- 2077 Chaitra · 4 marks
Log-distance path loss model
Short answer
The log-distance model predicts average path loss as PL(d)=PL(d0)+10n log(d/d0), where n is path loss exponent. A log-normal shadowing term Xσ (zero-mean Gaussian) can be added for random variations. Common n: free space 2, urban cellular 2.7–3.5.
Explain log-distance path loss model.
The log-distance path loss model states that the average received power falls off logarithmically with distance, whether indoors or outdoors. The average path loss is proportional to the n-th power of distance:
PL(d) ∝ (d/d0)ⁿ
PL(d) [dB] = PL(d0) + 10n log(d/d0)
- n = path loss exponent: how fast loss grows with distance.
- d0 = close-in reference distance in the far field (1 km for large cells, 100 m or 1 m for micro/indoor cells).
- PL(d0) = loss at d0, measured or found from free space: 20 log(4πd0/λ).
| Environment | n |
|---|---|
| Free space | 2 |
| Urban cellular radio | 2.7 – 3.5 |
| Shadowed urban cellular | 3 – 5 |
| In building, LOS | 1.6 – 1.8 |
| Obstructed in building | 4 – 6 |
| Obstructed in factories | 2 – 3 |
Log-normal shadowing: at the same distance, actual loss varies with surroundings, so a zero-mean Gaussian term Xσ (in dB, σ typically 6–12 dB) is added:
PL(d) = PL(d0) + 10n log(d/d0) + Xσ
Example: PL(d0 = 100 m) = 70 dB, n = 3.5 → at 1 km, PL = 70 + 35 × log 10 = 105 dB.
✓ Answer checked by Claude Opus 5.5 (high effort)
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