Source-linked AI summary
Path-Specific Geometric-Stochastic Channel Model for Scattering from ISAC Targets: A Unified Measurement-Based Characterization of Robots, Humans, and Automobiles at 28 GHz
Neeraj Varshney, Jelena Senic, Jack Chuang, Samuel Berweger, Steve Blandino, Jian Wang, Camillo Gentile, Nada Golmie
TL;DR
ISAC channel models often lack measurement-resolved path geometry across target classes, limiting path-specific characterization. This paper combines a unified 28 GHz campaign with a geometry-anchored stochastic model, and synthesized realizations closely match measured pathloss evolution and fluctuations.
Problem
Existing target-scattering models often use assumed target representations or aggregate RCS and channel metrics rather than measurement-resolved, path-specific geometry.
Source: §I · p. 2Method
The paper measures nine targets at 28 GHz and builds a path-specific geometric–stochastic model that maps extracted paths to incident points and associated RCS.
Source: §I · p. 2Results
Synthesized realizations closely agree with measured pathloss evolution under dynamic motion and reproduce large-scale trends and path-level fluctuations.
Source: §VII · p. 14Takeaways & Limitations
The resulting measurement-tuned, geometry-driven representation is compatible with communication-oriented abstractions and suited to ISAC network simulation and evaluation.
Source: §VII · p. 14
Abstract
from arXiv · showhide
This paper develops a channel model for scattering from a broad class of integrated sensing and communication (ISAC) targets-robots, humans, and automobiles-based on a unified measurement campaign at 28~GHz. Nine targets are characterized from numerous transmitter--receiver configurations per target, spanning full bistatic and aspect angles and thus covering backward to forward scattering. Repeated acquisitions are collected for each configuration to capture target motion and dynamics, yielding nearly 117\,000 acquisitions in total. Measurements are collected with a 2~GHz-wide channel sounder equipped with a 256-element phased-array antenna, followed by digital beamforming and super-resolution processing for reliable extraction of multiple paths in delay and 2D angle, with average estimation errors of 0.1~ns and 0.2$^\circ$ respectively. From these measurements, we reduce a \emph{path-specific} channel representation in which the scattering is modeled as a cluster of paths whose center is defined by the bistatic specular \emph{geometry}; the cluster shape is described \emph{stochastically}. To ensure physically grounded spatio--temporal consistency, extracted paths are mapped to incident points on the target, each with an associated radar cross section (RCS) that is compatible with the 3GPP TR~38.901 ISAC channel model, and are subsequently mapped back to path properties for channel synthesis. The resulting statistical distributions are well behaved, physically interpretable, and consistent across targets, geometries, and motion. Comparison between measured and synthesized channel realizations demonstrates close agreement in pathloss trends and fluctuation behavior. Together, these results yield a high-fidelity, measurement-derived channel representation suitable for ISAC simulation, target modeling, and system design.
I. INTRODUCTION
The paper addresses the lack of unified, path-resolved target-scattering models by pairing a 28 GHz multi-target measurement campaign with a geometry-anchored stochastic channel model. Its measurements support path extraction and incident-point characterization across target classes, geometries, and motion.
I. INTRODUCTION
- ISAC sensing needs target-dependent scattering information that captures how multipath structure changes with target motion, orientation, and structure.The introduction connects this need to detection, identification, classification, and tracking.Source: §I · p. 1
- Prior RCS studies use varied platforms and procedures, while scalar RCS distributions do not represent resolvable paths or their spatial consistency.Existing structured and channel models also commonly validate aggregate power or rely on assumed target representations rather than measurement-resolved paths.Source: §I · pp. 1–2
- The proposed model organizes scattering into path clusters anchored at the specular reflection point and describes cluster shape stochastically.Extracted paths are mapped to target incident points for spatial–temporal consistency and incident-point-specific RCS characterization.Source: §I · p. 2, 2) Super-resolution path extraction · p. 2
II. MEASUREMENT CAMPAIGN
- The unified campaign measures nine robot, human, and automobile targets at 28 GHz across numerous TX–RX configurations and repeated acquisitions.Configurations span bistatic and aspect angles, and repeated measurements capture target motion and dynamics, yielding nearly 117 000 acquisitions.Source: §I · p. 2, §II · pp. 2, 4
2) Super-resolution path extraction:
- A 256-element phased-array receiver, digital beamforming, and super-resolution processing recover multiple paths with average errors of 0.1 ns in delay and 0.2° in angle.The approach is designed to extract paths even from compact targets such as UAVs and robotic arms.Source: 2) Super-resolution path extraction · p. 2
II. MEASUREMENT CAMPAIGN
- The campaign varies aspect angle ϕ and bistatic angle β through different TX–RX arrangements for mobile targets and stationary automobiles.For robots and humans, the RX remains fixed while the TX moves; for automobiles, the RX moves while the TX scans a semicircle.Source: §II · pp. 3–4
III. MEASUREMENT SYSTEM
The measurement system uses a 28 GHz bistatic sounder and processes phase-coherent array measurements into paths resolved jointly in delay and two-dimensional angle. Digital beamforming and SAGE super-resolution support extraction of multiple paths.
A. 28 GHz Channel Sounder
- The NIST receiver combines four stacked 8 × 8 phased-array boards into a 256-element aperture for enhanced angular resolution.The transmitter and receiver operate as independent platforms for flexible bistatic configurations.Source: A. 28 GHz Channel Sounder · p. 4
III. MEASUREMENT SYSTEM
- The geometric framework maps measured paths to target incident points and defines the cluster center where the bistatic specular axis intersects a canonical ellipsoid.The figure also illustrates incident points distributed conically around that axis.Source: Figure 3 · p. 5
A. 28 GHz Channel Sounder
- A 2 GHz probing signal produces calibrated, phase-coherent channel impulse responses across the receiver array.The probe is centered at 28.5 GHz, and CIR calibration achieves at least 55 dB delay-domain sidelobe suppression.Source: A. 28 GHz Channel Sounder · p. 5
B. Path Extraction
- Calibrated digital weights beamform measurements from all 256 elements in post-processing, correcting array non-idealities and synthesizing beams without increasing sweep time.The digitally synthesized beams achieve at least 18 dB angular-domain sidelobe suppression.Source: B. Path Extraction · p. 5
- SAGE extracts propagation paths jointly in delay and 2D angle, improving delay and angle resolution by more than a factor of five.Controlled validation reports average estimation errors of 0.1 ns in delay and 0.2° in angle of arrival.Source: B. Path Extraction · p. 5
C. Path-to–Incident-Point Mapping
The mapping procedure converts measured paths into target-surface incident points and associated bistatic RCS values. It uses bistatic geometry and filters mapped points against the target bounds.
C. Path-to–Incident-Point Mapping
- Each extracted path is represented by a target-surface incident point and intrinsic bistatic RCS, with measured phase retained for later scattering calculations.These quantities provide the scattering primitives used in subsequent model sections.Source: C. Path-to–Incident-Point Mapping · pp. 5–6
- The bistatic range surface–line construction uses measured delay and the TX, RX, and incident-point geometry to solve for the path’s target location.The incident point lies along the RX-side ray, and the measured delay constrains total TX–point–RX path length.Source: C. Path-to–Incident-Point Mapping · pp. 5–6
- The mapping is valid for first-order target interactions, and 3D gating retains only paths whose mapped points lie within target bounds.Paths from surrounding objects map outside the known target volume and are filtered.Source: C. Path-to–Incident-Point Mapping · p. 6
- Incident-point RCS is obtained from the calibrated bistatic radar equation, with absolute scaling established through metal-sphere calibration.The path phase is retained to enable coherent computation of composite RCS.Source: C. Path-to–Incident-Point Mapping · p. 6
- For one van acquisition, eight mapped paths span multiple surface features, while the strongest lies near the bistatic-specular scattering location.Marker color in the visualization represents estimated RCS.Source: C. Path-to–Incident-Point Mapping · p. 6, Figure 4 · p. 6
IV. CHANNEL MODEL: GEOMETRY
The geometry model anchors each target’s path cluster at the bistatic specular point and describes its shape stochastically through path count and distance offset.
A. Cluster Center
- The cluster center is the surface point satisfying bistatic specular geometry, referenced on a canonical ellipsoid whose simplifications are absorbed by the stochastic model.The measurements show the strongest path most often originates at the bistatic specular location.Source: A. Cluster Center · p. 6, §IV · p. 6
B. Path Count
- Across targets, per-acquisition path counts fit a Poisson distribution with target-dependent mean λ, supported by KS goodness-of-fit testing.Representative empirical distributions and fits appear in Fig. 5.Source: B. Path Count · p. 7
C. Distance Offset
- The distance offset is the radial deviation of an incident point from the cluster center and follows a target-dependent Gamma distribution.The same aggregation and KS-testing procedure is used for this and subsequent statistical characterizations; representative fits appear in Fig. 6.Source: C. Distance Offset · p. 7, B. Path Count · p. 7
D. Angle Offset
The angle offsets describe incident-point orientation around the specular axis: elevation is forward-weighted, while azimuth is approximately uniform.
D. Angle Offset
- The incident-point vector’s orientation relative to the specular axis is expressed through elevation-like and azimuthal offsets; azimuth selects a point on the conical surface.Zero elevation offset means alignment with the specular axis, with larger values indicating greater deviation.Source: D. Angle Offset · p. 7
- Elevation offsets are strongly forward-weighted, peaking at 0° and decaying monotonically with increasing angle.The fitted decay rates are summarized in Table II and illustrated in Fig. 7.Source: D. Angle Offset · p. 7
- Azimuthal offsets are approximately uniform over [0°, 360°), as shown empirically in Fig. 8..Source: D. Angle Offset · p. 7
E. Parameter Analysis
Across nine targets, the fitted geometry parameters show patterns associated with target size, curvature, surface composition, and geometric complexity.
E. Parameter Analysis
- Fitted geometry parameters reveal cross-target patterns associated with size, curvature, surface composition, and geometric complexity.The representative distributions include path count, distance offset, elevation offset, and azimuth offset.Source: E. Parameter Analysis · p. 7, Figure 5 · p. 8, Figure 6 · p. 8
- Path counts generally rise with human and automobile size, while the compact robotic arm produces more paths than size alone predicts.Its metallic, articulated, multifaceted structure introduces additional sub-specular scattering mechanisms.Source: E. Parameter Analysis · p. 7, Figure 5 · p. 8
- Larger targets produce wider distance-offset spreads; compact targets have tighter distributions, with the robotic arm exceeding its size-based expectation.The robotic arm’s complex metallic geometry generates multiple nearby reflections around the specular point.Source: E. Parameter Analysis · p. 7, Figure 6 · p. 8
- Azimuth offsets are approximately uniform and elevation offsets are forward-weighted across target classes, consistent with cluster-centered geometry without artificial anisotropy.The elevation density peaks at zero degrees.Source: E. Parameter Analysis · p. 7, Figure 7 · p. 8, Figure 8 · p. 8
- Automobiles have broader angular spreads than humans, while robots remain broad despite smaller dimensions, consistent with metallic, articulated, geometrically complex structures.The angular parameter reflects size, material composition, and geometric complexity rather than size alone.Source: E. Parameter Analysis · p. 9
V. CHANNEL MODEL: RCS
The RCS model follows a 3GPP-compatible decomposition into mean, geometry-dependent, and stochastic factors. It models angular dependence by aligning measured responses to the bistatic specular axis and fitting a normalized directional template with bistatic weighting.
A. Composite RCS
- The composite RCS represents the total coherent scattering strength of the target’s incident points.The model decomposes it into mean, deterministic geometry-dependent, and stochastic fluctuation factors, maintaining compatibility with 3GPP TR 38.901.Source: §V · p. 9, A. Composite RCS · p. 9
1) Mean Composite RCS:
- σM is the linear mean composite RCS across a target’s acquisitions, averaging over geometry and small-scale fading.It represents the average strength of the cluster and is reported in dBsm for each target class.Source: 1) Mean Composite RCS · p. 9
2) Deterministic Composite RCS:
- σD(β, ϕ) models systematic composite-RCS variation with bistatic angle β and target aspect angle ϕ.β describes TX–cluster-center–RX geometry; ϕ parameterizes the target’s directional response in the RX-centric global coordinate system.Source: 2) Deterministic Composite RCS · p. 9
- Shifting each measured sweep by −β/2 aligns its specular response at ϕ = 0°; the aligned responses form a fitted angular template.The method applies bistatic weighting, jointly optimizes the listed parameters, and normalizes the deterministic factor to unit mean; Fig. 9 shows representative fits.Source: 2) Deterministic Composite RCS · p. 9
3) Stochastic Composite RCS:
The stochastic composite-RCS factor captures residual fluctuations after mean and deterministic geometry effects are removed. The incident-point model characterizes normalized point RCS by distance offset, while measured path phases are modeled as independent uniform draws.
3) Stochastic Composite RCS:
- σS captures residual composite-RCS fluctuations after removing the mean and deterministic geometry-dependent factors.It is modeled as a unit-mean Lognormal random variable so it does not bias expected composite RCS; its spread is reported in dB.Source: 3) Stochastic Composite RCS · pp. 10–11
B. Incident-Point RCS
- Normalized incident-point RCS removes absolute cluster strength, isolating how individual point powers depend on scattering geometry.The underlying composite RCS is the model developed in the preceding subsection.Source: B. Incident-Point RCS · p. 11
- Normalized incident-point RCS decays with distance from the cluster center, and its distribution at a given offset is well modeled by a linear-domain Gaussian.Both its mean and standard deviation depend on the offset and are parameterized by target class.Source: B. Incident-Point RCS · p. 11
- Path phases are empirically modeled as independent uniform draws over [0, 2π), consistent with short-wavelength geometric separation at 28 GHz.The paper attributes the observed uniform distribution to decorrelated phase differences between resolvable points.Source: B. Incident-Point RCS · p. 11
C. Parameter Analysis
Across nine targets, the fitted composite- and incident-point RCS parameters show physically interpretable trends associated with target size, materials, facets, and geometric complexity. The analysis distinguishes targets through their mean strength, directional response, residual fluctuation, and point-level redistribution.
C. Parameter Analysis
- Across nine targets, fitted composite- and incident-point RCS parameters show physically interpretable trends that support the proposed two-level decomposition.The reported trends reflect differences in target size, material composition, facet structure, and geometric complexity.Source: C. Parameter Analysis · p. 11
- Mean composite RCS increases with target size and illuminated surface extent; the measured vehicles follow sedan < SUV < van.The corresponding values are 9.98 dBsm for the sedan, 13.36 dBsm for the SUV, and 20.88 dBsm for the van.Source: C. Parameter Analysis · p. 11
- Stable, oriented facets produce pronounced directional lobes, while humans and the AMR show comparatively weak angular variation.The fitted automobile patterns are broad and high-gain, whereas human and AMR patterns tend toward isotropic responses; Fig. 9 presents representative fits.Source: C. Parameter Analysis · p. 11
- Targets with strong deterministic directionality generally have smaller residual fluctuation spreads, while humans show the largest; the van is an exception.Despite strong directionality, the van has elevated residual variance, which the paper relates to its many independently varying scattering regions; Fig. 10 shows representative distributions.Source: C. Parameter Analysis · pp. 11–12
- Automobiles and the AMR show slower point-RCS decay with distance, while humans and the robotic arm show larger spreads and the UAV shows rapid decay with small variance.These patterns are interpreted in relation to illuminated surface extent, local-facet variability, and the UAV’s localized scattering region; Fig. 11 shows parameter trends.Source: C. Parameter Analysis · p. 12, Figure 11 · p. 12
VI. CHANNEL REALIZATION
Channel realizations combine the geometric scattering framework with the RCS model through cluster-, incident-point-, and path-level steps. The procedure starts from instantaneous target geometry, samples and weights incident points, then maps them to path properties for channel synthesis.
A. Channel Realization Procedure
- The realization procedure combines the geometric scattering framework with the RCS model across cluster, incident-point, and path levels.Fig. 12 distinguishes geometric inputs, stochastic inputs, and intermediate inputs or outputs.Source: A. Channel Realization Procedure · p. 12, Figure 12 · p. 13
1) Cluster Level:
- At cluster level, instantaneous target geometry determines the bistatic-specular cluster center and axis, and the composite RCS is evaluated from the resulting angles.Nondirectional targets may use a sphere instead of an ellipsoid, with a point scatterer as the compact-target limit.Source: 1) Cluster Level · pp. 12–13
2) Incident-Point Level:
- At incident-point level, the procedure samples a path count and instantiates points around the cluster, then redistributes composite RCS across them.Point offsets are sampled using the specified distance and elevation distributions and a uniform azimuth; point RCS depends on distance offset and is scaled by composite RCS.Source: 2) Incident-Point Level · p. 13
3) Path Level:
- At path level, each incident point and its RCS determine path geometry, delay, angles, and complex amplitude for synthesizing the instantaneous channel response.The path amplitude uses the bistatic radar equation and an independent random phase.Source: 3) Path Level · p. 13
B. Example Realizations
Synthesized realizations closely match measured pathloss trends and fluctuations across validation and extrapolation, while target-specific trajectories reproduce pathloss changes associated with motion and aspect. The conclusion reports consistent, interpretable model behavior across heterogeneous targets, geometries, and motion.
B. Example Realizations
- For the UAV, pathloss minima during 0°–180° rotation align with measured RCS peaks at favorable aspect angles.In the extrapolation interval, the UAV recedes from TX and RX, producing increasing pathloss.Source: B. Example Realizations · pp. 13–14
- Across the human, AMR, robotic-arm, and van examples, pathloss changes track the described approach, recession, or articulated motion.For the van, pathloss reduction while the TX moves coincides with measured RCS peaks from the automobile side.Source: B. Example Realizations · p. 14
- Close agreement in pathloss trends and fluctuation statistics across validation and extrapolation demonstrates capture of motion-induced dynamics across target classes.The first half replicates measured motion; the second introduces controlled trajectory variations beyond measurement conditions.Source: B. Example Realizations · pp. 13–14, Figure 13 · p. 14
VII. CONCLUSION
- Across nine heterogeneous targets, larger and more extended targets produce broader clusters, while material composition and geometric complexity vary angular spread and power fluctuations.The inferred statistical behavior is stable across geometries and motion, and synthesized realizations closely match measured pathloss evolution.Source: §VII · p. 14
APPENDIX A
The appendix evaluates planar-wave beamforming at the campaign’s minimum RX distance and reports small magnitude and phase deviations relative to far-field references. A controlled geometry experiment also reports average delay and AoA extraction errors.
APPENDIX A
- At 2.5 m, the near-field magnitude pattern remains close to the far-field pattern, with 9.46% NRMSE versus the far-field pattern over the full angular cut.The largest deviations occur below −23 dB, away from the main peak.Source: Appendix A · p. 14, Figure 14 · p. 15
- At 2.5 m, array-gain defocusing is 0.19 dB below the far-field value, within the measurement system’s reported 0.48 dB path-gain error.The paper concludes that this defocusing causes negligible estimation error in path gain or RCS.Source: Appendix A · p. 15
- At 2.5 m, the residual phase difference from the 4.4 m pattern remains below 7° over the considered angular region.The paper describes this deviation as on the order of the system phase uncertainty.Source: Appendix A · p. 15, Figure 14 · p. 15
APPENDIX B
- The controlled validation experiment reports average extraction errors of 0.1 ns in delay and 0.2° in AoA.The receiver was measured at 120 control points with known geometry; Fig. 15 presents empirical CDFs of delay and AoA errors.Source: Appendix B · p. 15, Figure 15 · p. 15