channel estimation for multicell multiuser massive MIMO uplink over Rician fading channels,”IEEE Trans. Veh. Technol., vol. 66, no. 10, pp. 8872–8882, Oct. 2017

    2017

  26. [26]

    Massive MIMO with spatially correlated Rician fading channels,

    ¨O. ¨Ozdogan, E. Bj ¨ornson, and E. G. Larsson, “Massive MIMO with spatially correlated Rician fading channels,”IEEE Trans. Commun., vol. 67, no. 5, pp. 3234–3250, May 2019

    2019

  27. [27]

    Massive MIMO for maximal spectral efficiency: How many users and pilots should be allocated?

    E. Bj ¨ornson et al., “Massive MIMO for maximal spectral efficiency: How many users and pilots should be allocated?”IEEE Trans. Wireless Commun., vol. 15, no. 2, pp. 1293–1308, Feb. 2016

    2016

  28. [28]

    Cell-free massive MIMO versus small cells,

    H. Q. Ngo et al., “Cell-free massive MIMO versus small cells,”IEEE Trans. Wireless Commun., vol. 16, no. 3, pp. 1834–1850, Mar. 2017

    2017

  29. [29]

    MIMO zero-forcing detection analysis for correlated and estimated Rician fading,

    C. Siriteanu et al., “MIMO zero-forcing detection analysis for correlated and estimated Rician fading,”IEEE Trans. Veh. Technol., vol. 61, no. 7, pp. 3087–3099, Sep. 2012

    2012

  30. [30]

    Asymptotic analysis of RZF in large-scale MU- MIMO systems over Rician channels,

    A. Kammoun et al., “Asymptotic analysis of RZF in large-scale MU- MIMO systems over Rician channels,”IEEE Trans. Inf. Theory, vol. 65, no. 11, pp. 7268–7286, Nov. 2019

    2019

  31. [31]

    Achievable rate optimization for MIMO systems with reconfigurable intelligent surfaces,

    N. S. Perovi ´c et al., “Achievable rate optimization for MIMO systems with reconfigurable intelligent surfaces,”IEEE Trans. Wireless Com- mun., vol. 20, no. 6, pp. 3865–3882, Jun. 2021

    2021