What is the difference between a Friis free space calculation and a two ray ground reflection model?
Propagation Models
The Friis equation assumes a single, unobstructed path between transmitter and receiver. In practice, the ground surface reflects a portion of the transmitted signal, creating a second path. The reflected signal arrives with a phase shift determined by the path length difference (geometric) and the reflection coefficient (material-dependent). When these two signals combine at the receiver, they can add constructively (gain) or destructively (loss), depending on the relative phase.
| Parameter | Free Space | Urban | Indoor |
|---|---|---|---|
| Path Loss Model | Friis (1/r²) | Okumura-Hata | IEEE 802.11 |
| Fading Margin | 0 dB | 10-30 dB | 5-15 dB |
| Multipath | None | Severe | Moderate-severe |
| Typical Range | Line of sight | 1-30 km | 10-100 m |
| Shadow Fading (σ) | 0 dB | 6-12 dB | 3-8 dB |
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
Frequently Asked Questions
What is the breakpoint distance?
d_bp = 4h₁h₂/λ. For h₁ = h₂ = 10m at 2 GHz (λ = 0.15m): d_bp = 4 × 10 × 10 / 0.15 = 2667m. For the same heights at 28 GHz (λ = 0.011m): d_bp = 36,364m. At mmWave, the breakpoint is very far, so the two-ray model simplifies to free-space for most practical distances.
When does neither model work?
In non-line-of-sight (NLOS) conditions: buildings, hills, or terrain block the direct path. In these cases: empirical models (Okumura-Hata, WINNER, 3GPP TR 38.901) or ray-tracing tools are needed. NLOS propagation is dominated by diffraction, scattering, and reflections that neither the Friis nor two-ray model captures.
What about for mmWave?
At mmWave, the ground reflection coefficient is high (0.8-0.95 for smooth surfaces) and the Fresnel zone is very small, so even small obstructions can block the line of sight. The two-ray model applies for open, smooth terrain. For urban environments: 3GPP channel models with NLOS/LOS probability functions are the standard for 5G mmWave planning.