- 2079 Bhadra · 4+4 marks
Numerical: Hata path loss for medium city
Short answer
For fc=950 MHz, hte=45 m, hre=5 m, d=10 km, medium-city correction is a(hre)=9.03 dB. Hata urban path loss is 149.64 dB and free-space path loss is 112.0 dB, so Hata is about 37.6 dB higher because urban propagation has extra diffraction, scattering and a larger distance exponent.
In mobile propagation in a cellular system, find the correction factor and pathloss for a medium size city assuming carrier frequency as 950 MHz, height of transmitting antenna at base station is 45 m, propagation distance between antennas is 10 km and height of receiving antenna in mobile station is 5 m. Compute free space pathloss and compare it with Hata pathloss.
Hata model (urban):
L50 = 69.55 + 26.16 log fc − 13.82 log hte − a(hre)
+ (44.9 − 6.55 log hte) log d
Medium city:
a(hre) = (1.1 log fc − 0.7)hre − (1.56 log fc − 0.8) dB
Given: fc = 950 MHz, hte = 45 m, hre = 5 m, d = 10 km. All values are inside Hata's validity range (150–1500 MHz, 30–200 m, 1–10 m, 1–20 km).
Correction factor
log 950 = 2.9777
a(hre) = (1.1×2.9777 − 0.7)×5 − (1.56×2.9777 − 0.8)
= (2.5755)×5 − 3.8452
= 12.877 − 3.845
= 9.03 dB
Hata path loss
26.16 log 950 = 77.90
13.82 log 45 = 22.85
44.9 − 6.55 log 45 = 44.9 − 10.83 = 34.07
log 10 = 1
L50 = 69.55 + 77.90 − 22.85 − 9.03 + 34.07×1
= 149.64 dB
Free space path loss
LFS = 32.44 + 20 log f(MHz) + 20 log d(km)
= 32.44 + 59.55 + 20
= 112.00 dB
Comparison
L50 − LFS = 149.64 − 112.00 = 37.64 dB
| Quantity | Value |
|---|---|
| Correction factor a(hre) | 9.03 dB |
| Hata path loss | 149.64 dB |
| Free space loss | 112.00 dB |
| Excess loss | 37.64 dB |
Answer: a(hre) = 9.03 dB, Hata path loss = 149.64 dB, free space loss = 112.0 dB. The Hata loss is about 37.6 dB higher, because a real city has buildings, ground reflection, diffraction and scattering that free space ignores; also loss in Hata rises at (44.9 − 6.55 log hte) ≈ 34 dB/decade, compared with 20 dB/decade in free space.
✓ Answer checked by Claude Opus 5.5 (high effort)
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