---
title: "Rayleigh versus Rician fading channel"
subject: "Wireless Communication"
chapter: 3
key: "semester_7/wireless_communication:rayleigh-vs-rician-fading"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/rayleigh-vs-rician-fading
site: BCT Engineering
---

# Rayleigh versus Rician fading channel

Wireless Communication · Chapter 3: Radio Wave Propagation in Mobile Networks

- Asked in: 2071 Magh, 2 marks
- Video: [Rayleigh and Ricean Distribution - Mobile Radio Propagation - Mobile Communication System](https://www.youtube.com/watch?v=kuNLZLTZNfw) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/rayleigh-vs-rician-fading
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3

## Question

With appropriate expressions, distinguish between Rayleigh fading channel and 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.

## Answer

**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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Rician fading differs from Rayleigh fading because Rician has:
   A. No LOS path
   B. A dominant LOS component plus scattered waves
   C. Only Doppler
   D. A log-normal envelope
   Answer: B. Rayleigh has no LOS; Rician has one strong dominant component plus weak scattered waves. (Key point: When each applies)

2. The Rician factor K is defined as:
   A. A/sigma
   B. sigma^2/A^2
   C. A^2/(2 sigma^2)
   D. 2 sigma^2 A
   Answer: C. K = A^2/(2 sigma^2), the ratio of dominant power to scattered power. (Key point: Rician factor)

3. What happens to the Rician distribution as A tends to 0?
   A. It becomes Rayleigh
   B. It becomes Gaussian with large mean
   C. It becomes log-normal
   D. It becomes uniform
   Answer: A. With no dominant path (K to 0), the Rician pdf reduces to Rayleigh. (Key point: Limit case)

## Related in Wireless Communication

- [Frequency selective fading and Rayleigh distribution](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afrequency-selective-rayleigh) — Wireless Communication, chapter 3
- [Short note: Rayleigh and Ricean fading distribution](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Arayleigh-ricean-distribution-note) — Wireless Communication, chapter 3
- [Doppler spread fading; delay spread numerical](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adoppler-fading-delay-spread-profile) — Wireless Communication, chapter 3
- [Forward/reverse channel and 5G versus 4G](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aforward-reverse-5g-vs-4g) — Wireless Communication, chapter 1, asked 2×

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