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Geometry-Aided Channel Deduction with Partial Channel Estimates and Uncalibrated Digital Twin

Hongning Ruan, Zhaoyang Zhang, Zirui Chen, Ziqing Xing, Zhaohui Yang, Mérouane Debbah

arXiv:2609.37277v1eess.SPcs.LG

TL;DR

High-dimensional MIMO-OFDM CSI acquisition can require substantial pilot overhead or accurate positional and environmental information. GCD combines approximate digital-twin geometry with partial pilot estimates using structural prompts and a channel-deduction network. The authors report high-quality acquisition, robustness, and cross-scenario generalization.

  • Problem

    High-dimensional CSI acquisition is challenging with low pilot overhead, while existing learning approaches also need to generalize across changing scenarios and pilot configurations.

    Source: A. Background · p. 1

  • Method

    GCD fuses approximate digital-twin geometry, converted into a structural prompt, with pilot-based partial channel estimates in a channel-deduction network.

    Source: C. Motivations and Contributions · p. 3, §III · p. 5

  • Results

    The proposed schemes achieve high-quality channel acquisition with low pilot overhead, robustness to biased geometry, and cross-scenario generalization.

    Source: §V · p. 15

  • Takeaways & Limitations

    Environmental geometry, pilot patterns, and system configurations can serve as prompts for multi-scenario pre-training toward more general wireless models.

    Source: §V · p. 15

    In unseen scenarios, hard testing samples still incur inevitable performance degradation under significant distribution shift.

    Source: 3) Finetuning in New Scenarios · p. 12

Abstract

from arXiv · show

The acquisition of high-dimensional channel state information (CSI) in wireless MIMO-OFDM communications usually requires high pilot overhead, or relies on accurate and complete positional or environmental information. In this paper, we propose a geometry-aided channel deduction (GCD) approach, which utilizes an uncalibrated digital twin (DT) with only approximate environmental geometry and positions to assist the channel acquisition. The key rationale behind is that, even imprecise geometric information, which can be easily obtained in advance through radio sensing technologies or existing geographic databases, provides certain structural features about the current channel; meanwhile, the coarse instantaneous channel estimates using only a small amount of pilots provide dedicated information that aligns with the channel structure and further compensates for the geometry inaccuracy and other channel unknowns. To this end, we first extract geometric features from the DT, which contain only simple structural information of the channel. Then we propose random prompt augmentation, a novel method to generate an appropriate prompt that converts geometric multi-path structure into a CSI-like representation while suppressing the disturbance of other unknown channel parameters. The prompt is then fused with the pilot-based instantaneous channel estimate via a channel deduction network. To further enhance the network's versatility, we incorporate pilot configurations into the existing learning architecture to support variable pilot patterns. Comprehensive experiments validate the superiority of the proposed method, which demonstrates high channel acquisition quality, low pilot overhead, and strong robustness. Furthermore, the structural prompt also serves as scenario-related context, enabling our approach to generalize well in new scenarios.

I. INTRODUCTION

High-dimensional CSI makes low-overhead acquisition difficult, while pilot-only, pilot-free, and hybrid approaches face limits in complexity, positioning accuracy, or deployment costs. GCD combines approximate geometric structure with partial pilot estimates, then uses prompts and neural networks to support accurate, robust acquisition across scenarios and pilot patterns.

A. Background

  • High-dimensional CSI makes low-pilot acquisition challenging, while learning methods also need to generalize across changing scenarios and adapt to diverse pilot patterns.The background identifies these factors as relevant to real-world deployment.Source: A. Background · p. 1

1) Pilot-Based Channel Estimation:

  • Pilot-based interpolation and learned estimation can reduce pilot use, but complex multipath may exceed limited pilots and many neural networks are tailored to specific pilot configurations.Pilot-based path-parameter estimation can also involve high computational complexity.Source: 1) Pilot-Based Channel Estimation · pp. 1–2

2) Pilot-Free Channel Prediction:

  • Pilot-free prediction from past channels or positions faces mobility, accumulated prediction errors, positioning-accuracy demands, and weak generalization; calibrated DT methods also require scenario-specific data and computation.Without pilots, the cited discussion says complete CSI is practically unavailable, limiting more complex tasks such as detection and precoding in multipath scenarios.Source: 2) Pilot-Free Channel Prediction · p. 2

3) Hybrid Channel Acquisition:

  • Hybrid methods combine pilots with auxiliary information, but image sensing, historical channel data, and full DTs bring sensing, data-collection, or environmental-information costs.Partial pilots can relax the accuracy requirements for auxiliary information.Source: 3) Hybrid Channel Acquisition · p. 2

C. Motivations and Contributions

  • Approximate maps and transceiver positions can provide channel path structure; partial pilots can compensate for geometric errors and unknown channel factors, avoiding the need for a calibrated DT.The proposed design uses offline ray tracing and user-side neighborhood sampling rather than continuous online ray tracing.Source: C. Motivations and Contributions · pp. 2–3
  • GCD fuses DT-derived geometry with partial CSI, while random prompt augmentation creates CSI-like structural prompts and suppresses unknown features.GCDNet and mask-enhanced mGCDNet provide fusion implementations, with mGCDNet incorporating pilot positions for variable configurations; experiments report accuracy, robustness, and cross-scenario generalization.Source: C. Motivations and Contributions · p. 3

II. SYSTEM MODEL

The system model describes propagation as a collection of paths whose geometry, scattering, and antenna responses determine the received field. It expresses the channel frequency response through path delays and path coefficients.

A. Electromagnetic Wave Propagation

  • An antenna's direction-dependent radiation pattern combines complex amplitude gain and polarization, and its far field scales with inverse distance and a phase term.The pattern is normalized so a value of one corresponds to a lossless isotropic antenna.Source: A. Electromagnetic Wave Propagation · p. 3
  • The propagation channel comprises paths with lengths, departure and arrival directions, and scattering matrices; the line-of-sight path has an identity scattering matrix.Each scattering matrix represents attenuation and phase shift from environmental interactions, including polarization-component effects.Source: A. Electromagnetic Wave Propagation · p. 3
  • The channel frequency response uses each path's delay, τp = dp/c, while its coefficient accounts for propagation distance, antenna patterns, environmental interactions, and polarization mismatch.The propagation delay is path length divided by the speed of light.Source: A. Electromagnetic Wave Propagation · p. 4

B. Channel Model

The model represents a MIMO-OFDM downlink channel over antennas and subcarriers, with pilots sampling a subset of that spatial-frequency grid. Pilot observations provide partial CSI, which the paper assumes is noise-free by default.

B. Channel Model

  • The downlink channel is a spatial-frequency matrix H with Nt antenna rows and Nc subcarrier columns.The system uses a base station with Nt antennas serving single-antenna users over Nc subcarriers.Source: B. Channel Model · p. 4
  • Pilots sample an evenly spaced subset of antenna and subcarrier indices, with interval and start values defining the spatial and frequency patterns.The sampled indices form the partial channel Hπ.Source: B. Channel Model · p. 4
  • At pilot positions, successive antenna transmissions yield partial channel estimates; the model assumes clean, noise-free partial CSI by default.The channel is treated as approximately constant within a coherence-time block.Source: B. Channel Model · p. 4

C. Obtainable Channel Features

The channel is decomposed into geometric structure that can be computed from available environmental information and a second component containing difficult-to-obtain channel factors. The paper argues that this structure makes the unknown features low-dimensional relative to the full channel.

C. Obtainable Channel Features

  • The model rewrites the channel using a geometric phase component and a path-coefficient component, with the geometric component encoding antenna- and subcarrier-dependent phase offsets.Its path parameters describe channel structure and can be computed from an environmental map and transceiver positions, although geometric errors make the high-frequency phase unpredictable.Source: C. Obtainable Channel Features · p. 4
  • The remaining path coefficient combines distance attenuation with material-dependent scattering, antenna patterns, hardware conditions, and an unpredictable high-frequency phase term.Only the large-scale distance attenuation is explicitly obtainable in the stated factorization.Source: C. Obtainable Channel Features · p. 5
  • Geometric features are shared structural information across the channel grid, whereas the unknown component has low underlying dimensionality and can be compensated with minimal pilot overhead.The paper presents this as a route to complete channel acquisition despite the channel's O(NtNc) data dimension.Source: C. Obtainable Channel Features · p. 5

III. PROPOSED FRAMEWORK

GCD combines approximate digital-twin geometry with a pilot-based partial channel estimate to produce the complete channel. It represents geometric paths as a CSI-like prompt and fuses that prompt with the partial estimate.

III. PROPOSED FRAMEWORK

  • GCD fuses a geometric scenario prompt with a pilot-based partial channel estimate in a user-side neural network to generate the complete channel.Source: §III · p. 5

A. Geometric Feature Extraction

B. Random Prompt Augmentation

  • Random prompt augmentation converts path parameters into a pseudo-channel representation under the channel model, enabling fusion with partial CSI in a shared feature format.Source: B. Random Prompt Augmentation · pp. 5–6
  • Random placeholders replace unknown channel factors in pseudo-channels; varying their realizations is intended to suppress those unknowns and focus learning on shared geometric structure.Source: B. Random Prompt Augmentation · p. 6

C. Channel Deduction Network

GCDNet maps partial CSI to a complete-shaped representation, fuses it with geometric pseudo channels, and refines the fused output. Mask-enhanced GCDNet adds pilot-position information so the network can handle variable pilot patterns.

1) GCDNet:

  • GCDNet pre-maps partial CSI, fuses it with pseudo channels, then refines the fused representation into the output CSI.The fusion module combines features from the pseudo channels and pre-mapped partial CSI.Source: 1) GCDNet · p. 6
  • CMixer implements the pre-mapping and refinement modules, while attention enables interaction between pseudo-channel and partial-CSI features.The CMixer modules operate in the spatial-frequency domain; fusion uses a Transformer encoder.Source: 1) GCDNet · pp. 6–7

2) Mask-Enhanced GCDNet:

  • The original pre-mapping module ignores pilot settings, restricting GCDNet to a fixed pilot pattern.The fixed pattern includes fixed pilot intervals and starts.Source: 2) Mask-Enhanced GCDNet · p. 7
  • mGCDNet replaces pre-mapping with mCMixer, which uses the padded CSI and pilot mask to support various pilot patterns.The padded CSI is concatenated with the pilot mask before mCMixer pre-maps it.Source: 2) Mask-Enhanced GCDNet · p. 7

D. Training and Inference

Training samples CSI and user positions across scenarios and pilot configurations, then normalizes channel inputs and learns to reconstruct complete CSI. The evaluation setup uses 12 scenarios across four cities, with specified propagation, array, and pilot-pattern settings.

D. Training and Inference

  • Training samples a scenario, CSI-position pair, and pilot pattern at each step, allowing multi-scenario and multi-pattern learning.For a single training scenario, the procedure reduces to single-scenario learning.Source: D. Training and Inference · p. 7
  • Inputs are normalized using average power estimated from the observed pilots, and the network is trained with MSE between normalized true and reconstructed CSI.At inference, inputs are normalized similarly and the output is denormalized to recover the absolute magnitude scale.Source: D. Training and Inference · pp. 7–8
  • Online inference comprises neighborhood search, pseudo-CSI construction, and a network forward pass; ray tracing and feature extraction are offline.The stated neighborhood-search complexity is O(N log n).Source: D. Training and Inference · p. 8

1) Scenario Setup:

  • The evaluation scenarios use environmental maps from four cities, with three manually selected base-station positions per city.The cities are San Francisco, Shanghai, Singapore, and London, yielding 12 scenarios.Source: 1) Scenario Setup · p. 8, Figure 4 · p. 8, Figure 5 · p. 8
  • The simulated channels use up to five reflections, a 16-element ULA, 5 GHz center frequency, and 256 subcarriers across 40 MHz.Users are distributed within a 400 m × 400 m area around each base station; pilot settings include fixed or variable intervals and starts.Source: 1) Scenario Setup · p. 8

2) Baselines and Parameter Settings:

The experiments compare geometry-aided channel deduction with learning-based and classical channel-acquisition baselines, including variants adapted to variable pilot patterns. Acquisition quality is measured with NMSE and cosine correlation, while average achievable rate evaluates precoding performance.

2) Baselines and Parameter Settings:

  • Mask-enhanced CMixer and PCMixer baselines support variable pilot patterns; larger variants double hidden dimensions and have substantially higher complexity than (m)GCDNet.mCMixer uses the prior mGCDNet mask enhancement, while mPCMixer concatenates the partial estimate with the pilot mask.Source: 2) Baselines and Parameter Settings · p. 9
  • The comparison includes diffusion-model posterior sampling implemented with an eight-block DiT of hidden size 512, trained for 10,000 epochs.The denoising network replaces the original CNN in the referenced implementation.Source: 2) Baselines and Parameter Settings · p. 9
  • Classical references include LMMSE with covariance estimated from training data and LMMSE-BP, which adds geometry-based basis projection.LMMSE-BP incorporates the basis-projection idea proposed in.Source: 2) Baselines and Parameter Settings · p. 9

3) Evaluation Metrics:

  • NMSE and cosine correlation assess acquisition quality, while average achievable rate measures precoding performance using the acquired CSI.The precoder is maximum ratio transmission with a unit-power vector.Source: 3) Evaluation Metrics · p. 9

B. Single-Scenario Learning

The single-scenario experiments test whether mask enhancement enables learning across fixed and variable pilot patterns. Under variable patterns, mGCDNet performs best among the compared schemes and is more robust to input noise in VRVS than FRVS.

B. Single-Scenario Learning

  • The single-scenario training, validation, and test sets contain 40,000, 10,000, and 10,000 samples, respectively.All three splits are from San Francisco BS 1.Source: B. Single-Scenario Learning · p. 9

1) Training under Different Pilot Pattern Settings:

  • Mask-free schemes fail under FRVS without pilot-pattern information and cannot support VRVS because their network structures fix the partial-channel size.With fixed pilot patterns, PCMixer and GCDNet outperform CMixer.Source: 1) Training under Different Pilot… · p. 9
  • Under FRVS and VRVS, mGCDNet achieves the best performance, even with fewer parameters and FLOPs than mPCMixer-L or mCMixer-L.The authors report that the quantitative results in Table V further validate mGCDNet’s superiority under variable pilot configurations.Source: 1) Training under Different Pilot… · p. 10, Table V · p. 10
  • With variable pilot patterns, mGCDNet is more robust to input noise under VRVS than FRVS, while all schemes degrade as SNR decreases.The authors relate the VRVS robustness to the richer training pilot configurations.Source: 1) Training under Different Pilot… · p. 10

2) Performance under Different Pilot Intervals:

Across pilot intervals, mGCDNet consistently outperforms the other schemes, including when pilot resources are scarce. The experiments also examine prompt length and positional error as factors affecting its performance.

2) Performance under Different Pilot Intervals:

  • mGCDNet consistently outperforms other schemes across pilot intervals; DMPS and LMMSE work effectively only with abundant pilots, while mCMixer degrades with very few pilots.LMMSE-BP improves on LMMSE but depends heavily on the initial LMMSE estimate; mPCMixer and mGCDNet operate across the tested intervals.Source: 2) Performance under Different Pilot… · p. 10, Figure 7 · p. 11

3) Impact of Prompt Length and Position Error:

  • Increasing prompt length first improves mGCDNet’s performance and then approaches a plateau; even one neighboring sample outperforms the other schemes by a wide margin.The plotted prompt length is the number of neighboring samples used to construct pseudo channels from geometric features.Source: 3) Impact of Prompt Length and… · p. 10, Figure 8 · p. 11
  • Repeating the nearest neighbor with different random placeholders performs nearly as well as using distinct neighbors, indicating gains primarily come from multiple placeholder realizations.Using distinct neighbors is slightly more robust to position errors than repeating one neighbor.Source: 3) Impact of Prompt Length and… · pp. 10–11
  • As user-position error grows, mGCDNet and mPCMixer degrade; mGCDNet retains an advantage over other schemes when the error scale is below 4 m.Position error is sampled uniformly over a square with side length 2l; distinct neighbors provide slightly stronger robustness than reusing the nearest one.Source: 3) Impact of Prompt Length and… · p. 11, Figure 8 · p. 11

C. Multi-Scenario Learning

The multi-scenario experiments train on six scenarios and assess performance across twelve, including unseen scenarios and tests with imperfect geometry. mGCDNet generalizes to unseen scenarios, maintains satisfactory performance under several geometric inaccuracies, and adapts to new scenarios through finetuning.

1) Performance in Original and New Scenarios:

2) Performance under Non-Ideal Geometric Information:

  • Under imperfect geometry, mGCDNet maintains satisfactory performance on most samples; reducing retained paths or maximum path depth degrades NMSE, with stable performance when more than 8–16 paths and depth of at least 3 are retained.Traffic conditions cause little performance change, while building information can matter more because it may alter path number or visibility.Source: 2) Performance under Non-Ideal… · p. 12, Figure 11 · p. 13, Figure 12 · p. 13

3) Finetuning in New Scenarios:

  • After multi-scenario pretraining, mGCDNet adapts to Singapore BS 1 with few finetuning steps while maintaining performance in prior scenarios; mCMixer and mPCMixer show catastrophic forgetting.The comparison evaluates the new scenario and a previous scenario after finetuning.Source: Figure 13 · p. 13, 3) Finetuning in New Scenarios · p. 13

4) Generalization across System Configurations:

mGCDNet generalizes to some unseen system configurations and performs favorably in the ASU Campus scenario. Across prompt-design comparisons, it leads in single- and multi-scenario learning, while the alternatives vary in how well they use contextual geometric information.

4) Generalization across System Configurations:

  • The evaluation regenerates data for 12 scenarios with new system configurations, adds ASU Campus, trains on six scenarios, and evaluates across all 13.ASU Campus data come from Wireless Insite; the other regenerated scenarios use Sionna RT.Source: 4) Generalization across System… · pp. 13–14
  • Baseline schemes fail in unseen system configurations, while mGCDNet generalizes on some test samples, especially Singapore BS 1.The authors suggest broader training-scenario coverage or computation-efficient fine-tuning as ways to improve performance in new configurations.Source: 4) Generalization across System… · p. 14
  • mGCDNet shows significant advantages over baselines in ASU Campus, with Table IX reporting NMSE and ρ for three example scenarios.The supplied passages do not state the table's cell values.Source: 4) Generalization across System… · p. 14, Figure 15 · p. 14, Table IX · p. 14

D. Ablation Studies on Prompt Design

  • In single-scenario learning, mGCDNet performs best and deterministic-prompt mGCDNet (D) ranks second; mBCFNet and mGCFNet perform poorly.Increasing prompt length reduces mBCFNet and mGCFNet performance, which the authors interpret as ineffective use of auxiliary geometry.Source: Figure 16 · p. 14, D. Ablation Studies on Prompt Design · p. 15
  • In unseen scenarios, mGCDNet, mGCDNet (D), and mBCFNet perform well with contextual prompts, whereas mGCFNet fails; mGCDNet leads overall in both training settings.The authors attribute mGCFNet's failure to not leveraging the channel model and thus lacking generalization under changed data distributions.Source: Figure 17 · p. 14, D. Ablation Studies on Prompt Design · p. 15
  • The alternatives represent geometry with learned Transformer-pooled path features (mGCFNet) or path-derived basis matrices (mBCFNet), rather than the proposed prompt design.All methods fuse partial CSI with geometric features; the comparison varies how the geometric features are handled.Source: D. Ablation Studies on Prompt Design · pp. 14–15
  • In learned scenarios, all schemes improve as prompt length increases, indicating that each can use contextual prompt information after multi-scenario training.The authors contrast this with single-scenario learning, where mBCFNet and mGCFNet declined as prompt length increased.Source: Figure 18 · p. 15, D. Ablation Studies on Prompt Design · p. 15

V. CONCLUSION

The conclusion presents GCD as a framework that combines digital-twin geometry with coarse pilot estimates, using channel-structure-aware prompts and fusion networks that support variable pilot configurations. The authors report high-quality acquisition with low pilot overhead, robustness to biased geometry, and cross-scenario generalization.

V. CONCLUSION

  • GCD extracts geometric prior information from a digital twin and fuses it with pilot-based coarse channel estimates.The conclusion describes prompt generation and augmentation designed around the physical structure of channel data.Source: §V · p. 15
  • The proposed schemes achieve high-quality channel acquisition with low pilot overhead, robustness to biased geometry, and cross-scenario generalization.Source: §V · p. 15
  • The authors argue that accessible prompts and pre-training across scenarios, pilot patterns, and system configurations can help wireless models learn universal knowledge.They also identify modality transformation and physically structured network design as contributors to learning efficiency.Source: §V · p. 15
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