What is the two-ray ground reflection model?
The two-ray model combines the direct ray with a ray reflected from flat ground. For a ground reflection coefficient near −1 (grazing incidence), received power oscillates with distance up to a breakpoint near db = 4πhthr/λ and beyond it falls as Pr ≈ PtGtGrht²hr²/d⁴, i.e., 40 dB per decade, independent of frequency.[1][2]
Why does the ground reflection cancel at long range?
At grazing angles the reflected wave arrives almost in antiphase with the direct wave (reflection coefficient ≈ −1) and with a path difference approximately 2hthr/d. As d grows, the phase difference shrinks and the two rays increasingly cancel, producing the d⁻⁴ law.[1]
How high should antennas be?
Received power beyond the breakpoint grows as (hthr)², so doubling either antenna height adds 6 dB; this is why base stations, gateways and point-to-point antennas are mounted high.[1]
What are the model’s limits?
It assumes flat, smooth ground, no obstruction and far-field antennas; real terrain, clutter and buildings call for models such as ITU-R P.526 diffraction or empirical models.[3][2]
Frequently asked questions
What is the breakpoint for 2.4 GHz with 10 m and 1.5 m antennas?
About 4π·10·1.5/0.125 ≈ 1.5 km.
Does two-ray apply indoors?
Rarely; indoor propagation is dominated by multiple reflections and walls.
Is the d⁻⁴ law frequency independent?
In the idealized model, yes, beyond the breakpoint.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “Antennas and Propagation for Wireless Communication Systems, 2nd ed.”. S. R. Saunders and A. Aragón-Zavala, Wiley. 2007.
- “Wireless Communications, 2nd ed.”. A. F. Molisch, Wiley. 2011.
- “Recommendation ITU-R P.526: Propagation by diffraction”. ITU-R. current edition.