First-order diffraction on real terrain, measured: shadowed links found only at high ray counts, median 44 dB below ITM

[adhabnr-ux]

Hi Sionna team, I'm a high-school member of the NVIDIA 6G Developer Program. I'm building an open tool that
checks carriers' FCC 4G coverage claims around Arizona schools on tribal land, where almost no one runs speed
tests. I use Sionna RT to cross-check a terrain-diffraction model. This follows up on #1018, where @faycalaa
explained that RT supports first-order diffraction only. I measured what that means on a real rural scene, and
I have three questions.

Setup. sionna-rt 2.1.0, CPU (LLVM, llvm_ad_mono_polarized). Copernicus GLO-30 terrain as a triangle mesh
(505 × 541 grid, 544k triangles, ground with ε_r = 15 and σ = 0.005 S/m, medium-dry ground per ITU-R P.527). One 45.7 m registered tower near Whiteriver, AZ, at
850 MHz, with isotropic V-pol antennas. There are 30 receivers at 1.5 m, 1.7–8.4 km away, that a terrain
profile says are shadowed. Receiver heights come from bilinear interpolation of the same grid used to build the mesh.

Results (PathSolver, los=True, specular_reflection=True, refraction=False):

setting	receivers with any path (of 30)
max_depth=1, diffraction=True, 1e6 samples	12
same, 3e6 / 1e7 / 3e7 / 1e8 samples	21 / 23 / 24 / 26
max_depth=2 or 3	12 (no new receivers; one gain moves 1.5 dB)
edge_diffraction=True	12 (identical gains)
diffraction_lit_region=False	0
diffraction=False	0

• The gains that are found have converged: the median change from 3e7 to 1e8 samples is 0.75 dB.
• They are a median 44 dB weaker than NTIA ITM point-to-point (range 11–80 dB) on the same terrain profile.
• They are a median 62 dB weaker than an ITU-R P.526 Bullington knife-edge.
• On the 30 line-of-sight receivers, Sionna matches free space to 0.01 dB in 24 of 30 cases, so the geometry
  and registration look right.

Figure, code and CSV:

• https://github.com/adhabnr-ux/coverage-truth/blob/main/figures/sionna_terrain_diffraction.png
• https://github.com/adhabnr-ux/coverage-truth/blob/main/ct/diffraction_ablation.py
• https://github.com/adhabnr-ux/coverage-truth/blob/main/results/diffraction_ablation.csv

Questions

1. Path discovery depends strongly on samples_per_src, going from 12 to 26 of 30 between 1e6 and 1e8 samples.
   Is that expected, because diffracting edges are found by the sampled rays? Is there a recommended sample
   count, or a way to make edge candidates deterministic for large terrain meshes?
2. Every path disappears with diffraction_lit_region=False, even though these receivers are geometrically
   shadowed by the terrain. Am I right that on a smooth terrain mesh the diffracting ridge-crest edge is a
   nearly flat wedge, so the receiver falls in that wedge's "lit" region? If so, is the very weak result simply
   what a first-order UTD wedge coefficient gives at a wedge angle near 180°?
3. For rural coverage over hills, would you recommend a hybrid? For example, Sionna RT for line-of-sight and
   multipath, plus a terrain-profile diffraction model (ITU-R P.526 or ITM) for shadowed links. Would a tutorial
   or example showing that comparison be a useful contribution? I'm happy to write it.

Thanks. I also have three small PRs open (#1191–#1193).

[Wahaj18]

Not from the Sionna team, but I went through the sionna-rt source for this and I think it explains 1 and 2.

1. Sample dependence. Yes, it's expected. Diffraction candidates aren't enumerated from the mesh. In sb_candidate_generator.py, each ray that hits a triangle can sample a diffraction interaction, and sample_wedge_diffraction_point() (utils/wedges.py) then picks one point on the silhouette of that hit triangle (primitive_silhouette_projection with a random sample). The diffracted direction is sampled on the Keller cone (sample_keller_cone_with_measure() in utils/ray_tracing.py), and the candidate only survives if that ray reaches a receiver. So a given crest edge has to be (a) on a triangle that one of your rays hits, (b) the edge picked on that triangle, and (c) diffracted towards the receiver. With 544k triangles most of the relevant ones are hit rarely, which matches your 12 → 26 curve. I don't see a deterministic edge list in the current solver. The practical levers are more samples, or a smaller mesh: crop the DEM to a corridor around the TX–RX profiles, or decimate it away from the ridges, so the same sample budget covers far fewer triangles.

2. diffraction_lit_region=False. It's stricter than "receiver is behind the terrain". In image_method.py the diffracted segment is kept only if it points behind the 0-face and in front of the n-face of that specific wedge (dot(k, nn) > 0 and dot(k, n0) < 0), and the source must be in the shadow region of the target. In the Keller-cone sampler the shadow interval is exterior_angle - phi_i. For a ridge made of two DEM triangles that are almost coplanar, the exterior angle is π plus a small δ, so the wedge's own shadow region is at most δ wide. A hill on a 30 m grid bends the path over many small edges, each with a few degrees of δ, while first-order diffraction has to do the whole bend at one edge. I think that's why no edge has your receivers in its shadow region, and every path you do get is classified as lit-region.

Two follow-ups:

• Where are the diffraction vertices for the 12–26 paths you do find? If they sit off the vertical TX–RX plane (an edge visible from both ends, off to the side), they're lit-region paths that go around the hill rather than over it. That would also explain why they're so weak.
• On the strength, I think it's the wedges themselves: as n → 1 (exterior angle → π) the UTD wedge coefficient goes to zero, since a flat surface has no edge to diffract from. So near-coplanar DEM wedges give very little energy even when the geometry is right. Compared with a Bullington or P.526 knife-edge, which lumps the whole obstacle into one sharp edge, a 40–60 dB gap doesn't surprise me.

3. I can't speak for the maintainers. For shadowed rural links, using a terrain-profile model (P.526 or ITM) for the diffraction part and RT for LOS and multipath is what I'd do too, and your ablation table would make a good example.