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SPARC: Sparse Path-Aware Residual Calibrator for Wireless Ray Tracing at Upper Mid-Band

Mingjun Ying, Guanyue Qian, Xinquan Wang, Xingchen Liu, Ishaan S. Gupte, Peijie Ma, Dipankar Shakya, Theodore S. Rappaport

arXiv:2609.06077v1eess.SP

TL;DR

Raw RT can have large per-path power errors in cluttered indoor environments, and the fixed-geometry material bound does not account for the observed bias. SPARC learns a sparse per-path residual correction from one completed RT simulation; it reduces RMSE in both measured indoor environments and also reports pooled and transmitter-held-out results.

  • Problem

    Reliable site-specific prediction in cluttered indoor environments requires calibration, while material perturbations alone cannot explain the observed per-path bias.

    Source: §I · pp. 1–2

  • Method

    SPARC learns a sparse linear per-path residual correction from matched paths and standard RT features produced by one completed simulation.

    Source: §I · p. 1

  • Results

    Per-path power RMSE falls from 18.74 to 4.74 dB in InF and from 23.12 to 5.39 dB in InH; pooled InF+InH training achieves 5.73 dB RMSE, and TX-location-held-out testing yields 4.99 dB in InF and 5.85 dB in InH.

    Source: §I · pp. 1–2

  • Takeaways & Limitations

    SPARC provides a post-processing calibration layer for site-specific per-path power prediction without ray-tracer modification or additional RT runs.

    Source: §VI · p. 6

Abstract

from arXiv · show

Accurate site-specific ray tracing (RT) is essential for upper mid-band network planning, yet raw RT can produce per-path multipath component (MPC) power errors on the order of 19--24~dB in cluttered indoor environments. A fixed-geometry material-sensitivity bound shows that a 30% relative-permittivity perturbation changes each surface interaction by at most 6.28~dB across the considered indoor materials. However, even MPCs with only one surface interaction exhibit a 19.2~dB mean RT--measurement bias, suggesting that missing clutter, displaced surfaces, and simplified 3D geometry dominate the per-path RT error. We propose SPARC (Sparse Path-Aware Residual Calibrator), a lightweight per-path calibration method that learns a sparse linear residual model from one completed RT simulation. SPARC uses standard RT features selected per fold by nested cross-validation, with ridge regularization and power-gated path matching; four features recur in both environments. Using measured indoor factory (InF) and indoor hotspot (InH) datasets at 6.75 and 16.95~GHz, SPARC reduces per-path power RMSE from 18.74 to 4.74~dB in InF and from 23.12 to 5.39~dB in InH. A jointly trained InF+InH model achieves 5.73~dB RMSE. When all links from one transmitter location are held out for testing, SPARC achieves 4.99~dB RMSE in InF and 5.85~dB RMSE in InH. SPARC therefore provides a practical post-processing calibration layer for site-specific per-path power prediction without ray-tracer modification or additional RT runs.

I. INTRODUCTION

Reliable site-specific prediction in cluttered indoor environments requires calibration because raw RT can have large power errors. SPARC learns a sparse per-path correction from one completed simulation, with results indicating that scene inaccuracies—not material perturbations alone—dominate the error.

I. INTRODUCTION

  • Prior calibration approaches often tune materials at link level and require repeated RT evaluations, whereas path-level attenuation based on scatterer size depends on object geometry rarely available in standard RT outputs.The passage also distinguishes scene-model error remedies and statistical channel models from calibration of individual traced-path power.Source: §I · p. 1
  • The paper asks whether path-level features from a completed RT simulation can correct per-path power error that material calibration may not address.It attributes the remaining gap to 3D scene inaccuracies that cause RT to trace incorrect paths.Source: §I · p. 1
  • Per-path power RMSE falls from 18.74 to 4.74 dB in InF and from 23.12 to 5.39 dB in InH with SPARC.The method learns a sparse correction from one completed RT simulation and requires no additional RT evaluations at deployment.Source: §I · p. 1
  • A ±30% relative-permittivity perturbation shifts each interaction by at most 1.91 dB for concrete, 1.68 dB for glass, 3.74 dB for plywood, and 6.28 dB for wood, while measured per-bounce bias exceeds 19 dB.The bound indicates that material calibration alone cannot close the observed gap.Source: §I · p. 2
  • A single SPARC model trained on pooled InF and InH measurements achieves 5.73 dB per-path power RMSE; holding out entire TX locations yields 4.99 dB (InF) and 5.85 dB (InH).Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model aligns RT paths with measured dominant MPCs on a band-limited delay grid, then formulates their power mismatch for calibration. Matching, power gating, and the distinction between material and scene-geometry error define the training data and residual target.

A. Wideband Channel and Measurement Model

  • The measurement model forms a band-limited PDP by convolving RT paths with a sinc(Bt) kernel at B = 1 GHz and summing them on the measurement delay grid.Calibration targets the integrated energy, in dBm, of each dominant matched MPC; RT and physical channels can contain different path sets.Source: A. Wideband Channel and Measurement… · p. 2

B. Indoor Measurement and Matched-Path Problem

  • The InF campaign covers three TX and twelve RX locations in a 36×22 m2 open-plan factory, while InH covers four TX and twenty RX locations in a 109×44 m2 multi-room office.The respective TX–RX separation ranges are 9–37 m and 11–97 m; measurements use sub-nanosecond PTP-based synchronization.Source: B. Indoor Measurement and Matched-Path… · p. 2
  • The Hungarian algorithm pairs RT paths with measured dominant peaks within a 10 ns delay tolerance, and power gates of 30 dB for InF and 38 dB for InH reject candidate matches.The wider InH gate reflects its larger TX–RX separation range; the gate cleans training data, while deployment applies SPARC to every RT path and raises RMSE by 0.4/1.0 dB in InF/InH as an upper bound.Source: B. Indoor Measurement and Matched-Path… · p. 2
  • The conceptual dB-domain error decomposition separates material effects on fixed paths from topology mismatch such as clutter omission or scene abstraction, plus peak-extraction and other unmodeled residuals.The material and geometry contributions are not separately identifiable; the exclusion argument only requires a bound on the material contribution along the RT-traced path.Source: B. Indoor Measurement and Matched-Path… · p. 2
  • Each matched path has an RT feature vector xℓ in R19 and belongs to a TX–RX–frequency group qℓ; the pooled dataset contains power-gated matched MPCs across links and both carrier frequencies.The decomposition’s material-error bound applies whether or not the RT path is physically realized.Source: B. Indoor Measurement and Matched-Path… · p. 2
  • Material-domain calibration perturbs the nominal material vector, while residual-space calibration learns a correction from path features that can absorb predictable errors, including scene-geometry errors.Material tuning can reduce error only along paths whose topology remains unchanged under perturbation.Source: B. Indoor Measurement and Matched-Path… · pp. 2–3

III. PROPOSED CALIBRATION METHOD

SPARC calibrates per-MPC power from matched pairs produced by one completed RT simulation, using sparse ridge regression. The method section follows a material-sensitivity bound establishing why a residual-space approach is needed.

III. PROPOSED CALIBRATION METHOD

  • SPARC takes matched MPC pairs from one completed RT simulation and outputs calibrated per-MPC power via sparse ridge regression.The described procedure is detailed in Algorithm 1.Source: §III · p. 3
  • The method establishes a material-sensitivity bound before applying residual-space calibration to address power error beyond material effects.The passage identifies this bound as the rationale for a residual-space approach.Source: §III · p. 3

A. Material-Correctable Bound Under Fixed Geometry

The fixed-geometry material bound is too small to explain the observed per-path RT–measurement bias, pointing to scene inaccuracies that alter traced paths. It applies only to material-dependent changes along an already traced path.

A. Material-Correctable Bound Under Fixed Geometry

  • Theorem 1 bounds material-driven power change on a fixed traced path by the sum of per-interaction sensitivity limits; path creation, blockage, rerouting, and interaction-order changes remain outside this bound.Its assumptions include twice-continuously differentiable interaction functions on compact convex admissible sets and bounded material perturbations.Source: A. Material-Correctable Bound Under… · p. 3
  • 19.2, 23.5, and 23.1 dB are the measured mean biases for single-, double-, and triple-bounce MPCs, while the three-bounce material-correctable ceiling is below 18.84 dB.The global per-interaction bound is 6.28 dB, attained for wood under ±30% relative-permittivity perturbation.Source: A. Material-Correctable Bound Under… · p. 3, Figure 1 · p. 4
  • Because material parameters change Fresnel loss along existing paths but cannot account for topology changes, the residual error is attributed predominantly to 3D scene inaccuracies.The proposed path-feature correction targets structured geometry-related error without rerunning RT.Source: A. Material-Correctable Bound Under… · p. 3

B. SPARC Calibrator

SPARC models the per-path correction as a sparse linear residual function of selected RT features. It chooses the feature subset and ridge strength using fold-specific cross-validation.

B. SPARC Calibrator

  • SPARC restricts the correction to a linear function of a standardized, selected feature vector, then estimates its weights by ridge regression.The feature vector is standardized using means and standard deviations from the training fold.Source: B. SPARC Calibrator · p. 4
  • Nineteen candidate path features are ranked by absolute ridge coefficients, and top-k subsets are evaluated using inner leave-one-group-out cross-validation.Candidates include RT power, bounce count, distance, delay, material indicators, and angular or interaction features.Source: B. SPARC Calibrator · p. 4
  • The procedure selects feature-subset size and ridge strength using inner-CV RMSE, with the ridge grid spanning 0.1 to 1000.The selected subset and penalty are refit for prediction on the held-out fold.Source: B. SPARC Calibrator · p. 4

IV. EXPERIMENTAL SETUP

The evaluation uses NYURay simulations and power-gated matches between dominant RT paths and measured peaks. Cross-validation and transfer tests assess prediction across links, frequencies, and environments.

IV. EXPERIMENTAL SETUP

  • NYURay simulations launch 200,000 rays per link with maximum depth 3, enable diffraction and refraction, and disable diffuse scattering.SPARC uses standard RT outputs that are also available from other commercial or open-source ray tracers.Source: §IV · p. 4
  • Power-gated dominant RT paths are matched to measured peaks, and RMSE in dB is the primary metric for integrated peak energy on a 1 GHz band-limited PDP.Leave-one-group-out folds hold out all matched MPCs from one TX–RX pair at one carrier frequency.Source: §IV · p. 4
  • The evaluation includes training-efficiency curves over 100 random link-level splits and cross-environment transfer without adaptation.Transfer trains on one environment’s matched paths and predicts the other environment.Source: §IV · p. 4
  • Five methods are compared: uncalibrated RT, material least squares, a global mean offset, gradient boosting, and SPARC.Gradient boosting and SPARC use the same power-gated matched MPC set, 19 features, and leave-one-group-out cross-validation.Source: §IV · p. 4

A. Main Calibration Comparison

SPARC achieves lower per-path RMSE than the listed calibration baselines in InF and InH. The section also reports reduced aggregate received-power error and illustrates calibration on a held-out InF pair.

A. Main Calibration Comparison

B. Feature Interpretation

Four standard RT features recur across InF and InH, with predicted power the most influential. Sparse feature selection offers interpretability and deployment benefits without a practical RMSE penalty relative to all-feature ridge.

B. Feature Interpretation

  • Predicted RT power is the most influential feature; frequency, TX–RX distance, and squared bounce count also recur in both environments.Nested CV retains 9–10 of 19 candidates per fold in InF and 6–8 in InH; weaker paths carry larger errors, and squared bounce count encodes per-bounce accumulation.Source: B. Feature Interpretation · p. 5
  • All-feature ridge yields 4.81 dB InF RMSE versus 4.74 dB for the sparse model, while inner CV never retains all 19 features.The four recurring features are standard RT outputs and need neither object-level geometry nor environment-specific labels.Source: B. Feature Interpretation · p. 5
  • Five linear estimators span only 0.13 dB RMSE, indicating that the linear regularizer choice is not critical.The reported comparison uses ridge, Lasso, elastic net, Bayesian ridge, and Huber estimators.Source: B. Feature Interpretation · p. 5

C. Cross-Environment Generalization

Joint InF+InH training achieves 5.73 dB overall RMSE, within 1 dB of per-environment performance. Direct transfer is less accurate, while leave-one-TX-out testing reports RMSE below 6 dB in both environments.

C. Cross-Environment Generalization

  • Joint InF+InH training yields 5.73 dB overall RMSE, with 5.48/6.08 dB in InF/InH, within 1 dB of per-environment performance.Per-environment SPARC achieves 4.74 dB in InF and 5.39 dB in InH.Source: C. Cross-Environment Generalization · p. 6
  • Direct transfer yields 8.80/9.59 dB RMSE for InH→InF/InF→InH, while joint training recovers most of the gap.The reported comparison indicates environment-specific residual structure.Source: C. Cross-Environment Generalization · p. 6
  • Leave-one-TX-out testing yields 4.99/5.85 dB RMSE in InF/InH, and 7–8 training pairs achieve within 1 dB of full-data performance.Table III summarizes cross-environment validation at 6.75 and 16.95 GHz.Source: C. Cross-Environment Generalization · pp. 5–6, Table III · p. 5

VI. CONCLUSION

The conclusion presents SPARC as sparse per-path calibration from one completed RT run and identifies 3D scene inaccuracies as the dominant error source. It reports lower per-path RMSE in both measured environments and performance on held-out transmitter locations.

VI. CONCLUSION

  • SPARC reduces per-path RMSE from 18.74 to 4.74 dB in InF and from 23.12 to 5.39 dB in InH.It surpasses gradient boosting by 1.18 and 0.47 dB, respectively.Source: §VI · p. 6
  • The material-sensitivity bound places ±30% material perturbations below 2 dB per structural interaction, while measured per-bounce bias exceeds 19 dB.The conclusion identifies 3D scene inaccuracies as the dominant RT error source.Source: §VI · p. 6
  • Joint training yields 5.73 dB RMSE and leave-one-TX-out validation yields 4.99/5.85 dB in InF/InH.The sparse feature subset comes from one completed RT run, uses standard RT outputs, and requires no ray-tracer modification.Source: §VI · p. 6
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