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arxiv: 2604.07219 · v1 · submitted 2026-04-08 · 💻 cs.IT · eess.SP· math.IT

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Robust Hybrid Beamforming with Liquid Crystal Antennas and Liquid Neural Networks

Xinquan Wang , Mingjun Ying , Hongren Chen , Guanyue Qian , Xingchen Liu , Peijie Ma , Dipankar Shakya , Christos Argyropoulos
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Theodore S. Rappaport
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:14 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords hybrid beamformingliquid crystal antennasliquid neural networkssub-terahertz communicationsMU-MIMOspectral efficiencybeam steeringchannel estimation
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The pith

Liquid crystal antennas paired with liquid neural networks enable robust hybrid beamforming for sub-terahertz wireless systems.

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

The paper proposes a hybrid beamforming architecture for sub-terahertz multi-user MIMO communications that uses liquid crystal antennas to perform analog beam steering through voltage-controlled changes in material permittivity, eliminating the need for conventional phase shifters. It combines this hardware with a liquid neural network whose dynamics are defined by ordinary differential equations to track and adapt to time-varying channel conditions, while manifold optimization narrows the space of possible digital precoders. Validation occurs on site-specific ray-tracing simulations of 108 GHz urban channels that match the hardware operating band. A reader would care because sub-terahertz bands promise large unused spectrum for future networks but introduce severe hardware constraints and rapid channel fluctuations that current approaches struggle to handle.

Core claim

The authors establish that integrating reconfigurable liquid crystal antennas as the analog beamforming stage with ordinary differential equation-defined liquid neural networks for digital beamforming, further refined by manifold optimization, produces an 88.6 percent gain in spectral efficiency along with improved tolerance to imperfect channel estimates relative to learning-aided gradient descent and gated recurrent unit baselines, while delivering 1.9 times the spectral efficiency of the 3GPP TR 38.901 antenna model when tested on simulated 108 GHz New York urban propagation channels.

What carries the argument

The hybrid beamforming architecture that places voltage-tunable liquid crystal antennas in the analog stage for permittivity-based beam steering and uses an ordinary differential equation liquid neural network to model temporal channel evolution for the digital stage.

If this is right

  • Sub-terahertz systems can achieve usable data rates without depending on high-loss phase shifters at the analog stage.
  • Liquid neural networks can capture and exploit the shortened channel coherence times that arise from higher Doppler spread at elevated carrier frequencies.
  • Manifold optimization can compress the digital precoding search space enough to make real-time adaptation feasible.
  • The framework maintains performance advantages even when channel estimates contain errors typical of high-frequency operation.

Where Pith is reading between the lines

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

  • If liquid crystal antennas can be produced at scale with repeatable characteristics, they could simplify the deployment of dense sub-terahertz base stations.
  • The continuous-time modeling approach may extend naturally to other frequency bands where propagation varies rapidly with mobility or environment.
  • Hardware-software co-design of this form could reduce overall power consumption by avoiding always-on digital compensation for analog imperfections.
  • Testing the same combination across multiple city layouts or with measured rather than simulated channels would reveal how sensitive the reported gains are to the specific propagation assumptions.

Load-bearing premise

The ray-tracing simulations at 108 GHz accurately represent real sub-terahertz propagation effects and the liquid crystal antenna hardware delivers the modeled voltage-driven beam steering without significant unaccounted losses or fabrication variations.

What would settle it

Direct over-the-air measurements of spectral efficiency using physical liquid crystal antenna prototypes and deployed liquid neural network controllers in a real 108 GHz urban environment, compared against the same baselines under identical imperfect channel conditions.

Figures

Figures reproduced from arXiv: 2604.07219 by Christos Argyropoulos, Dipankar Shakya, Guanyue Qian, Hongren Chen, Mingjun Ying, Peijie Ma, Theodore S. Rappaport, Xingchen Liu, Xinquan Wang.

Figure 1
Figure 1. Figure 1: Schematic of the LC antenna used. (a) Model of the LC-based antenna structure consisting of 48 unit cells. (b) Model of a single LC unit cell integrated into the ground plane (yellow) of a widened microstrip feed line (red). (c) Lateral cross-sectional schematic of a single unit cell showing the LC cavity, biasing electrodes, and the electric-field-induced reorientation of the LC molecules, which modifies … view at source ↗
Figure 4
Figure 4. Figure 4: Robustness evaluation SE vs. channel estimation error (CEE) at P = 30 dBm. The proposed LNN approach demonstrates higher robustness to imperfect CSI compared to the LAGD and GRU base￾lines. shown in the figure, the LNN (LC) demonstrates significantly stronger robustness against high CEE compared to LAGD (LC). Specifically, the LNN (LC) experiences only a 31.7% reduction in SE (from 8.8 to 6.0 bps/Hz), wher… view at source ↗
Figure 3
Figure 3. Figure 3: SE vs. BS total transmit power budget P at CEE = −10 dB. The LNN with LC antennas achieves 88.6% higher SE than LAGD at P = 30 dBm. All LC antenna configurations outperform their 3GPP counterparts by over 1.9 times in SE. To emphasize the effect of LC antennas, we compare all three methods using 3GPP TR 38.901 antennas [4]. B. Evaluation on Beamforming Performance In [PITH_FULL_IMAGE:figures/full_fig_p005… view at source ↗
read the original abstract

Sub-terahertz (sub-THz) multi-user multiple-input multiple-output (MU-MIMO) systems unlock immense bandwidth for 6G wireless communications. However, practical deployment of wireless systems in sub-THz bands faces critical challenges such as increased atmospheric absorption, reduced channel coherence time due to increased Doppler spread at higher carrier frequencies, and hardware bottlenecks as low-loss sub-THz phase shifters are difficult to realize. To overcome the hardware and channel estimation challenges of sub-THz systems, this paper proposes a hybrid beamforming (BF) framework that integrates reconfigurable liquid crystal (LC) antennas with a liquid neural network (LNN) for transmitter. Specifically, we employ an LC antenna as the analog BF stage of a hybrid BF architecture, exploiting its voltage-driven permittivity tunability to achieve high-gain beam steering without the need for lossy phase shifters. For digital BF, we utilize an ordinary differential equations-defined LNN to learn temporal channel dynamics, and use a manifold optimization technique to compress the search space. We validated the proposed method on simulated site-specific 108 GHz ray-tracing channels in an urban scenario using NYURay, a ray-tracing simulator validated against 142 GHz propagation measurements. The 108 GHz carrier frequency matches the operating band of the LC antenna hardware. The proposed method achieves an 88.6\% spectral efficiency (SE) gain and higher robustness to imperfect channel estimation compared to the learning-aided gradient descent and gated recurrent unit machine learning baselines, and 1.9 times higher SE than the 3GPP TR~38.901 standard antenna model, highlighting the potential of LC-based hardware for sub-THz communications.

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 manuscript proposes a hybrid beamforming architecture for sub-THz MU-MIMO that uses reconfigurable liquid crystal (LC) antennas as the analog stage (exploiting voltage-tunable permittivity for beam steering) and liquid neural networks (LNNs defined by ODEs) for the digital stage to learn temporal channel dynamics, with manifold optimization to reduce complexity. It evaluates the scheme on 108 GHz site-specific urban ray-tracing channels generated by NYURay (validated against 142 GHz measurements) and reports an 88.6% spectral efficiency gain plus improved robustness to imperfect CSI relative to learning-aided gradient descent and GRU baselines, along with a 1.9× gain over the 3GPP TR 38.901 antenna model.

Significance. If the idealized LC hardware model and ray-tracing assumptions prove accurate, the work offers a hardware-aware approach to sub-THz beamforming that could mitigate phase-shifter losses and Doppler effects in 6G systems. The site-specific simulation methodology and direct comparison against a standardized antenna model are positive elements that ground the claims in realistic propagation data.

major comments (2)
  1. [Abstract and §IV] Abstract and §IV (Performance Evaluation): The reported 88.6% SE gain, robustness to imperfect CSI, and 1.9× improvement over 3GPP TR 38.901 all rest on an idealized LC antenna model (perfect voltage-driven permittivity tuning with zero insertion loss and ideal beam patterns) and NYURay traces at 108 GHz. No measured S-parameters, beam patterns, or hardware-in-the-loop results for the referenced LC devices are provided, nor is there sensitivity analysis to voltage-dependent losses or fabrication variation; if these assumptions fail, the quantitative margins are not guaranteed.
  2. [§III] §III (LNN and Manifold Optimization): The LNN is trained on simulated channels and manifold optimization is used to compress the search space, but the manuscript provides no ablation on LNN hyperparameters (e.g., ODE solver tolerances, hidden units, or training data volume) and no explicit quantification of how robustness to imperfect CSI varies with CSI error variance; these omissions make the 'higher robustness' claim difficult to assess independently of the specific simulation settings.
minor comments (2)
  1. [§IV] Figure captions and axis labels in §IV should explicitly state the number of Monte Carlo realizations and whether error bars represent standard deviation or confidence intervals.
  2. [§II] Clarify in §II whether the LC antenna model incorporates any frequency-dependent loss terms at 108 GHz or assumes frequency-flat behavior matching the 142 GHz validation data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript. We address each major comment in detail below, providing clarifications grounded in the paper's methodology and proposing targeted revisions to improve transparency and robustness of the claims.

read point-by-point responses

  1. Referee: [Abstract and §IV] Abstract and §IV (Performance Evaluation): The reported 88.6% SE gain, robustness to imperfect CSI, and 1.9× improvement over 3GPP TR 38.901 all rest on an idealized LC antenna model (perfect voltage-driven permittivity tuning with zero insertion loss and ideal beam patterns) and NYURay traces at 108 GHz. No measured S-parameters, beam patterns, or hardware-in-the-loop results for the referenced LC devices are provided, nor is there sensitivity analysis to voltage-dependent losses or fabrication variation; if these assumptions fail, the quantitative margins are not guaranteed.

    Authors: We appreciate the referee's emphasis on hardware realism. The LC antenna model is derived from established physical characterizations of liquid crystal permittivity tuning in the sub-THz regime, consistent with the operating frequency of the referenced devices and aligned with the validated NYURay simulator (cross-checked against 142 GHz measurements). While the study is simulation-based and does not include new hardware measurements, we will revise §IV to incorporate a sensitivity analysis quantifying the effects of insertion loss and fabrication variations on the reported spectral efficiency gains. This addition will explicitly bound the performance margins under non-ideal conditions and strengthen the interpretation of the 88.6% gain and 1.9× improvement over the 3GPP model. revision: partial

  2. Referee: [§III] §III (LNN and Manifold Optimization): The LNN is trained on simulated channels and manifold optimization is used to compress the search space, but the manuscript provides no ablation on LNN hyperparameters (e.g., ODE solver tolerances, hidden units, or training data volume) and no explicit quantification of how robustness to imperfect CSI varies with CSI error variance; these omissions make the 'higher robustness' claim difficult to assess independently of the specific simulation settings.

    Authors: We agree that systematic ablations and explicit robustness curves would improve reproducibility and allow independent assessment of the LNN's advantages. In the revised manuscript, we will expand §III with an ablation study varying key hyperparameters (ODE solver tolerances, hidden units, and training data volume) and their impact on convergence and spectral efficiency. We will also add a new plot in §IV showing spectral efficiency versus CSI error variance for the proposed LNN approach compared to the gradient descent and GRU baselines, thereby providing direct quantitative support for the improved robustness claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are simulation outputs on external channel data

full rationale

The paper's performance claims (88.6% SE gain, robustness, 1.9x improvement) are obtained by running the proposed LC+LNN hybrid beamformer on site-specific 108 GHz channels generated by the independent NYURay ray-tracing simulator. The LNN is trained to predict temporal dynamics on those channels, manifold optimization reduces the analog beamformer search space, and SE is computed end-to-end; none of these steps algebraically forces the reported margins by re-using fitted constants or self-referential definitions. The channel model and LC antenna response are taken as external inputs (validated against measurements in prior literature), and the numerical gains are falsifiable against other simulators or hardware. No self-citation chain or ansatz smuggling is required for the central quantitative results.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The framework rests on standard wireless propagation assumptions and simulation fidelity rather than new physical postulates.

free parameters (2)
  • LNN training hyperparameters
    Parameters of the ODE-defined liquid neural network are learned from simulated channel data.
  • Manifold optimization parameters
    Compression parameters for the digital beamforming search space are chosen to make the optimization tractable.
axioms (2)
  • domain assumption NYURay ray-tracing at 108 GHz produces channels representative of real sub-THz urban propagation
    Validation against 142 GHz measurements is cited but the frequency offset and site-specific modeling assumptions are not further justified in the abstract.
  • domain assumption Liquid crystal antenna permittivity can be tuned by voltage to produce ideal high-gain beams without additional insertion loss or mutual coupling effects
    This is the core hardware modeling assumption enabling the analog beamforming stage.

pith-pipeline@v0.9.0 · 5637 in / 1494 out tokens · 34023 ms · 2026-05-10T17:14:20.961439+00:00 · methodology

discussion (0)

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