Methodology

Physics-based.
Standards-traceable.

Every number FresnelPath produces traces to a published standard or a credible public dataset. This page documents which ones and why.

ITU-R Recommendations

Standards implemented

FresnelPath implements these recommendations directly or wraps reference implementations published by the ITU-R study groups. Every citation below corresponds to working code.

Recommendation What it covers Used for
P.526-15 Propagation by diffraction Knife-edge, Bullington, Deygout, and Epstein-Peterson diffraction loss calculations
P.529-3 Terrestrial land mobile service Okumura-Hata empirical model, 150–2000 MHz, urban/suburban/rural correction factors
P.530-18 Line-of-sight propagation Effective path length reduction factor for rain attenuation on terrestrial links
P.676-12 Attenuation by atmospheric gases O₂ and H₂O absorption applied in P.1812-6 path calculations
P.838-3 Rain specific attenuation γR = k·R^α dB/km rain model; coefficients tabled per frequency (H/V polarisation)
P.1546-6 Point-to-area propagation Statistical area sweep for LoRaWAN coverage planning, 30 MHz–4 GHz, 1–1000 km
P.1812-6 Path-specific prediction method Primary terrain-aware model for point-to-point analysis, 30 MHz–6 GHz, includes clutter, time%, troposcatter
P.2108-1 §3.1 Clutter loss Terrestrial terminal clutter loss applied in ITWOM 3.0 (zero clutter → numerically identical to ITM)
P.372-16 Radio noise Noise floor presets: −109/−114/−117 dBm for business/residential/rural environments at 868 MHz
P.453-14 Radio refractive index Effective Earth radius k-factor = 4/3 for standard atmospheric refraction in terrain analysis

Also implemented

COST-231 — Okumura-Hata extension for 1500–2000 MHz NTIA Report 82-100 — Longley-Rice ITM Semtech AN1200.13 — LoRa SNR thresholds SF7–SF12 LoRa Alliance RP002-1.0.5 — 12-region frequency and duty-cycle parameters

Model Hierarchy

How the right model gets chosen

FresnelPath selects the propagation model automatically based on the terrain along your path. You can also override the selection manually.

1

FSPL baseline — always computed

Free-Space Path Loss (Friis equation) runs on every analysis as the lower bound: L = 20·log₁₀(d) + 20·log₁₀(f) + 32.44 dB. The constant is 32.44 — not 40.05, which corresponds to a different unit convention.

2

Single obstacle → Knife-Edge diffraction (ITU-R P.526-15)

When a single dominant ridge obstructs the path, knife-edge diffraction applies the Fresnel-Kirchhoff integral. The v-parameter encodes obstacle geometry: v = h·√(2(d₁+d₂)/(λ·d₁·d₂)). Loss at v = 0 is ~6 dB.

3

2–10 obstacles → Bullington method (ITU-R P.526-15)

Multiple ridges in rolling terrain. Bullington reduces the multi-obstacle problem to an equivalent single equivalent knife-edge, giving a practical estimate without the computational cost of full Deygout.

4

>10 obstacles or δh > 150 m → Deygout method (ITU-R P.526-15)

Complex or extreme terrain with many obstructions. Deygout applies recursive sub-path analysis to each dominant obstacle. A convex-hull pre-filter reduces hundreds of terrain points to the relevant obstacles, keeping computation tractable.

5

Irregular terrain → ITM (Longley-Rice, NTIA Report 82-100)

When terrain is rough and irregular, the Irregular Terrain Model handles 20 MHz–20 GHz at 1–2000 km across 7 radio climate zones. ITM is the fallback that handles what the diffraction methods can't.

Additive on any model

Rain attenuation

Rain attenuation (ITU-R P.838-3) applies additively on top of any propagation model. It's negligible at 868 MHz but significant above 3 GHz. Off by default; opt-in per analysis.

Area analysis

ITU-R P.1546-6 regional sweep

For planning coverage rings rather than a single path, P.1546-6 provides statistical point-to-area predictions at time percentages of 1%, 10%, or 50% across a configurable grid.

Limitations — be precise about precision

  • Terrain data is Copernicus GLO-30 at 30 m spatial resolution (~4 m RMSE). Features smaller than 30 m — a building, a tree line, a wall — may not appear in the profile.
  • The k-factor of 4/3 assumes standard atmospheric refraction. Ducting, temperature inversions, and anomalous propagation conditions require P.1812's time-percentage parameter.
  • FresnelPath is a planning and analysis tool. A link that models as viable still requires field verification before infrastructure commitment.

Validation Suite

How we know the numbers are right

The propagation engine has a dedicated test suite covering every model, diffraction method, and atmospheric component. Three named invariants anchor the most important correctness guarantees.

Invariant 1

ITWOM ≡ ITM at zero clutter

Setting clutter height to 0 in ITWOM 3.0 produces path loss numerically identical to plain ITM. Any test on our CI that asserts ITWOM == ITM sets clutter_height_m = 0. This is the integration test that can't be faked.

Invariant 2

FSPL constant = 32.44

The Free-Space Path Loss constant in our Friis implementation is 32.44, not 40.05. These correspond to different unit conventions (km+MHz vs m+Hz). Tests assert the exact constant; a wrong value fails immediately.

Invariant 3

Knife-edge loss at v = 0 ≈ 6 dB

The ITU-R P.526-15 knife-edge formula produces approximately 6 dB loss when the v-parameter equals zero (path just grazing the obstacle). Our tests validate this exact boundary condition against the standard.

Test coverage by component

  • ITU-R P.1546-6 (regional planning, ERP/field-strength unit conversion, coverage radius round-trip)
  • ITU-R P.1812-6 (frequency/distance bounds, clutter monotonicity, time-percentage range)
  • Okumura-Hata / COST-231 (urban 900 MHz loss monotonicity, environment corrections)
  • ITM (climate zones, point-to-point vs area modes)
  • ITWOM (zero-clutter invariant, clutter loss monotonic scaling)
  • Diffraction (v-parameter formula, loss function, all four methods)
  • Rain attenuation (negligible at 868 MHz, significant above 3 GHz)
  • Fresnel zone (r₁ formula, 60% clearance threshold)

References

Primary sources

These are the documents and datasets the product cites in code, tests, and documentation.

ITU-R Recommendations P.526-15, P.529-3, P.530-18, P.676-12, P.838-3, P.1546-6, P.1812-6, P.2108-1, P.372-16, P.453-14

itu.int/pub/R-REC-P →

Longley A.G., Rice P.L. — "Prediction of Tropospheric Radio Transmission over Irregular Terrain: A Computer Method" NTIA Report 82-100 (1968/1982)

Forms the basis of the ITM (Irregular Terrain Model) implemented in FresnelPath.

COST Action 231 — "Digital Mobile Radio towards Future Generation Systems" (1999)

Source for the COST-231 extension of Okumura-Hata to 1500–2000 MHz with metropolitan correction Cm.

Semtech Application Note AN1200.13 — "LoRa Modem Designer's Guide"

Source for LoRa SF7–SF12 SNR thresholds used in link margin calculations.

LoRa Alliance — "LoRaWAN Regional Parameters RP002-1.0.5" (October 2025)

Source for 12-region frequency plans, EIRP limits, duty cycle, and dwell time parameters.

Copernicus Global Land Service — GLO-30 Digital Elevation Model

30 m resolution DEM; tiles served via HTTPS range requests with AWS CDN fallback.

DOI: 10.5270/ESA-c5d3d65 →

European Commission JRC — PVGIS v5.2 (Photovoltaic Geographical Information System)

Solar irradiance database used for panel sizing and battery autonomy analysis.

re.jrc.ec.europa.eu →

Eeveetza (ITU) — Py1812 and Py1546 reference implementations

Open-source Python reference engines for P.1812-6 and P.1546-6 published by the ITU-R study group authors. FresnelPath wraps these engines rather than reimplementing the standards from scratch.