Okumura model and median path loss numerical

Okumura model

The Okumura model is an empirical model based on extensive measurements in and around Tokyo. It is one of the most widely used models for macrocell planning in urban areas.

L50(dB) = LF + Amu(f,d) − G(hte) − G(hre) − GAREA

• LF = free space loss.
• Amu(f,d) = median attenuation relative to free space in an urban area over quasi-smooth terrain, read from curves (reference hte = 200 m, hre = 3 m).
• G(hte) = BS antenna height gain = 20 log(hte/200), 30 m < hte < 1000 m.
• G(hre) = mobile antenna height gain = 10 log(hre/3) for hre ≤ 3 m; 20 log(hre/3) for 3 m < hre < 10 m.
• GAREA = gain due to environment (suburban, quasi-open, open), from curves.
• Valid for 150–1920 MHz (extendable to 3 GHz), d = 1–100 km.
• Merits: simple, accurate for urban/suburban cellular systems (about 10–14 dB standard deviation).
• Demerits: slow to respond to rapid terrain changes; works better in urban than rural areas; curves are hard to use in software (hence the Hata formula).

Calculation

Given: d = 50 km, hte = 100 m, hre = 10 m, f = 900 MHz, Amu = 43 dB, GAREA = 9 dB.

λ  = 3×10⁸ / 900×10⁶ = 0.3333 m
LF = 20 log(4π × 50 000 / 0.3333) = 125.51 dB

G(hte) = 20 log(100/200) = −6.02 dB
G(hre) = 20 log(10/3)    = 10.46 dB

L50 = 125.51 + 43 − (−6.02) − 10.46 − 9
    = 155.07 dB

Answer: Median path loss L50 ≈ 155.07 dB.