RF Range Calculation Methods

How the Kaonic Range Tool computes link quality and connection probability

Overview

The tool predicts RF link quality between Kaonic nodes using:

• Path loss: Free-space and two-ray models
• Terrain: Elevation data to check line-of-sight
• Buildings: OSM footprints to detect obstructions
• Polarization: Cross-polarization loss
• Shadowing: Log-normal fading for connection probability

1. Path Loss Models

Free Space Path Loss (FSPL)

Used for distances below the critical distance (typically short links):

FSPL(dB) = 20·log₁₀(d) + 20·log₁₀(f) + 20·log₁₀(4π/c)

Where d = distance (m), f = frequency (Hz), c = 299,792,458 m/s.

Two-Ray Ground Reflection

Used for distances beyond the critical distance (ground-bounce dominates):

PL(dB) = 40·log₁₀(d) − 10·log₁₀(G·hₜ²·hᵣ²)

Where G = combined antenna gain (linear), hₜ, hᵣ = antenna heights (m).

Critical Distance

Transition point between FSPL and two-ray:

d_c = 4π·hₜ·hᵣ / λ

Where λ = wavelength. Below d_c we use FSPL; above it we use two-ray.

2. Received Power

Received power at the antenna:

P_r(dBm) = P_t + G_t + G_r − PL

P_t = transmit power (dBm), G_t, G_r = antenna gains (dBi). Default gain: 3 dBi per antenna.

3. Line-of-Sight (LOS) Check

The ray between two antennas is sampled at 40 points. At each point we check:

• Terrain: Elevation from EU-DEM 25 m grid. Ray must clear terrain by at least 1 m (Fresnel clearance).
• Buildings: If the ray passes through a building footprint (from OSM), it must clear the roof by at least 2 m.

If either condition fails, the link is marked NLOS (non-line-of-sight).

4. NLOS and Additional Losses

Effect	Loss
NLOS (obstructed path)	+25 dB
Polarization mismatch	−20·log₁₀(|cos(Δθ)|)
Clutter (trees, foliage)	User-configurable (default 3 dB)

Polarization loss: 0° = aligned (no loss), 90° = cross-polarized (≈20 dB loss).

5. Connection Probability

We model shadowing as log-normal with standard deviation σ = 8 dB. The probability that received power exceeds the receiver sensitivity is:

P_conn = Φ((P_r − P_sens) / σ)

Where Φ = standard normal CDF, P_sens = sensitivity (dBm) for the chosen MCS. The displayed percentage is P_conn × 100.

6. Frequencies and Sensitivities

Band	Frequency	MCS options (sensitivity dBm)
Sub-GHz	868 MHz	MCS2 (−111) … MCS6 (−101)
2.4 GHz	2400 MHz	MCS0 (−112.5) … MCS6 (−92.5)

The tool evaluates all radio pairs and reports the best link (highest connection probability).

7. Data Sources

• Elevation: OpenTopoData EU-DEM 25 m (Europe)
• Buildings: Overpass API (OpenStreetMap)

8. Parameters Summary

Parameter	Value
Shadowing σ	8 dB
Fresnel clearance (terrain)	1 m
Building clearance	2 m above roof
Default antenna gain	3 dBi

Note: Results are planning estimates. Actual performance depends on site-specific conditions, antenna placement, and interference.

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