---
title: "Fading types by delay spread and Doppler spread"
subject: "Wireless Communication"
chapter: 3
key: "semester_7/wireless_communication:fading-types-delay-doppler"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/fading-types-delay-doppler
site: BCT Engineering
---

# Fading types by delay spread and Doppler spread

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

- Asked in: 2081 Baisakh, 1+3 marks; 2073 Magh, 2+2 marks (asked 2 times)
- Video: [Types of Small Scale Fading | Wireless Communication](https://www.youtube.com/watch?v=vjCsTsFnNqo) — GURUKULA
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/fading-types-delay-doppler
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3

## Question

Define fading. Describe briefly its different types based on delay spread and Doppler spread.

## Short answer

Fading is rapid fluctuation of signal amplitude/phase due to multipath. Based on delay spread: flat fading (Bs << Bc, no ISI) and frequency-selective (Bs > Bc, ISI). Based on Doppler: fast fading (Ts > Tc, channel changes within a symbol) and slow fading (Ts << Tc).

## Answer

**Fading** is the rapid fluctuation of the amplitude, phase or multipath delay of a radio signal over a short time or short distance, caused by interference between two or more versions of the transmitted signal arriving at slightly different times (multipath).

Small-scale fading is classified independently by two mechanisms: **multipath time delay spread** and **Doppler spread**.

#### Based on multipath delay spread (time dispersion)
**1. Flat fading**
- Bs ≪ Bc and Ts ≫ στ (signal bandwidth smaller than coherence bandwidth).
- All frequency components fade together; spectral shape is kept, only gain changes.
- No ISI. Amplitude usually Rayleigh distributed. Example: narrowband voice channel.

**2. Frequency selective fading**
- Bs > Bc and Ts < στ.
- Different frequencies fade differently; the channel causes ISI and the received signal is distorted.
- Needs equalizers, RAKE or OFDM. A common rule: frequency selective if Ts < 10στ.

#### Based on Doppler spread (frequency dispersion)
**3. Fast fading**
- Tc < Ts and BD > Bs: the channel changes within one symbol.
- Causes frequency dispersion (time-selective fading) and signal distortion. Occurs at very low data rates or high speeds.

**4. Slow fading**
- Tc ≫ Ts and BD ≪ Bs: channel is nearly constant over many symbols.
- Channel changes slowly compared with the symbol rate.

| Basis | Type | Condition |
|---|---|---|
| Delay spread | Flat | Bs ≪ Bc, Ts ≫ στ |
| Delay spread | Freq. selective | Bs > Bc, Ts < στ |
| Doppler spread | Fast | Ts > Tc, Bs < BD |
| Doppler spread | Slow | Ts ≪ Tc, Bs ≫ BD |

The two classifications are independent, so a channel can be, for example, flat and slow fading at the same time.

## Check yourself

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

1. Fading is caused mainly by:
   A. Thermal noise
   B. Low transmit power
   C. Antenna gain loss
   D. Interference between multiple versions of the signal arriving at slightly different times
   Answer: D. Multipath components add constructively and destructively. (Key point: Fading definition)

2. Flat fading occurs when:
   A. Tc < Ts
   B. Bs << Bc and Ts >> sigma_tau
   C. Bs > Bc
   D. Ts < sigma_tau
   Answer: B. Signal bandwidth is smaller than coherence bandwidth, so all frequencies fade together without ISI. (Key point: Flat fading)

3. Which problem comes with frequency selective fading?
   A. Only a gain change
   B. No distortion
   C. Intersymbol interference
   D. Doppler shift only
   Answer: C. With Bs > Bc, different frequencies fade differently, causing ISI and needing equalizers, RAKE or OFDM. (Key point: Frequency selective fading)

4. Fast fading is defined by:
   A. Ts << Tc
   B. Bs < Bc
   C. Tc > Ts
   D. Tc < Ts and BD > Bs
   Answer: D. The channel changes within one symbol. (Key point: Fast fading)

5. The delay-spread and Doppler-spread classifications are:
   A. Mutually exclusive
   B. The same
   C. Applicable only to indoor links
   D. Independent, so a channel can be flat and slow at once
   Answer: D. They depend on different mechanisms. (Key point: Independence)

## Related in Wireless Communication

- [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
- [Doppler spread, coherence bandwidth, fading classes](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adoppler-coherence-fading-classification) — Wireless Communication, chapter 3
- [Fading factors and Doppler shift derivation](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afading-factors-doppler-shift) — Wireless Communication, chapter 3
- [Coherence bandwidth and delay spread relation](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afrequency-selective-coherence-delay) — Wireless Communication, chapter 3
- [Numerical: rms delay spread; flat or selective for AMPS/GSM](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Arms-delay-spread-amps-gsm) — Wireless Communication, chapter 3
- [Frequency dispersion and Doppler spread derivation](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afrequency-dispersion-doppler-spread) — Wireless Communication, chapter 3