---
title: "Coherence bandwidth/time and types of fading"
subject: "Wireless Communication"
chapter: 3
key: "semester_7/wireless_communication:coherence-significance-fading-types"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/coherence-significance-fading-types
site: BCT Engineering
---

# Coherence bandwidth/time and types of fading

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

- Asked in: 2082 Baisakh, 3+5 marks
- Video: [3 Delay Spread, Coherence Bandwidth Explained Module 1 | 7th Sem WCS 22 Scheme](https://www.youtube.com/watch?v=h8PqDAG6sLg) — VTU Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/coherence-significance-fading-types
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3

## Question

Define the terms coherence bandwidth and coherence time explaining their significance in mobile radio propagation. Explain fading with its various types.

## Short answer

Coherence bandwidth Bc is the frequency range of flat channel response, inversely related to delay spread; it determines flat versus frequency-selective fading. Coherence time Tc is the time channel remains constant, inversely related to Doppler spread; it determines slow versus fast fading. Fading types: flat, frequency-selective, fast, slow, plus large-scale shadowing.

## Answer

#### Coherence bandwidth
**Coherence bandwidth (Bc)** is the statistical range of frequencies over which the channel passes all spectral components with approximately equal gain and linear phase. It is inversely proportional to the rms delay spread:

```text
Bc ≈ 1/(50στ)   for 0.9 frequency correlation
Bc ≈ 1/(5στ)    for 0.5 frequency correlation
```
**Significance:** if the signal bandwidth Bs < Bc, the signal sees flat fading with no ISI; if Bs > Bc, it sees frequency selective fading and ISI, so equalizers or OFDM are needed.

#### Coherence time
**Coherence time (Tc)** is the time over which the channel impulse response is essentially invariant. It is inversely proportional to maximum Doppler shift fm = v/λ:

```text
Tc ≈ 9/(16π fm)  ≈ 0.179/fm
Tc ≈ 0.423/fm    (geometric mean rule, used in practice)
```
**Significance:** if the symbol period Ts < Tc, the channel is slow fading; if Ts > Tc, it is fast fading and the signal is distorted. It also sets the spacing needed for time diversity and interleaving.

#### Fading and its types
**Fading** is the rapid variation of the received signal amplitude and phase over short time or distance, caused by constructive and destructive addition of multipath waves and by motion.

**Based on multipath time delay spread:**
1. **Flat fading:** Bs ≪ Bc, Ts ≫ στ. All frequencies fade together, no ISI; spectral shape preserved.
2. **Frequency selective fading:** Bs > Bc, Ts < στ. Different frequencies fade differently; causes ISI.

**Based on Doppler spread:**
3. **Fast fading:** Ts > Tc, Bs < BD. Channel varies within a symbol; time-selective distortion.
4. **Slow fading:** Ts ≪ Tc, Bs ≫ BD. Channel constant over many symbols.

| Type | Condition | Effect |
|---|---|---|
| Flat | Bs ≪ Bc | Gain varies, no ISI |
| Frequency selective | Bs > Bc | ISI, distortion |
| Fast | Ts > Tc | Distortion from Doppler |
| Slow | Ts ≪ Tc | Channel static per symbol |

**Large-scale fading** (shadowing by hills and buildings) is the slower variation of the mean signal over hundreds of wavelengths; it is usually log-normally distributed.

## Check yourself

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

1. If Bs < Bc, the signal experiences:
   A. Frequency selective fading
   B. Flat fading, no ISI
   C. Fast fading
   D. ISI
   Answer: B. The channel gain is nearly constant over the signal bandwidth. (Key point: Bc and flat fading)

2. Which coherence time expression is used in practice?
   A. 0.423/fm
   B. 1/(50 fm)
   C. fm/0.423
   D. 9 fm/16
   Answer: A. Geometric mean rule gives Tc = 0.423/fm. (Key point: Tc rule of thumb)

3. Slow fading means:
   A. Ts << Tc
   B. Ts > Tc
   C. Bs < BD
   D. Bs > Bc
   Answer: A. The channel is static over many symbols. (Key point: Slow vs fast)

4. Large-scale fading (shadowing) is typically distributed:
   A. Rayleigh
   B. Exponentially
   C. Uniformly
   D. Log-normally
   Answer: D. It varies slowly over hundreds of wavelengths. (Key point: Large-scale fading)

## Close variants set in other exams

- [Significance of coherence bandwidth and time](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acoherence-bandwidth-time-significance) — Wireless Communication, chapter 3, asked 3×

## Related in Wireless Communication

- [Coherence bandwidth/time and indoor propagation factors](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acoherence-indoor-propagation-factors) — 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
- [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
- [Large scale path loss and small scale fading](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Alarge-scale-loss-small-fading) — Wireless Communication, chapter 3

## Related in other subjects

- [Path loss in radio wave propagation](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Apath-loss-derivation) — Propagation and Antenna, chapter 5, asked 2×