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Scattering Mechanisms and Modeling for Terahertz Wireless Communications
Shihao Ju, Syed Hashim Ali Shah, Muhammad Affan Javed, Jun Li, Girish Palteru, Jyotish Robin, Yunchou Xing, Ojas Kanhere, Theodore S. Rappaport
TL;DR
Scattering at mmWave and Terahertz frequencies is less studied even as rough surfaces may create important propagation paths, including in NLOS settings. This paper compares two scattering models and examines rough-surface reflection loss; simulations and measurements show frequency- and roughness-related scattering effects and agreement within 2 dB for a measured DS-model comparison.
Problem
Terahertz frequencies remain relatively little studied in communications, although scattered rays may dominate NLOS links and matter for accurate propagation simulation.
Source: §I · p. 1Method
The paper characterizes surface roughness, incorporates scattering loss into rough-surface reflection, and compares DS and RCS model predictions across materials and frequencies.
Source: §II · p. 2, A. Rough Surface Reflection… · p. 2, §III · p. 2Results
Simulated scattering relative to reflection increases with frequency and surface roughness, and DS-model peak received power agrees with measurements within 2 dB.
Source: §IV · p. 6, §V · p. 7Takeaways & Limitations
Scattered-ray power should be considered in realistic mmWave and Terahertz propagation simulations, especially for NLOS links where scattered rays may dominate.
Source: §I · p. 1
Abstract
from arXiv · showhide
This paper provides an analysis of radio wave scattering for frequencies ranging from the microwave to the Terahertz band (e.g., 1 GHz - 1 THz), by studying the scattering power reradiated from various types of materials with different surface roughnesses. First, fundamentals of scattering and reflection are developed and explained for use in wireless mobile radio, and the effect of scattering on the reflection coefficient for rough surfaces is investigated. Received power is derived using two popular scattering models - the directive scattering (DS) model and the radar cross section (RCS) model through simulations over a wide range of frequencies, materials, and orientations for the two models, and measurements confirm the accuracy of the DS model at 140 GHz. This paper shows that scattering can become a prominent propagation mechanism as frequencies extend to millimeter-wave (mmWave) and beyond, but at other times can be treated like simple reflection. Knowledge of scattering effects is critical for appropriate and realistic channel models, which further support the development of massive multiple input-multiple output (MIMO) techniques, localization, ray tracing tool design, and imaging for future 5G and 6G wireless systems.
I. INTRODUCTION
As wireless systems move toward mmWave and Terahertz frequencies, scattering may become a significant propagation mechanism, but remains little investigated in communications. Modeling it matters for realistic propagation environments and 3D ray tracing, especially for NLOS links.
I. INTRODUCTION
- Terahertz communications offer bandwidth from tens to hundreds of GHz, yet Terahertz frequencies remain relatively little studied in communications.The passage gives 300 GHz to 3 THz as an example range.Source: §I · p. 1
- At mmWave and Terahertz frequencies, surface roughness may make scattered paths comparable in power to reflected paths in particular directions.Scattering can partially compensate for other propagation losses above 30 GHz.Source: §I · p. 1
- Accurate propagation simulation at mmWave and Terahertz frequencies requires accounting for scattered-ray power, particularly when NLOS scattered rays may dominate a link.Three-dimensional scattering models are relevant to site-specific 3D ray tracing.Source: §I · p. 1
- The paper compares the DS and RCS scattering models, discusses their assumptions and use cases, and evaluates predictions against measurements.Its numerical comparisons cover practical materials and surface roughness.Source: §I · p. 1
II. FUNDAMENTALS OF SCATTERING
Scattering depends on surface roughness relative to the incident wavelength: a smooth surface reflects specularly, whereas a rough one also reradiates energy in other directions. The section introduces criteria and parameters for characterizing that roughness.
II. FUNDAMENTALS OF SCATTERING
- A smooth surface reflects in the specular direction, while a rough surface produces both a primary specular reflection and diffuse scattering into other directions.The figure defines incident, reflected, and scattered angles, with reflection obeying θi = θr.Source: §II · p. 1, Figure 1 · p. 2
- At hundreds of GHz, wavelengths can become comparable to surface roughness, so surfaces may reradiate energy at many angles rather than only the reflected angle.At lower frequencies, small protuberances relative to wavelength often make scattering negligible.Source: §II · pp. 1–2
- The Rayleigh Criterion sets a critical height hc based on incident angle and frequency; a surface is smooth when its height range h0 is below hc and rough when it exceeds hc.The criterion is stated for a particular wavelength or frequency.Source: §II · p. 2
- Surface roughness is characterized by rms height hrms for vertical variation and correlation length lc for horizontal variation.The passage describes 1/lc as a measure of horizontal roughness and lc as the distance beyond which surface heights are statistically independent.Source: §II · p. 2
A. Rough Surface Reflection Coefficient Model
The rough-surface reflection coefficient incorporates scattering loss into the specular reflected component. It predicts reflected-direction loss, not the power scattered into any particular direction.
A. Rough Surface Reflection Coefficient Model
- The rough-surface reflection coefficient Γrough is formed by multiplying the smooth-surface coefficient Γsmooth by a scattering loss factor ρs.The loss factor accounts for incident power reradiated through scattering rather than retained in the reflected wave.Source: A. Rough Surface Reflection… · p. 2
- The coefficient can predict received power in the reflected direction, but ρs does not reveal scattered-power strength in any particular direction.The smooth-surface coefficient also incorporates penetration loss.Source: A. Rough Surface Reflection… · p. 2
- The cited Beckmann-Kirchhoff-based loss factor applies to dielectric and metallic surfaces but assumes small incident angles, making reflected-power predictions potentially unreliable at large angles.An extension to arbitrary incident and scattering angles is described as agreeing with experimental data at many angles, including a 70° incidence example.Source: A. Rough Surface Reflection… · p. 2
III. SCATTERING MODELS
The paper compares an optics-based directive scattering model with a radar-oriented RCS model. The comparison spans frequencies, materials, and surface properties to assess their predictions.
III. SCATTERING MODELS
- The DS model is widely used in optics, whereas the RCS model is well known in radar and relies on empirical field-measurement values.The passage gives 4A, with A as projected building surface visible from the receiver, as an empirical RCS approximation for buildings.Source: §III · p. 2
- The models are compared at 1, 10, 100, and 1000 GHz using three exemplar materials with different surface properties.The listed parameters include rms height, scattering coefficient, correlation length, lobe-width parameter, and dielectric constant.Source: §III · pp. 2–3
- Table I presents exemplar materials and their parameters for the model comparison.The cited text identifies surface roughness, scattering coefficient, correlation length, scattering lobe width, and dielectric constant among the parameters.Source: Table I · p. 3, §III · p. 3
A. Directive Scattering Model
The DS model describes scattered electric fields across scattering angles and uses them to derive received power. In the 500 GHz example, scattered power in the specular direction exceeds reflected power for rough Material 3 at small incident angles.
A. Directive Scattering Model
- The single-lobe DS model steers its main scattering lobe toward specular reflection and ignores backscatter, while the dual-lobe version includes forward scatter and backscatter.The model calculates scattered electric field at a scattering angle for incident angles from 0° to 90° and scattering angles from −90° to 90°.Source: A. Directive Scattering Model · p. 3
- The scattering coefficient S is defined as the fraction of incident electromagnetic wave that is scattered, and the model calculates the scattered electric field at angle Ψ.The field magnitude also depends on the transmitted and incident field magnitudes and the distances in the link geometry.Source: A. Directive Scattering Model · p. 3
- At θi = 1°, 30°, and 45°, scattered power in the specular direction exceeds reflected power for rough Material 3 at 500 GHz.The comparison uses the simulated conditions listed in Table II.Source: Table II · p. 3, A. Directive Scattering Model · p. 3
- Higher αR produces a narrower scattering lobe, while smaller αR produces a wider one.αR controls lobe width in the DS scattering pattern.Source: A. Directive Scattering Model · p. 3, Figure 2 · p. 3
- Received power is obtained from scattered-wave power flux density and receiver aperture, or equivalently from the scattered field, receiver gain, and wavelength.The received-power relation is given in the supplied equation.Source: A. Directive Scattering Model · p. 3
B. Radar Cross Section Model
The RCS model estimates power scattered toward the receiver by combining contributions from surface roughness at different scales. Its frequency-dependent weighting shifts the modeled contribution from smooth-surface to rough-surface scattering for rough surfaces.
B. Radar Cross Section Model
- RCS measures power density scattered toward the receiver relative to the illuminating wave’s power density; the model originates in radar and often assumes a perfect electrical conductor.RCS values for propagation environments are generally derived empirically from measurements.Source: B. Radar Cross Section Model · p. 4
- The analysis uses monostatic RCS for simplicity, while bistatic RCS allows the transmitter and receiver to be spatially separate.For comparison with monostatic RCS, the paper considers DS with co-located transmitter and receiver, Ψ = −2θi, and equal constant antenna apertures across frequencies.Source: B. Radar Cross Section Model · pp. 4–5
- The monostatic received-power expression uses transmitted power, antenna gain, wavelength, and RCS to calculate power at the receiver.The setup takes the transmitter and receiver to be co-located with the scatterer at distance d.Source: B. Radar Cross Section Model · p. 4
- The RCS formulation separates large- and small-scale surface roughness by treating the surface as patches with distinct scales.The paper describes the two roughness scales by analogy to long and short ocean waves.Source: B. Radar Cross Section Model · p. 4
- The RCS combines small-scale rough-surface and large-scale smooth-surface contributions, with the smooth term weighted by |χs|².For simplicity, the paper assumes unit length along one dimension and uses two-dimensional RCS per unit length.Source: B. Radar Cross Section Model · p. 4
- As frequency decreases, χs approaches 1 and the smooth-surface term dominates; in the Terahertz band χs becomes negligible for rough surfaces, making σrough more significant.χs is the rough-surface height characteristic weighting factor, with hrms denoting the small-scale surface’s rms height.Source: B. Radar Cross Section Model · p. 4
- The rough-surface contribution is calculated from weighted cross sections of small-scale patches with randomly oriented slopes and Gaussian surface-height distributions.Patch orientation is characterized by slope hx = tan Ω.Source: B. Radar Cross Section Model · pp. 4–5
IV. NUMERICAL RESULTS
Simulations compare DS and RCS scattering predictions across frequencies, materials, and incident angles, while 142 GHz drywall measurements test the dual-lobe DS model. The results show that scattering depends on frequency, surface roughness, and angle, and that measured and modeled power can be close to the specular direction.
IV. NUMERICAL RESULTS
- Simulations cover three materials, 1 GHz–1 THz, and incident angles from 0° to 90°; measurements use drywall at 142 GHz with angles from 10° to 80°.The simulations assume monostatic, vertically polarized links; the measurements sample scattered power from -80° to 80° in 10° steps.Source: §IV · pp. 5–6
- Received monostatic scattered power rises with frequency, ranges from -30 to -150 dBm for DS and -40 to -150 dBm for RCS, and falls sharply toward grazing incidence.At grazing incidence most incident power is reflected.Source: §IV · p. 5, Figure 4 · p. 6
- At 100 GHz, rougher surfaces produce more received scattered power at small incident angles, but material predictions converge near 90° as σrough approaches zero.Near 90°, σsmooth dominates and is identical across the three materials.Source: §IV · p. 5
- For Material 2 at 100 GHz and 1 THz, DS backscatter follows the envelope of RCS backscatter as incident angle increases.The authors note that empirical RCS parameters can be fitted to field measurements for different materials, roughnesses, permittivities, and frequencies.Source: §IV · p. 5, Figure 5 · p. 6
- At 142 GHz, measured peak total power occurs at the specular angle and is 9.4 dB greater at 80° than at 10° incidence; backscatter at 10° and 30° is over 20 dB below the peak.Measured power stays within 10 dB of the peak over ±10° around the specular angle, likely in part because of antenna patterns.Source: §IV · p. 6, Figure 6 · p. 7
- Within 2 dB, the dual-lobe DS model plus reflected power predicts measured peak received power at 142 GHz for drywall across four incident angles.The comparison covers incident angles of 10°, 30°, 60°, and 80°; the model fit uses Λ from 0.5 to 0.8.Source: §IV · p. 6, Figure 7 · p. 7
V. CONCLUSION
The conclusion finds that DS and RCS predictions and measurements show scattering depends on frequency, surface, and incidence angle. At 142 GHz, the DS model plus rough-surface reflection predicts drywall peak power within 2 dB of measurements, while measured backscatter at small incidence angles is over 20 dB below the peak.
V. CONCLUSION
- At 142 GHz, DS plus rough-surface reflection predicts drywall peak received power within 2 dB of measurements; measured backscatter at incidence angles of 30° or less is over 20 dB below the peak.The paper concludes that drywall may be approximated as reflective, especially near grazing incidence.Source: §V · p. 7
- Simulated backscatter from both models decreases toward grazing incidence, while scattered power relative to reflected power increases with frequency and surface roughness.Near normal incidence, forward-scattered power from a rough surface can exceed specular reflected power; near grazing, reflected power dominates.Source: §V · p. 7
- The paper concludes that Terahertz scattering depends on the surface and impinging angle, and that smooth drywall may be treated as reflective only as a first-order approximation, especially near grazing.The conclusion identifies DS and RCS as the two models investigated.Source: §V · p. 7