Free-space path loss
A radio signal spreads out as it travels, so the power reaching a receiving antenna falls with distance. In free space, with a clear line of sight, the loss between two isotropic antennas is:
FSPL (dB) = 20 log10(d) + 20 log10(f) + 32.45
with d in kilometers and f in megahertz. Doubling the distance or the frequency adds 6 dB of loss.
The link budget
The received level is the transmit power plus the gains, minus the losses:
Received (dBm) = Tx power + Tx antenna gain + Rx antenna gain − cable losses − FSPL
The link margin is the received level minus the receiver’s sensitivity. It must cover fading from rain, foliage, multipath and obstructions. Engineers usually aim for 10 to 20 dB.
Example
A 2.4 GHz Wi-Fi link over 1 mile (1.61 km), 20 dBm transmitter, 2 dBi antennas, 1 dB of cable loss, receiver sensitivity −85 dBm:
- FSPL: 20 log(1.61) + 20 log(2,400) + 32.45 ≈ 104.2 dB;
- received level: 20 + 2 + 2 − 1 − 104.2 ≈ −81.2 dBm;
- margin: about 3.8 dB, too thin for a reliable link.
Swapping the 2 dBi antennas for 15 dBi directional antennas at both ends adds 26 dB and gives a comfortable 30 dB margin.
The Fresnel zone
A clear visual line of sight is not enough. Radio waves need an ellipsoid-shaped region around the direct path, the first Fresnel zone, to be mostly clear. Its radius at mid-path is:
r (m) ≈ 8.66 × √(d km ÷ f GHz)
For 1 mile at 2.4 GHz, that is about 7 m (23 ft). Keep at least 60% of it free of trees, buildings and terrain, and remember the earth’s curvature on long links.
Beyond free space
Free-space loss is the best case. Real links add:
- walls and floors: 3 to 15 dB each indoors;
- vegetation: several dB per tree, more when wet;
- rain: significant above about 10 GHz;
- multipath fading in cluttered environments.
Regulations
EIRP (transmit power plus antenna gain minus losses) is what regulators limit. In the US, point-to-multipoint 2.4 GHz systems are generally limited to 36 dBm EIRP, with higher allowances for fixed point-to-point links under FCC Part 15 rules.