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.
The breakpoint distance d_bp = 4h₁h₂/λ is the distance where the two signals transition from oscillating in and out of phase (causing interference lobes) to being nearly anti-phase (causing 1/R⁴ decay). Below the breakpoint: constructive interference can provide up to 6 dB gain over free space. Above the breakpoint: the path loss increases at 40 dB/decade, which is 20 dB/decade worse than free space.
For practical outdoor propagation at microwave and mmWave frequencies: the two-ray model is a useful approximation for open terrain with low antenna heights. For urban environments with many reflecting surfaces: more complex models (ray tracing, statistical models like 3GPP TR 38.901) are needed because the signal arrives via many reflected, diffracted, and scattered paths.
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.