- 2071 Magh · 2 marks
Rayleigh versus Rician fading channel
Short answer
Rayleigh fading occurs with no line-of-sight and has envelope PDF p(r) = (r/sigma^2) exp(-r^2/2sigma^2). Rician fading has a dominant LOS component and PDF p(r) = (r/sigma^2) exp(-(r^2+A^2)/2sigma^2) I0(Ar/sigma^2), with Rician factor K = A^2/(2sigma^2). As K goes to zero, Rician reduces to Rayleigh.
With appropriate expressions, distinguish between Rayleigh fading channel and Rician fading channel.
Rayleigh fading happens when there is no line-of-sight (LOS) path and the received signal is the sum of many scattered waves of similar strength. Rician fading happens when there is one strong dominant (LOS) component plus many weak scattered waves.
| Point | Rayleigh | Rician |
|---|---|---|
| LOS path | Absent | Present (dominant) |
| PDF of envelope r | p(r) = (r/σ²) e^(−r²/2σ²), r ≥ 0 | p(r) = (r/σ²) e^(−(r²+A²)/2σ²) I₀(Ar/σ²), r ≥ 0 |
| Parameter | σ² (power of scattered part) | K = A²/(2σ²) (Rician factor) |
| Fade depth | Deep fades, worst case | Milder fades |
| Typical place | Dense urban, no LOS | Open area, microcells, indoor LOS |
Here A is the peak amplitude of the dominant signal and I₀ is the modified Bessel function of the first kind and zero order. When A → 0 (K → 0 or −∞ dB) the Rician distribution reduces to Rayleigh.
✓ Answer checked by Claude Opus 5.5 (high effort)
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