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RF Range Calculation Methods

How the Kaonic Network Planning 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)	User-configurable (default 25 dB; can be much higher)
Polarization mismatch	−20·log₁₀(|cos(Δθ)|)
Clutter (trees, foliage)	User-configurable (default 10 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 K1S modulation. The displayed percentage is P_conn × 100.

6. K1S Modulation Options

Sensitivity and data rate come from the K1S performance spec. You select a modulation per node; options include:

• MR-OFDM Options 1–4 (MCS 0–6): bandwidths 200–1200 kHz, sensitivities from −113 dBm (best) to −92 dBm
• MR-O-QPSK at 100/200/1000/2000 kchip/s: bandwidths 100–2000 kHz, sensitivities down to −123 dBm

TX power limits: Sub-GHz 1 W (30 dBm), 2.4 GHz 250 mW (24 dBm). MR-OFDM uses back-off for higher MCS: MCS 4 = 1.5 dB, MCS 5 = 3 dB, MCS 6 = 5 dB.

Both nodes must use the same channel bandwidth; otherwise the link is marked as incompatible.

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	Default
Clutter loss	10 dB
Implementation margin	12 dB
NLOS loss	25 dB (adjustable; severe obstructions can need 40+ dB)
Shadowing σ	8 dB
Fresnel clearance (terrain)	1 m
Building clearance	2 m above roof
Default antenna gain	3 dBi
TX max (Sub-GHz)	30 dBm (1 W), minus MCS back-off
TX max (2.4 GHz)	24 dBm (250 mW), minus MCS back-off

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