Scenario: You need to place a LoRa gateway to cover agricultural sensors spread across a 3 km radius. Sensors use SF12 (spreading factor 12) at 868 MHz with +14 dBm TX power and 2 dBi omnidirectional antennas. Will they reach the gateway?
Step 1: Calculate Free Space Path Loss (FSPL)
FSPL = 20·log₁₀(d_km) + 20·log₁₀(f_MHz) + 32.45
= 20·log(3) + 20·log(868) + 32.45
= 9.54 + 59.16 + 32.45
= 101.15 dB
Step 2: Add environmental losses
Rural farmland (light vegetation, undulating terrain):
Foliage attenuation: 5 dB (spring/summer)
Ground reflection loss: 3 dB
Fresnel zone obstruction: 2 dB (trees at 40% of first Fresnel zone)
Total environmental loss: 10 dB
Step 3: Calculate received signal strength
TX power: +14 dBm
TX antenna gain: +2 dBi
FSPL: -101.15 dB
Environmental: -10 dB
RX antenna gain: +6 dBi (directional Yagi at gateway)
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Received power: -89.15 dBm
Step 4: Compare to receiver sensitivity
LoRa receiver (SF12, 125 kHz bandwidth): -137 dBm sensitivity
Link margin = Received power - Sensitivity
= -89.15 - (-137)
= +47.85 dB
Step 5: Evaluate link quality
Typical link margin targets:
10-15 dB: Marginal (works in ideal conditions, fails in rain/storms)
15-20 dB: Acceptable (reliable most of the time)
20-30 dB: Good (works through moderate fading)
>30 dB: Excellent (very reliable, tolerates heavy rain/foliage)
This link: 47.85 dB = Excellent
Result: A single gateway at 3 km with a 6 dBi antenna provides robust coverage even through heavy rain and full foliage. The 47 dB margin allows reducing TX power to +8 dBm (saving 75% battery energy) while maintaining 41 dB margin, or extending range to 6-8 km in favorable terrain.