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Site-specific Channel Modeling Based on Remote-Sensing Maps for 6G Space--Air--Ground Digital Twins

Peijie Liu, Pan Tang, Jianhua Zhang, Lei Tian, Bin Ao, Boyang He, Hao Zheng

arXiv:2608.30168v1eess.SP

TL;DR

Wide-area site-specific RT modeling is constrained by difficult-to-obtain 3D maps and missing local, time-varying multipath. The paper proposes RS-ART, which combines remote-sensing-based scene construction, measurement-derived statistics, and RT multipath augmentation. In 4.60 GHz UAV validation, it improves agreement with measured path loss, delay-spread, and Doppler-spread statistics.

  • Problem

    Complete 3D maps are difficult to obtain over wide areas, while 3D RT scenes may omit local and time-varying objects that contribute measurable multipath.

  • Method

    RS-ART combines deterministic RT from satellite remote-sensing imagery, measurement-derived channel statistics, and RT augmentation with additional short-delay LoS-tail paths and power reallocation.

  • Results

    Path loss RMSE decreases from 5.45 to 4.35 dB, while RMS delay spread and normalized Doppler spread RMSEs decrease by 53.03% and 26.48%, respectively.

  • Takeaways & Limitations

    The framework provides a site-specific channel modeling approach for 6G space–air–ground digital-twin studies while reducing dependence on pre-existing 3D maps.

Abstract

from arXiv · show

Site-specific channel models are essential for wireless digital twins of 6G space--air--ground communication systems. However, 3D maps are difficult to obtain over wide areas, which limits large-area site-specific channel modeling. To address this issue, this paper proposes a remote-sensing-based augmented ray-tracing channel modeling framework. The framework comprises a deterministic RT branch, a measurement-statistical branch, and an RT augmentation branch. To overcome the difficulty of acquiring large-area 3D maps, the deterministic RT branch reconstructs a 3D RT scene from satellite remote-sensing imagery and calibrates its electromagnetic material parameters using measured path loss. To provide the statistical parameters required for RT augmentation, the measurement-statistical branch establishes the marginal distributions and interparameter dependence models of the channel parameters. Specifically, a wideband UAV channel measurement campaign is conducted at 4.60 GHz, and a proposed multipath estimation method estimates the complex amplitudes, delays, and Doppler shifts of the measured multipath. To bridge the gap between RT predictions and measurements, the RT augmentation branch organizes the RT multipath into LoS, LoS-tail, and NLoS components, generates additional short-delay LoS-tail paths, and reallocates the component and path powers according to the measurement-derived statistics while preserving the total RT received power. The validation results show that the proposed framework reduces the path loss RMSE from 5.45 to 4.35 dB and, relative to calibrated RT, decreases the RMS delay spread and normalized Doppler spread RMSEs by 53.03 and 26.48, respectively. The proposed framework provides a site-specific channel modeling approach for 6G space--air--ground digital-twin studies.

I. INTRODUCTION

The paper addresses wide-area site-specific RT modeling when complete 3D maps are difficult to obtain and RT scenes omit local, time-varying multipath. It proposes RS-ART, combining remote-sensing-based RT, measurement-derived statistics, and RT augmentation, and reports improved agreement with measured channel statistics.

  • Motivation: Complete 3D map inputs are difficult to obtain over wide areas, limiting large-area site-specific RT modeling.Existing sources may require geographic databases, height estimation, dedicated surveying, or local data acquisition.
  • Framework: RS-ART constructs a 3D RT scene from satellite remote-sensing imagery, calibrates electromagnetic material parameters, and incorporates measurement-derived channel statistics.Its three branches are deterministic RT, measurement-statistical, and RT augmentation.
  • Measurement-statistical branch: The multipath extraction method jointly estimates measured path amplitudes, delays, and Doppler shifts for subsequent statistical modeling.The extracted paths support models of path counts, component power ratios, RMS delay spreads, and normalized Doppler spreads.
  • RT augmentation branch: RT augmentation generates additional short-delay LoS-tail paths and reallocates component and path powers according to measured statistics.The framework retains RT-resolved propagation information while supplementing multipath not represented by the RT scene.
  • Validation: The 4.60 GHz UAV validation reduces path loss RMSE from 5.45 to 4.35 dB and decreases RMS delay spread and normalized Doppler spread RMSEs by 53.03% and 26.48%.Validation uses position-matched RT results and measured channels.
  • Channel composition: The channel composition uses LoS, LoS-tail, and NLoS components, with LoS links containing all three and NLoS links retaining only the NLoS channel.The direct path supplies the LoS reference delay and Doppler, while LoS-tail paths include RT-resolved and statistically generated parts.

III. CHANNEL MEASUREMENT AND PARAMETER EXTRACTION METHOD

The measurement campaign uses a moving airborne transmitter and fixed ground receiver to form calibration-referenced delay–Doppler channel observations. Correlation and two-dimensional DFT processing account for calibration response, delay resolution, finite slow-time sampling, and Doppler leakage.

  • Measurement system and campaign: The campaign uses a fixed ground receiver and a UAV-mounted transmitter moving at approximately 150 m altitude, with RTK-based position matching.The airborne and ground RTK systems record positions at 10 Hz, and measurement frames are aligned to timestamps.
  • Measurement principle: A slow-time DFT converts correlation-derived delay profiles into a calibration-referenced two-dimensional delay–Doppler channel response.Each column of the correlation output is a delay profile for one retained snapshot.
  • Measurement principle: The sounder transmits a periodically repeated BPSK PN probing waveform, and each CIR is obtained by correlating received IQ snapshots with a direct-connected calibration reference.The calibration reference is applied to every retained snapshot.
  • Measurement principle: The measured delay–Doppler response is convolved with the calibration pulse along delay and corrupted by measurement noise.The calibration pulse is subsequently included in the multipath dictionary.
  • Measurement principle: Finite slow-time observation and off-grid Doppler shifts spread a path across multiple Doppler bins, while the calibration response broadens it in delay.These effects produce Doppler-domain spectral leakage and delay-domain broadening in the measured response.

C. Proposed Multipath Extraction Method

The proposed extraction method detects candidate delay–Doppler bins and refines them into continuous multipath parameters using sparse matching pursuit. It estimates complex coefficients, delays, and Doppler shifts while retaining paths that exceed a power threshold.

  • Coarse candidate detection: CA-CFAR detection, local-maximum testing, and Doppler-support masking identify candidate delay–Doppler bins from the measured power map.The detector uses a target false-alarm probability of 10^-5 and initializes candidates in physical delay–Doppler coordinates.
  • Parameter representation: The extracted path representation contains complex coefficient, propagation delay, and Doppler shift, distinguishing measured parameters from RT parameters.The actual retained path count satisfies N_est ≤ N_max, with N_max = 60 in the implementation.
  • Sparse refinement: OMP refines each candidate on a local two-dimensional grid and re-estimates selected complex coefficients by regularized least squares.The atom model incorporates calibration-pulse delay response and off-grid Doppler leakage.
  • Validation: At 15 dB SNR, synthetic validation identifies most high-power components, while weak and off-grid paths remain more difficult to estimate.The test uses 15 off-grid paths within τ ≤ 1.5 µs and |ν| ≤ 300 Hz.
  • Validation: For measured frames, sparse reconstruction captures isolated high-power peaks, while background energy and diffuse structures remain in the residual.Because measured multipath is dense, the finite extracted set does not represent every component.

IV. DETERMINISTIC RT BRANCH

The deterministic RT branch reconstructs a 3D scene from satellite imagery without explicit heights by combining tiled monocular depth estimation, alignment, metric scaling, and object regularization. The resulting mesh is exported for Sionna RT.

  • Remote-Sensing-Based 3D Reconstruction: Satellite imagery with 0.50 m ground sampling lacks explicit heights, so tiled monocular depth estimation produces a relative depth map.Overlapping tiles avoid resizing the full scene into one low-resolution model input.
  • Remote-Sensing-Based 3D Reconstruction: Tile predictions are tilt-corrected, scale-aligned to a full-map reference, and fused through overlap-based cosine-weighted averaging.Shared building regions provide the common scale needed to reduce tile-boundary discontinuities.
  • Remote-Sensing-Based 3D Reconstruction: Relative depth is converted to metric height by setting the maximum building height to H_max = 120.00 m and zeroing heights below 5.00 m.Connected components with footprint area below A_min = 50.00 m^2 are removed before mesh construction.
  • Remote-Sensing-Based 3D Reconstruction: Component-wise regularization separates adjacent buildings, clips wall transitions, and flattens rounded monocular-depth roofs into planar RT surfaces.Each retained component is preserved as an independent object in the reconstructed scene.
  • Remote-Sensing-Based 3D Reconstruction: The processed height map becomes a triangular mesh, whose objects and ground plane are exported through Blender and converted to Sionna RT XML.Initial material names are assigned before conversion with the Mitsuba Blender plugin.

B. RT Path Classification

The RT path-classification scheme partitions simulated paths into LoS, RT-resolved LoS-tail, and residual-NLoS components using LoS labels and excess-delay thresholds. It constructs the LoS-related components only when a direct LoS path exists.

  • RT Path Classification: The RT output represents each path by coefficient, delay, Doppler shift, and a LoS indicator derived from its interaction count.The indicator distinguishes direct LoS from paths involving interactions.
  • RT Path Classification: The total RT received power is formed from the powers of all N_RT paths, while component assignments organize those paths for subsequent augmentation.The RT path power is determined by the squared magnitude of its complex coefficient.
  • RT Path Classification: For LoS links, non-LoS paths with 0 < Δτ_i ≤ τ_T are classified as RT-resolved tail candidates, while later paths enter residual NLoS.The threshold τ_T is used only for links containing an RT LoS path.
  • RT Path Classification: If no RT path is labeled LoS, the LoS and LoS-tail components are not constructed for that link.The classification therefore falls back to non-LoS paths without a direct-path reference delay.
  • RT Path Classification: The three path groups are the direct LoS component, RT-resolved LoS-tail component, and NLoS component.The direct LoS component contains only the direct RT path when one is present.

C. RT Electromagnetic Parameter Calibration

The electromagnetic calibration branch optimizes object-level relative permittivity and conductivity against measured path loss while keeping scene geometry and link configurations fixed. Calibration improves overall agreement, especially for NLoS links.

  • RT Electromagnetic Parameter Calibration: Calibration minimizes the error between measured and Sionna RT path losses by optimizing each reconstructed object’s relative permittivity and conductivity.Scene geometry, ground-receiver position, antenna configuration, and measured transmitter positions remain fixed.
  • RT Electromagnetic Parameter Calibration: The differentiable RT solver back-propagates the calibration loss through mini-batches, and Adam runs for 200 iterations with learning rate 0.04.The material state with the lowest calibration-link RMSE is retained.
  • RT Electromagnetic Parameter Calibration: 1.10 dB: overall path loss RMSE decreases from 5.45 dB to 4.35 dB, a 20.18% reduction after calibration.The same total path loss definition is used for RT-LoS and RT-NLoS links.
  • RT Electromagnetic Parameter Calibration: 2.78 dB: NLoS path loss RMSE decreases from 5.91 dB to 3.13 dB, whereas the LoS reduction is 0.05 dB, from 4.10 dB to 4.05 dB.The direct zero-interaction path does not depend on reconstructed-object parameters, limiting calibration’s LoS effect.
  • RT Electromagnetic Parameter Calibration: Calibrated relative permittivities range from approximately 1.60 to 8.00 and conductivities from approximately 0.04 to 0.33 S/m.These are effective object-level parameters because reconstructed objects may combine walls, windows, and roofs.

A. Marginal Distributions of LoS-Link Parameters

The measurement-statistical branch extracts LoS-tail, residual-NLoS, and NLoS channel statistics, fits marginal distributions, and evaluates their agreement with measured histograms.

  • Measurement-derived statistics: LoS-tail statistics comprise tail power ratio, RMS delay spread, normalized Doppler spread, and detectable path count.The path count reflects the extraction configuration with Nmax = 60 and a 40.00 dB relative-power threshold.
  • Marginal fits: The fitted LoS-tail models use Beta, Weibull, and zero-truncated negative binomial distributions for their respective parameters.ηT uses Beta parameters α = 2.16 and β = 5.90; στ,T and κν,T use Weibull scale–shape pairs (18.81 ns, 1.72) and (0.02, 1.79), while NT uses rNB = 5.57 and pNB = 0.26.
  • Marginal fits: The LoS-tail fitted modes are approximately 0.20 for ηT, 10 ns for στ,T, 0.01 for κν,T, and 13 paths for NT.The NT mode differs from the largest measured histogram bars, which occur at approximately 17–18 paths.
  • Marginal fits: Residual-NLoS parameters use a Beta model for ξN and Weibull models for στ,N and κν,N, with fitted modes near 0, 85 ns, and 0.03.The fitted curves differ mainly in the first ξN bins and at the largest measured spread values.
  • Marginal fits: NLoS-link RMS delay spread and normalized Doppler spread follow Weibull distributions with scale–shape pairs (139.99 ns, 3.32) and (0.05, 2.73).Their fitted modes are 125.69 ns and 0.04, respectively, and the models are used for RT-NLoS spread sampling.

C. Gaussian Copula Dependence Modeling

The paper models dependence among channel-statistics parameters with Gaussian copulas after fitting their marginal distributions, revealing stronger associations in LoS-tail parameters than in residual-NLoS parameters.

  • Copula construction: Gaussian copulas model dependence within the LoS-tail, residual-NLoS, and NLoS-link parameter vectors.Measured parameters are transformed through fitted marginal CDFs, correlations are estimated in the Gaussian domain, and inverse CDFs recover sampled parameters.
  • LoS-tail dependence: The LoS-tail delay and Doppler spreads have correlation coefficient 0.51, while NT correlates with ηT, στ,T, and κν,T by 0.37, 0.49, and 0.22.Pairs involving ηT with στ,T or κν,T are omitted from the figure because their absolute coefficients are 0.01 and 0.09.
  • Residual-NLoS dependence: Residual-NLoS coefficient magnitudes remain below 0.20, with ξN–στ,N at −0.15 and κν,N correlations of 0.12 and 0.18.Neither measured nor generated samples show a clear linear trend for these pairs.
  • NLoS-link dependence: The NLoS-link RMS delay spread and normalized Doppler spread have coefficient 0.29, producing a weak positive trend in measured and generated samples.Generated points are sampled independently rather than paired with measurements at the same frame index.

A. NLoS Power Reallocation

The NLoS power-reallocation method reshapes retained RT paths to measurement-derived component statistics while preserving RT path locations, phases, and total received power.

  • Power reallocation: NLoS power reallocation retains RT path delays, Doppler shifts, and phases while adapting powers to sampled component statistics.For RT-LoS links it operates outside the LoS-tail delay region; for RT-NLoS links the NLoS component is the full channel.
  • Power allocation: The NLoS component receives state-dependent power, while total RT received power remains preserved.RT-NLoS links have no LoS-related power split; RT-LoS remaining power is divided between LoS and LoS-tail components.
  • Power optimization: The reallocation operator produces nonnegative powers summing to PN and approaches specified RMS delay and Doppler spreads without changing path locations or phases.The target spreads are residual-NLoS spreads for RT-LoS links and NLoS spreads for RT-NLoS links.
  • LoS-tail component: The LoS-tail model generates short-delay paths relative to the RT LoS path, with exponential excess-delay decay and random within-tail power variation.Generated Doppler samples are restricted to [−fmax, fmax], and the excess-delay region is bounded by τT.
  • LoS-tail component: The LoS-tail operator preserves RT-resolved tail paths, adds paths when NT exceeds their count, and reallocates combined powers toward sampled spreads.The realized count is max{NT, NT,RT}, so existing RT paths are not removed.

C. Channel Realization and Power Optimization

Channel realization samples measurement-derived parameters, allocates component powers, optimizes retained and generated path powers, and synthesizes channels while preserving RT structure and total power.

  • Channel realization: The realization flow samples statistical parameters, allocates component powers, generates required LoS-tail paths, optimizes powers, and synthesizes the channel.These stages are applied to RT-LoS and RT-NLoS links according to their available components.
  • NLoS power optimization: NLoS power optimization shapes retained RT powers toward state-dependent delay and Doppler targets while preserving RT locations and phases.If fewer than two paths are available, calibrated RT powers are normalized without spread adjustment.
  • LoS-tail generation: LoS-tail generation rescales the LoS component, retains RT-resolved tail paths, and adds Ngen sampled paths before joint power optimization.The combined support consists of RT-resolved and generated tail paths.
  • Validation realization: RS-ART retains RT-resolved paths, adds short-delay paths when required by NT, and adjusts component and path powers using sampled ratios and spreads.The measurement contains more paths and multipath power in the LoS-tail delay region than calibrated RT in the illustrated realization.
  • Evaluation design: The evaluation uses 1079 position-matched links; CDFs use one realization per link, whereas reported spread RMSEs average 20 independent realizations.These evaluation procedures compare route-level distributions with location-matched averages differently.

D. Validation for RT-LoS Links

For RT-LoS links, RS-ART generally moves component and channel statistics toward measurements, while aggregated CDFs and position-matched errors require separate interpretation.

  • LoS-tail statistics: RS-ART moves the LoS-tail median toward measurements: ηT changes from 0.01 to 0.19 versus measured 0.26, while στ,T changes from 2 to 13 ns versus 17 ns.The normalized Doppler spread median matches at 0.014, and the path-count median changes from 4 to 13 versus 17 measured paths.
  • LoS-tail statistics: For all four LoS-tail statistics, RS-ART is closer to the measured CDF than calibrated RT over the middle probability range.The remaining median differences are 0.07 for tail power ratio, 4 ns for RMS delay spread, and 4 paths for path count.
  • Residual-NLoS statistics: RS-ART matches the measured residual-NLoS ξN median at 0.06, while κν,N moves from 0.02 with calibrated RT to 0.05 versus 0.06 measured.The residual-NLoS delay-spread CDF lies between measured and fitted curves over approximately 50–200 ns, but differences remain above 200 ns and κν,N > 0.20.
  • Channel-level validation: Position-matched RS-ART reduces RMS delay spread RMSE from 87.64 ns to 42.76 ns and normalized Doppler spread RMSE from 0.0879 to 0.0682.The aggregated Doppler CDF can favor calibrated RT over part of the probability range, because it pools positions and uses one random realization per position.

E. Validation for RT-NLoS Links

For RT-NLoS links, joint power optimization improves position-matched spread errors while retaining the RT-predicted delay and Doppler locations; the section also situates these results within the overall validation.

  • RT-NLoS validation: 56.14%: RS-ART reduces RT-NLoS RMS delay spread RMSE from 126.31 ns to 55.40 ns.The normalized Doppler spread RMSE decreases from 0.0657 to 0.0267, a 59.38% reduction.
  • RT-NLoS validation: In RT-NLoS validation, all retained path powers are optimized jointly, while RT delay and Doppler locations remain unchanged.The NLoS component represents the full channel for RT-NLoS links.
  • Overall validation: RS-ART reduces the overall position-matched RMS delay spread RMSE from 97.85 to 45.96 ns and normalized Doppler spread RMSE from 0.0833 to 0.0612.These correspond to reductions of 53.03% and 26.48%, respectively.
  • Overall validation: Electromagnetic calibration reduces path loss RMSE from 5.45 to 4.35 dB across matched links.The summary separates path-loss calibration from RS-ART spread validation across all matched, RT-LoS, and RT-NLoS links.
  • Framework scope: RS-ART combines remote-sensing-based scene construction with measurement-derived statistics to address incomplete 3D maps and missing local, time-varying multipath.The framework supplements RT-LoS links with generated LoS-tail paths and adjusts path powers for both RT-LoS and RT-NLoS links.
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