- 2072 Magh · 8 marks
Large scale path loss and small scale fading
Short answer
Large-scale path loss gives the mean power over hundreds of metres, following a log-distance law with log-normal shadowing. Small-scale fading is the rapid amplitude and phase fluctuation over a few wavelengths, caused by multipath and Doppler. Their combination gives the total received signal variation.
Explain the mobile radio propagation in terms of large scale path loss and small scale fading.
Mobile radio propagation is described by two effects that act on very different distance scales: large-scale path loss (including shadowing) and small-scale fading. The received signal is their combination.
Pr (dBm)
|\ /\/\ small-scale fading (fast ripples)
| \/ \/\/\
| ---- \/\/\/\ local mean (shadowing)
| ---- \/\/\/\
| - - - - - - - - - - mean path loss ~ 10n log d
+----------------------------- log d
Large-scale path loss
- Describes the mean received power averaged over 5λ–40λ, as a function of T–R distance. It changes slowly over hundreds of metres.
- Distance-dependent loss: Pr ∝ 1/dⁿ; n = 2 in free space (Friis), 4 for two-ray at large d, 2.7–5 in urban areas.
PL(d) = PL(d0) + 10n log(d/d0) + Xσ
- Shadowing (log-normal fading): obstacles such as hills and buildings make the local mean vary randomly about the distance trend. Xσ is a zero-mean Gaussian in dB, with σ about 6–12 dB.
- Models: free space, two-ray, log-distance, Okumura, Hata, and indoor partition models.
- Used for coverage area, cell size, link budget and interference planning.
Small-scale fading
- Rapid change of amplitude and phase over a few wavelengths (fractions of a second), caused by multipath waves adding constructively and destructively. Signal may vary by 30–40 dB within half a wavelength.
- Effects: rapid amplitude changes, random frequency modulation (Doppler) and time dispersion (echoes, ISI).
- Factors: multipath, speed of the mobile, speed of surrounding objects, and signal bandwidth.
- Types: flat or frequency selective (by delay spread στ vs Ts), fast or slow (by coherence time Tc vs Ts).
- Statistics: Rayleigh envelope when there is no LOS path, Ricean when a strong LOS exists.
- Countered by diversity, equalization, interleaving and coding.
| Aspect | Large-scale path loss | Small-scale fading |
|---|---|---|
| Scale | 100s–1000s of m | ~λ/2 |
| Cause | Distance, shadowing | Multipath, Doppler |
| Distribution | Log-normal | Rayleigh / Ricean |
| Design use | Coverage, cell planning | Receiver/modem design |
✓ Answer checked by Claude Opus 5.5 (high effort)
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