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CoRF: Cross-Scene RF Synthesis by Learning Propagation and Preserving Array Physics

Kang Yang, Duaa Nakshbandi, Wan Du, Mani Srivastava

arXiv:2609.34399v1cs.NI

TL;DR

Existing RF neural fields fit scenes separately, so new-scene deployment requires substantial measurements and scene-specific optimization. CoRF conditions a canonical anchor field on sparse unordered references and analytically renders predicted propagation through the receiver-array model. Across simulated scenes, it beats the strongest baseline on unseen variants and entirely unseen categories.

  • Problem

    Existing RF neural fields fit each scene separately, requiring large target-scene measurement sets and new optimization for deployment.

    Source: §1 · p. 1

  • Method

    CoRF conditions canonical anchors on unordered target-scene spectra to predict query-specific propagation, then renders it with analytic receiver-array physics.

    Source: §1 · p. 2

  • Results

    7.09 dB PSNR on unseen variants and 6.97 dB PSNR on entirely unseen categories over the strongest baseline, using M = 32 references.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The pretrained propagation model remains frozen at deployment, with one reference-conditioning pass supporting synthesis at arbitrary query locations.

    Source: §1 · p. 2

    Performance gains narrow under simulation-to-real transfer when physical receiver responses differ from the nominal array model.

    Source: §5 · p. 10

Abstract

from arXiv · show

Existing radio-frequency (RF) neural fields fit each scene separately, making new-scene deployment measurement- and optimization-intensive. This work studies amortized cross-scene spatial spectrum synthesis, where a shared model learns propagation across scenes and instantiates an unseen scene from sparse target-scene measurements without scene-specific training. To achieve this, CoRF separates learned scene-dependent propagation from the known receiver-array observation model. An unordered set of spectrum-only references conditions a canonical anchor field, producing arrival directions and query-dependent component powers for each query. Analytic array physics maps these components to the receiver covariance and then to the spatial spectrum. This factorization keeps the pretrained propagation model frozen, enabling synthesis at arbitrary query locations after a single reference-conditioning pass. A necessary local reference-capacity bound and an error decomposition further characterize the formulation. Across 35 simulated scenes spanning seven categories, CoRF outperforms the strongest baseline by 7.09 dB PSNR on unseen variants of represented scene categories and by 6.97 dB on entirely unseen scene categories.

1 INTRODUCTION

Existing RF neural fields fit scenes separately, requiring large target-scene measurement sets and new optimization; CoRF instead amortizes propagation inference from sparse references. It retains analytic array physics and reports gains on two forms of unseen-scene generalization.

1 INTRODUCTION

  • Existing RF neural fields fit each scene separately, requiring large target-scene measurement sets and new scene-specific optimization for deployment.GRaF synthesizes queries from geographically nearby measurements and depends on local reference coverage.Source: §1 · p. 1
  • Cross-scene synthesis must address absent query-reference correspondence in RF spectra and avoid spending model capacity relearning the receiver-array response.Each spectrum superposes paths whose directions and powers vary with transmitter location, while the observation operator is set by receiver configuration.Source: §1 · pp. 1–2
  • CoRF separates learned scene-dependent propagation from the known receiver-array response, conditioning canonical anchors on unordered references and rendering predicted components analytically.The resulting field is reused across query locations without scene-specific fitting.Source: §1 · p. 2
  • 7.09 dB PSNR on unseen variants and 6.97 dB PSNR on entirely unseen categories over the strongest baseline, using M = 32 references.The evaluation spans 35 simulated scenes across seven categories.Source: §1 · p. 2

2 RELATED WORK

Prior RF reconstruction commonly fits scenes separately, while geometry-conditioned methods require explicit scene models. CoRF instead reuses a scene representation built from sparse measured spectra.

Spatial Spectrum Synthesis

  • Scene-specific RF neural fields and Gaussian representations require separate scene optimization, while geometry-conditioned methods such as RadTwin require a point cloud or mesh.CoRF uses measured spectra where a scene model is unavailable.Source: §2 · p. 2
  • Unlike GRaF, which needs geographically nearby spectra for each query, CoRF builds one reusable scene representation from a sparse reference set.This removes GRaF's local reference coverage requirement.Source: §2 · p. 2

Feed-Forward Reconstruction in Vision

  • Vision methods often exploit geometric correspondence between reference and query views, but RF spectra lack comparable correspondence because multipath directions and powers vary by transmitter location.CoRF conditions a canonical anchor field on unordered spectra to form a shared scene representation.Source: §2 · p. 2

Analytic Array Processing

  • CoRF predicts propagation for unmeasured transmitter locations and renders spectra with the analytic Bartlett response; explicit receiver response also permits calibration without retraining propagation.Learned hardware compensation can address broader mismatch but requires receiver-specific data.Source: §2 · p. 3, Figure 1 · p. 3

3 METHOD

CoRF conditions a shared canonical anchor field on unordered spectrum references, then predicts query-specific propagation and renders the result with analytic array physics. Its analysis bounds reference capacity and separates propagation errors from renderer mismatch; training and deployment also include optional targeted adaptations.

3 METHOD

  • At test time, a single reference set from an unseen scene constructs a reusable representation for synthesizing spectra at arbitrary query transmitter locations.The method samples a scene, an unordered reference set, and a query outside that set during training.Source: §3 · p. 3

3.1 CROSS-SCENE PROPAGATION FIELD

  • Canonical anchors combine global reference context with bearing-aligned evidence, then decode reusable scene structure into query-dependent propagation parameters.Anchor positions and occupancy are refined, while propagation strength adapts to the query transmitter location.Source: §3.1 · pp. 3–4

3.2 ANALYTIC ARRAY PHYSICS

  • Analytic array physics sums component covariance contributions and renders the Bartlett spectrum, while propagating component-power uncertainty to a query-level reliability signal.The renderer is a structured approximation under narrowband and far-field assumptions, with incoherent covariance components and no path cross terms.Source: §3.2 · pp. 4–5

3.3 THEORETICAL ANALYSIS

  • The analysis gives a necessary local reference-capacity bound and an error bound separating renderer mismatch from errors in predicted component powers and arrival directions.The reference bound explains why complementary references matter but does not determine the count needed in practice.Source: §3.3 · p. 5

3.4 TRAINING AND INFERENCE

  • Training pretrains reference encoders, then freezes them while learning reference-to-anchor projection and propagation; inference conditions anchors once and reuses them across queries.CoRFPR fits only mean component-power corrections using the same references; CoRFCAL calibrates the analytic response with separate additional spectra while propagation remains fixed.Source: §3.4 · p. 6

4 EVALUATION

The evaluation uses simulated scenes and matched sparse target-scene references to test per-scene performance, cross-scene generalization, reliability, receiver adaptation, ablations, beam management, and real-data transfer. Across held-out variants and categories, CoRFPR outperforms the strongest baseline on all four reported metrics.

4.2 GENERALIZATION TO UNSEEN VARIANTS OF KNOWN SCENE CATEGORIES; 4.3 GENERALIZATION TO UNSEEN SCENE CATEGORIES

  • 7.16 dB PSNR and 0.254 SSIM gains, with NMSE reduced by 0.279 and AoA error by 13.42°, distinguish CoRFPR from WRF-GS-FS on unseen variants; on unseen categories, the respective gains are 7.03 dB, 0.248, 0.276, and 13.36°.Both evaluations use M = 32 references; Table 2 aggregates five folds and Table 3 seven folds.Source: Table 2 · p. 7, Table 3 · p. 7, §4.2 · p. 7

4.1 PER-SCENE PERFORMANCE

  • Across 36 scenes, CoRFPR achieves 24.27 dB PSNR, 0.791 SSIM, 0.083 NMSE, and 7.68° AoA error, the best average performance on all four metrics.Relative to the strongest baseline for each metric, PSNR rises from 21.96 dB and SSIM from 0.705, while NMSE falls from 0.113 and AoA error from 8.91°.Source: Table 1 · p. 6, §4.1 · p. 7

4.4 COMPONENT-POWER RELIABILITY

  • Across 68,232 test queries, NMSE rises from 0.050 to 0.223 and SSIM falls from 0.828 to 0.630 between the lowest- and highest-uncertainty quintiles.Mean within-fold Spearman correlations are ρ = 0.53 for NMSE and ρ = −0.55 for SSIM; propagated power variance ranks synthesis reliability but is not calibrated pixel-level predictive uncertainty.Source: §4.4 · pp. 7–8, Figure 2 · p. 7

4.5 RECEIVER ARRAY ADAPTATION

  • With perturbed array specifications, calibration improves SSIM from 0.458–0.553 to 0.697–0.795 and PSNR by 4.6–7.1 dB while pretrained neural modules remain frozen.The tested errors match the three-parameter calibration model, so the results demonstrate correction of those specification errors, not arbitrary receiver mismatch.Source: §4.5 · p. 8, Table 4 · p. 8

4.6 ABLATION STUDY

  • Replacing analytic array physics with a learned CNN causes the largest ablation degradation, while removing bearing-aligned sampling or query conditioning also worsens results in both generalization settings.Without analytic rendering, unseen-variant PSNR falls from 22.95 to 16.09 dB and AoA error rises from 8.40° to 16.27°; removing query conditioning reduces PSNR by 2.20 dB on unseen variants and 4.51 dB on unseen categories. Removing bearing-aligned sampling reduces PSNR by 1.88 and 2.04 dB, respectively.Source: §4.6 · p. 8, Table 5 · p. 8

4.7 CASE STUDY: BEAM MANAGEMENT WITH SYNTHESIZED SPATIAL SPECTRA

  • With one selected beam, CoRF achieves 0.93 dB beam loss versus 5.02 dB for the strongest baseline; at four beams it reaches 0.46 dB, comparable to the baseline’s 0.44 dB at 16 beams.Reliability-aware allocation reduces loss for unseen variants at budgets of eight and 16 beams, but its gain disappears for unseen categories.Source: §4.7 · p. 9, Figure 3 · p. 9

4.8 GENERALIZATION TO REAL MEASUREMENTS

  • On measured scene S36, CoRFPR,CAL leads in PSNR, SSIM, and NMSE, while GRaF has marginally lower AoA error.Calibration improves PSNR by 1.95 dB over uncalibrated CoRF, and power refinement adds 0.71 dB without further measurements; neither recovers missing directions.Source: §4.8 · p. 9, Table 6 · p. 9

5 DISCUSSION AND CONCLUSION

CoRF synthesizes cross-scene RF spatial spectra from sparse target-scene measurements by conditioning canonical anchors and rendering predicted propagation components through analytic receiver-array physics. The paper reports about 7 dB PSNR gains over the strongest baseline on two simulated generalization settings and identifies transfer, modality, and scene-dynamics boundaries.

5 DISCUSSION AND CONCLUSION

  • Across 35 simulated scenes, CoRFPR exceeds the strongest baseline by about 7 dB PSNR on both unseen scene variants and excluded categories.The method separates learned scene-dependent propagation from analytic receiver-array response.Source: §5 · p. 10
  • The method is limited to spatial-spectrum references and static scenes, and simulation-to-real transfer is constrained when physical receiver responses differ from the nominal array model.The discussion proposes element-wise gain and phase calibration, modality-specific representations and reference strategies, and temporal representations with online reference updates as possible extensions.Source: §5 · p. 10

A ANALYTIC COMPONENT POWER UNCERTAINTY

The analysis propagates component-power uncertainty through the analytic decoder to the spatial spectrum, deriving exact power-domain moments and an approximate magnitude-domain variance. The reported proxy uses fixed normalization and represents only component-power uncertainty conditional on predicted means and directions.

Exact Power Domain Moments

  • With pairwise-uncorrelated component powers, the Bartlett power’s mean and variance are derived exactly, while substituting mean powers preserves the deterministic point prediction.The deterministic LOS contribution has zero variance.Source: A ANALYTIC COMPONENT POWER UNCERTAINTY · p. 15

Magnitude Domain Uncertainty

  • For magnitude uncertainty, CoRF uses a first-order delta approximation after the square-root transformation, but this approximation is not a distribution-free bound.At zero mean Bartlett power, the variance proxy is set to zero.Source: A ANALYTIC COMPONENT POWER UNCERTAINTY · p. 16

Normalization and Reported Uncertainty

  • Uncertainty propagation holds the deterministic prediction’s minimum and maximum fixed rather than normalizing each random realization, which would couple angular locations.The fixed affine normalization approximation is used for the reported uncertainty.Source: A ANALYTIC COMPONENT POWER UNCERTAINTY · p. 16

Reported Uncertainty

  • The calibrated variance is a component-power uncertainty proxy conditional on predicted means and directions, excluding errors in those predictions, scene-state estimation, renderer mismatch, and distribution shift.The temperature rescales the proxy and the residual variance floor is provided by ε0.Source: A ANALYTIC COMPONENT POWER UNCERTAINTY · p. 17

B OBSERVABILITY FROM REFERENCE SPECTRA

The analysis measures which scene variations reference spectra can constrain after accounting for unknown reference poses. It derives local sufficiency and reference-capacity bounds, while showing that reference utility also depends on overlap among the directions they constrain.

Effective Scene Information

  • A scene perturbation is indistinguishable from an unknown-pose perturbation to first order when its effective scene information vanishes.The effective information retains scene variations that cannot be absorbed by an infinitesimal pose change.Source: B OBSERVABILITY FROM REFERENCE SPECTRA · p. 17

Observable Dimension and Reference Sufficiency

  • Local sufficiency requires the references to span the locally observable scene subspace, whose dimension r⋆ counts independent scene directions after accounting for unknown pose.A finite collection of admissible reference row spaces can span this subspace when r⋆ is positive.Source: B OBSERVABILITY FROM REFERENCE SPECTRA · p. 18

Reference Capacity and Complementarity

  • A reference’s marginal observable dimension ranges from 0 to N−1; zero adds no new first-order direction, while larger values indicate greater complementarity.The bound follows from the per-element phases of an N-element array and the common-phase invariance of its magnitude spectrum.Source: B OBSERVABILITY FROM REFERENCE SPECTRA · pp. 18–19

Reference Complementarity

  • Reference utility depends on overlap between effective observable subspaces, not reference count alone.Different references can constrain overlapping scene directions, so the capacity bound is necessary but not sufficient.Source: B OBSERVABILITY FROM REFERENCE SPECTRA · p. 19

Scope

  • The analysis is local, noiseless, and first-order; its minimum reference budget is not a prediction of how many references a learned estimator needs for a target reconstruction accuracy.With measurement noise, a zero-marginal-rank reference may still improve statistical precision.Source: B OBSERVABILITY FROM REFERENCE SPECTRA · p. 19

C PROPAGATION-TO-SPECTRUM ERROR BOUND

This section characterizes how CoRF’s analytic renderer maps propagation-parameter errors to spatial-spectrum error, and describes optional measurement-based refinement of target-scene powers and receiver calibration. These adaptations keep the pretrained propagation model or predicted propagation parameters fixed and are reused for subsequent queries.

C PROPAGATION-TO-SPECTRUM ERROR BOUND

  • The rendered-spectrum error relative to the best representable spectrum is bounded by gmaxA4Em + 2gmaxA3LaEΩ, separating power and direction errors under fixed array sensitivities.Representation mismatch between the target and the best spectrum representable by the analytic renderer is captured separately by εphys.Source: C PROPAGATION-TO-SPECTRUM ERROR BOUND · pp. 19–21
  • The power-domain bound transfers directly to the normalized magnitude spectrum whenever both spectra have nonzero range.Source: C PROPAGATION-TO-SPECTRUM ERROR BOUND · p. 22
  • The bound is deterministic and worst-case, characterizes conversion of specified propagation errors rather than their estimation accuracy, and for planar arrays reflects ambiguity between directions with identical in-plane direction cosines.Source: C PROPAGATION-TO-SPECTRUM ERROR BOUND · pp. 21–22

D IMPLEMENTATION DETAILS

  • The appendix covers training objectives and hyperparameters, architecture, optional power refinement, receiver-array calibration, and the dataset.Source: D IMPLEMENTATION DETAILS · p. 22

D.1 TRAINING OBJECTIVES AND HYPERPARAMETERS

  • Training uses two stages: it pretrains and freezes the spectrum encoder and reference contextualizer, then trains the remaining propagation-field modules; each instance normally uses 32 references, excluding queries.Stage I uses supervised contrastive learning over scene identity; Stage II combines spectrum reconstruction, content-use, reference-separation, and uncertainty objectives.Source: §D.1 · pp. 22–23

D.2 MODEL ARCHITECTURE

  • The architecture uses an unordered-reference encoder and contextualizer, a 4,000-anchor canonical field, query and uncertainty heads, and an analytic receiver-array renderer.No positional encoding is applied to reference tokens, preserving permutation equivariance; the renderer constructs covariance and evaluates the Bartlett response.Source: §D.2 · pp. 24–25

D.3 TARGET-SCENE POWER REFINEMENT

  • Optional target-scene refinement corrects component powers using the same 32 reference measurements while freezing the pretrained propagation model and preserving anchor geometry and arrival directions.After a one-time fit, the correction is fixed and reused for target-scene queries; it is distinct from feed-forward conditioning.Source: §D.3 · pp. 25–26
  • In few-shot refinement, the same 32 references condition the field, 24 fit the residual model, and 8 select the checkpoint; no extra target-scene measurements are required.Refinement runs for up to 3,000 steps, with selection every 100 steps; the fitted residual model is fixed and reused for test queries.Source: §D.3 · p. 26
  • Per-scene refinement fits a residual model for up to 16,000 steps and can add a bounded exponential rescaling of explicit LOS power.The best validation-PSNR checkpoint is retained; the pretrained model remains frozen.Source: §D.3 · p. 26

D.4 RECEIVER ARRAY CALIBRATION

  • Receiver calibration changes only the analytic receiver response, using disjoint calibration measurements while keeping propagation predictions and the learned propagation field fixed.The calibrated response is reused for all queries collected with that receiver; the joint real-data protocol uses 32 conditioning and 64 calibration spectra, with test queries untouched.Source: §D.4 · pp. 26–28
  • Calibration models differ by receiver: simulated arrays fit orientation and two axis spacings, while real receivers fit per-element complex gain, position offsets, and angle-dependent response.For the 16-element real receiver, the model fits 1,120 scalar parameters in total.Source: §D.4 · p. 27

D.5 DATASET AND PREPROCESSING

The evaluation uses simulated indoor scenes and a real-measurement dataset, with shared preprocessing and sparse-reference protocols. Qualitative comparisons cover per-scene synthesis, unseen scene variants and categories, and reflection-dominated failures.

D.5 DATASET AND PREPROCESSING

  • 35 simulated scenes span seven categories with five variants each; real NeRF2 RFID measurements are reserved for simulation-to-real evaluation.The simulations share a generation pipeline and propagation regime, so category exclusion tests transfer within that distribution.Source: §D.5 · p. 28
  • Single-snapshot spectra are min-max normalized, while the analytic renderer's incoherent covariance sum approximates the coherent target construction.Scene geometry is isotropically rescaled to a canonical extent while preserving angular bearings and receiver orientation.Source: §D.5 · pp. 28–29

E ADDITIONAL EXPERIMENTAL RESULTS AND ANALYSES

  • Unseen-variant folds exclude one variant per category, unseen-category folds exclude all five variants of a category, and references come from training data while queries come from test data.The default reference budget is M = 32; simulated experiments share the same protocol, with within-fold PSNR standard deviation averaging 0.21 dB across three seeds.Source: §D.5 · p. 29, E ADDITIONAL EXPERIMENTAL RESULTS AND… · p. 29

E.1.1 PER-SCENE RESULTS

  • Across displayed per-scene examples, CoRFPR reaches 0.74–0.77 SSIM versus 0.51–0.58 for baselines, which often blur or misplace weaker multipath structure.Figure 4 compares ground truth, CoRFPR, and baselines across the evaluation settings.Source: §E.1.1 · p. 29, §E.1 · p. 29, Figure 4 · p. 30

E.1.2 UNSEEN SCENE VARIANTS

  • With M = 32 references, the strongest baseline reaches 0.29–0.38 SSIM across displayed unseen variants, while CoRFPR better preserves dominant and secondary lobe directions.Remaining CoRFPR errors mainly concern relative lobe strengths and the weakest components.Source: §E.1.2 · p. 29, Figure 4 · p. 30

E.1.3 UNSEEN SCENE CATEGORIES

  • When an entire category is held out, baselines reach 0.29–0.37 SSIM across displayed locations, while CoRFPR preserves dominant lobe directions.CoRFPR's remaining errors mainly concern relative lobe strengths.Source: Figure 4 · p. 30, §E.1.3 · p. 31

E.1.4 REFLECTION-DOMINATED FAILURE CASES

  • On 322 worst-tail queries with SSIM ≤0.50, CoRF predicts one or two broad lobes, and neither it nor the strongest baseline captures the full reflected structure.Across the ten displayed worst predictions, the strongest baseline scores 0.23–0.41 SSIM versus 0.16–0.26 for CoRF.Source: §E.1.4 · p. 31, Figure 5 · p. 31
  • Worst-tail errors are associated more with poorly matched reference spectra than with reference distance alone; narrow reflected arrivals tend to be smoothed into broader components.The best-matching reference has SSIM 0.52 for failure cases versus 0.69 otherwise, while nearest-reference distances are 0.76 versus 0.85 m.Source: §E.1.4 · p. 31

E.2.1 PER-SCENE RESULTS

The per-scene evaluation measures synthesis fidelity within each scene rather than cross-scene generalization. CoRFPR leads all scene-metric comparisons, while scene difficulty and variant-level variation are shared across methods.

E.2.1 PER-SCENE RESULTS

  • CoRFPR leads all 144 scene-metric comparisons, averaging gains of 2.02 dB PSNR and 0.073 SSIM and reducing AoA error by 1.07°.The per-scene averages reproduce Table 1 after rounding.Source: §E.2.1 · p. 32, Table 8 · p. 32
  • Per-scene SSIM correlates strongly between CoRFPR and each baseline (r = 0.93–0.98), with corridors among the hardest scenes and several bedrooms and classrooms among the easiest.These patterns suggest scene properties contribute substantially to performance variation across methods.Source: §E.2.1 · p. 32
  • Across categories, five-variant SSIM spreads of 0.09–0.16 are comparable to or larger than the average 0.073 gap between CoRFPR and the strongest baseline.The results motivate scene-level breakdowns rather than relying only on category averages.Source: §E.2.1 · p. 32

E.2.2 CROSS-SCENE VARIANT RESULTS

Scene-level breakdowns evaluate unseen variants with M = 32 target-scene references. CoRFPR's advantage persists across scenes, while sparse references substantially reduce baseline performance and source-scene transfer helps inconsistently.

E.2.2 CROSS-SCENE VARIANT RESULTS

  • Moving from full per-scene fitting to 32 target-scene references reduces baseline PSNR by 6.2–8.0 dB, while CoRFPR decreases by 1.34 dB, from 24.33 to 22.99 dB.For example, NeRF2 falls from 21.59 to 13.75 dB, GSRF from 20.41 to 12.40 dB, and WRF-GS from 22.01 to 15.85 dB.Source: §E.2.2 · pp. 32–33
  • CoRFPR's average PSNR gain is 7.13 dB over the strongest few-shot competitor and 8.72 dB over the strongest transfer competitor across 35 scenes.It leads on all 35 scenes against both baseline groups in these breakdowns.Source: §E.2.2 · pp. 32–33, Table 9 · p. 33, Table 10 · p. 33
  • Same-category source-scene adaptation helps GSRF by 0.29 dB on average, but NeRF2 loses 0.77 dB and WRF-GS loses 2.43 dB.NeRF2 improves on 9 scenes and WRF-GS on 4, while GSRF improves on 20.Source: §E.2.2 · p. 33
  • CoRFPR's unseen-variant SSIM decrease is largest for corridors (0.687 to 0.614) and smallest for lounges (0.805 to 0.779), with scene-level generalization gaps negatively correlated with per-scene SSIM (r = −0.64).Scenes that are difficult under per-scene fitting tend to lose more under unseen-scene inference with sparse references.Source: §E.2.2 · p. 34

E.2.3 CROSS-SCENE CATEGORY RESULTS

CoRFPR maintains a substantial advantage across the evaluated scene categories, while power refinement adds little accuracy beyond feed-forward CoRF. Predicted variance ranks query-level reliability, but it does not reliably localize errors within a spectrum.

E.2.3 CROSS-SCENE CATEGORY RESULTS

  • Excluding an entire category lowers CoRFPR’s unweighted scene-average SSIM from 0.750 to 0.743, a modest loss that varies by scene.The average PSNR and SSIM decreases are 0.14 dB and 0.007, respectively.Source: §E.2.3 · p. 35
  • CoRFPR exceeds GRaF in all four metrics in every category, while source-scene transfer shows no consistent advantage for same-category sources.With target references fixed, outside-category transfer changes PSNR by −0.02 dB for NeRF2, +0.07 dB for GSRF, and −0.70 dB for WRF-GS relative to within-category transfer.Source: §E.2.3 · p. 35
  • CoRFPR leads on all 35 scenes and all four metrics against both baseline families, across 280 scene-metric comparisons.The category-level SSIM margin over GRaF ranges from 0.18 on corridors to 0.41 on bedrooms, though absolute synthesis quality varies across scenes.Source: §E.2.3 · p. 35

E.2.4 POWER REFINEMENT

  • Joint power refinement changes PSNR by −0.03 dB on unseen variants and +0.01 dB on unseen categories; anchor-offset fitting gains 0.21 and 0.18 dB but takes 202 seconds.The query network overfits after about 50 optimization steps, and the selection gate rejects a fitted correction in 28 of 70 scene evaluations.Source: §E.2.4 · p. 35

E.3.1 FEED-FORWARD RELIABILITY

  • The lowest-variance 10% of 6,436 test queries achieve 0.889 SSIM and 0.017 NMSE, versus 0.553 SSIM and 0.326 NMSE for the highest-variance 10%.The separation also persists among queries whose ground-truth spectra have at least three lobes.Source: §E.3.1 · p. 36, Figure 6 · p. 36
  • Within-spectrum uncertainty localization is weak: predicted standard deviation and amplitude error have correlations of approximately −0.03, while 2σ coverage is about 0.93.The 1σ coverage is about 0.81, above the Gaussian reference of 0.68; the variance is more informative as a query-level reliability signal.Source: §E.3.1 · p. 36, Table 14 · p. 36

E.3.2 RELIABILITY AFTER POWER REFINEMENT

  • Carrying feed-forward variance alongside a power-refined mean nearly preserves Spearman correlation (0.603 to 0.599) and 1σ coverage (0.809 to 0.804).Recomputing variance at refined powers lowers correlation to 0.523; recalibration improves NLL but lowers 1σ coverage to 0.762 and raises cσ to 1.20.Source: §E.3.2 · pp. 36–37, Table 15 · p. 37

E.4 TOLERANCE TO ARRAY-PARAMETER ERROR

Receiver-geometry error degrades rendered spectra even with unchanged propagation estimates, while calibration recovers accuracy within the tested geometry family. CoRF-generated spectra also substantially improve downstream angular localization over baseline augmentation.

E.4 TOLERANCE TO ARRAY-PARAMETER ERROR

  • At the largest array perturbation, uncalibrated PSNR falls to 16.01 dB, while calibration keeps PSNR between 22.07 and 22.22 dB across the tested geometry range.The perturbations span up to 12° orientation error with +14% and −12% axis scaling; recovery is established for this modeled geometry family, not arbitrary receiver mismatch.Source: §E.4 · pp. 37–38
  • Calibration improves PSNR by 0.95 dB at the smallest nonzero perturbation and 6.06 dB at the largest, but changes it by −0.11 dB with exact geometry.With 8, 16, 32, and 64 calibration measurements, PSNR is 21.96, 22.03, 22.05, and 22.08 dB, respectively.Source: §E.4 · p. 38

E.5 CASE STUDY: ANGULAR LOCALIZATION WITH SYNTHESIZED SPATIAL SPECTRA

  • Augmenting 32 references with CoRF spectra reduces mean localization error from 28.27° to 4.11°, near the 3.05° obtained with the full ground-truth training set.The strongest baseline, NeRF2-FS, achieves 11.36°; CoRF also has the lowest mean error in each of the seven evaluated scenes.Source: §E.5 · pp. 38–39, Figure 7 · p. 39
  • With CoRF augmentation, 77% of test queries fall within 5° of the ground-truth direction, compared with 28%–35% for the baselines.Localization labels use true geometric directions, so synthesis errors affect training inputs rather than labels; across method–scene pairs, localization error correlates negatively with synthesis SSIM (Pearson r = −0.73).Source: §E.5 · p. 38

E.6 SIMULATION-TO-REAL TRANSFER STUDY

On measured scene S36, receiver calibration and power refinement improve transfer performance, while simulated-scene analyses probe reference dependence, budget, conditioning, and rendering choices. The results also identify limits: calibration and refinement cannot supply missing propagation components, and some diagnostics use narrow protocols.

E.6 SIMULATION-TO-REAL TRANSFER STUDY

  • On measured scene S36, CoRFPR,CAL leads in PSNR, SSIM, and NMSE, exceeding WRF-GS+ by 0.49 dB PSNR and 0.061 SSIM; combining calibration and refinement reaches 17.45 dB.The comparison uses a matched 96-spectrum budget; the larger 19.99 dB diagnostic additionally uses 612 validation spectra and does not establish that accuracy from metadata and 32 references alone.Source: §E.6 · pp. 39–40, Table 17 · p. 39

E.7.1 REFERENCE DEPENDENCE; E.7.3 REFERENCE-SET SAMPLING

  • Replacing target-scene references with the most damaging other-scene set reduces PSNR by 3.62 dB on unseen variants and 2.65 dB on unseen categories; random selections from the correct scene have much smaller fold-level variation.Across 100 reference sets, fold-averaged PSNR standard deviations are 0.026 dB and 0.037 dB; no set shifts fold-averaged PSNR by more than 0.12 dB from the original selection.Source: §E.7.1 · p. 40, Figure 8 · p. 41, §E.7.3 · p. 43

E.7.2 REFERENCE BUDGET

  • Average performance nearly saturates by M = 8, but small budgets are more selection-sensitive: at M = 1, the least favorable draw loses a median 2.4 dB on unseen variants and 2.1 dB on unseen categories.The least-favorable-draw loss falls to 0.53 dB and 0.30 dB at M = 8; M = 32 is substantially more robust, while additional references add little average benefit.Source: §E.7.2 · pp. 41–42, Table 18 · p. 41, Figure 9 · p. 42

E.7.4 LOCAL COVERAGE FOR GRAF

  • With budgets rising from M = 32 to M = 256, GRaF gains 4.24 dB PSNR while CoRF changes little; the PSNR gap narrows but remains 4.30 dB.This diagnostic uses one fold and one reference draw per budget, with test-selected GRaF neighbor count; unseen-category evaluation and spatially stratified GRaF references were not tested.Source: §E.7.4 · p. 44, Table 19 · p. 44

E.8.1 REFERENCE COORDINATES

  • On the tested folds, neither absolute- nor query-relative-coordinate conditioning gives a consistent accuracy gain over spectrum-only conditioning.Relative coordinates require rebuilding the conditioned field for each query, whereas absolute coordinates preserve once-per-scene conditioning.Source: §E.8.1 · p. 44

E.8.2 PRETRAINING OBJECTIVE

  • Supervised contrastive pretraining has the highest seed-0 PSNR and SSIM on both tested folds, but accuracy alone does not establish reference use.Seven of eight trained models respond to a changed reference set; the synthesis-loss-only model on the unseen-variant fold is exactly reference-blind despite 24.08 dB PSNR.Source: §E.8.2 · pp. 44–45, Table 20 · p. 44

E.8.3 SENSITIVITY TO ANCHOR RESOLUTION

  • The default K = 4000 anchor lattice achieves the highest PSNR (24.97 dB) and SSIM (0.794), with 0.083 NMSE; finer lattices cost more training time without improving accuracy.Training rises from 68 minutes at K = 4000 to 92 and 124 minutes at K = 6912 and 10976; substantially coarser lattices reduce PSNR by 0.30–0.45 dB.Source: §E.8.3 · p. 45, Figure 11 · p. 45

E.8.4 ORACLE RENDERER COMPARISON

  • The incoherent oracle is 0.38 dB below the coherent oracle in average PSNR, and feed-forward CoRF is another 0.66 dB below the incoherent oracle.For dense-multipath subsets, the incoherent-versus-coherent PSNR gap is 1.64 dB when the Ricean factor is below 0 dB and 1.74 dB when at least four paths lie within 10 dB of the strongest.Source: §E.8.4 · pp. 45–46, Table 21 · p. 46, Figure 12 · p. 46

E.9.1 DATA-COLLECTION EFFICIENCY

CoRF uses far fewer target-scene references than full-data per-scene fitting, while feed-forward deployment avoids scene-specific optimization. Its performance degrades as material properties shift, especially under the most severe tested shift.

E.9.1 DATA-COLLECTION EFFICIENCY

  • CoRF and CoRFPR use 32 target-scene references, approximately two orders of magnitude fewer measurements than the median 3376 used for full-data per-scene training.The reference-budget analysis reports that 32 references are already in the regime where additional references provide little improvement in average accuracy.Source: §E.9.1 · p. 46
  • Collecting 32 references is estimated at 5.3–32 minutes, compared with 9.4–56.3 hours for 3376 measurements; 64 separate calibration measurements add 10.7–64 minutes.These estimates assume 10 seconds to 1 minute of acquisition per location, and the reported protocol collects the calibration measurements for each scene.Source: §E.9.1 · p. 46
  • With 30 measurements, GSRF achieves 15.14 dB PSNR and 0.506 SSIM; with 2449 measurements, it comes within 0.44 dB PSNR and 0.014 SSIM of its full-data result.The full-data result on S36 is 21.98 dB PSNR and 0.814 SSIM.Source: §E.9.1 · p. 46

E.9.2 COMPUTATIONAL EFFICIENCY

  • Feed-forward CoRF conditions on 32 references in 10 ms; refinement takes 47–202 seconds, while feed-forward rendering takes about 8.5 ms per query.A complete CoRF test-scene map takes about 16–21 seconds end to end; GRaF takes about 48 minutes per map because neighbor retrieval and rendering take 2.9 seconds per query.Source: §E.9.2 · p. 47, Table 22 · p. 47

E.10 PHYSICAL DISTRIBUTION SHIFT

  • At the (2, 10) material-property shift, PSNR falls by 5.14 dB and AoA error rises from 8.49° to 21.66°; this is a stress test, not a typical deployment perturbation.Reducing material parameters yields small PSNR gains, while increasing them progressively degrades performance; the (1, 1) setting is the re-simulated control.Source: §E.10 · p. 47, Table 23 · p. 47
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