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

# Significance of coherence bandwidth and time

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

- Asked in: 2077 Chaitra, 4 marks; 2073 Magh, 4 marks (asked 2 times)
- Video: [What are Coherence Bandwidth and Coherence Time?](https://www.youtube.com/watch?v=bNMsizyWnK0) — Iain Explains Signals, Systems, and Digital Comms
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/coherence-bandwidth-time-significance
- 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.

## Short answer

Coherence bandwidth Bc is the frequency range over which channel is flat, inversely related to delay spread; if signal bandwidth exceeds Bc, frequency-selective fading and ISI occur. Coherence time Tc is the duration over which channel is unchanged, inversely related to Doppler spread; if symbol period exceeds Tc, fast fading occurs.

## Answer

#### Coherence bandwidth (Bc)
**Coherence bandwidth** is the range of frequencies over which the channel can be considered "flat", i.e. it passes all spectral components with nearly equal gain and linear phase. Two sinusoids separated by less than Bc have strongly correlated amplitudes.

It is inversely proportional to the rms delay spread στ:

```text
Bc ≈ 1/(50στ)   (correlation ≥ 0.9)
Bc ≈ 1/(5στ)    (correlation ≥ 0.5)
```

**Significance:**
- If signal bandwidth Bs < Bc: **flat fading**, no ISI, simple receiver.
- If Bs > Bc: **frequency selective fading**, causing ISI; equalizers, RAKE receivers or OFDM are needed.
- It sets the maximum symbol rate without equalization and the frequency spacing needed for frequency diversity.

#### Coherence time (Tc)
**Coherence time** is the time duration over which the channel impulse response is essentially unchanged. Two signals received within Tc have strongly correlated amplitudes. It is the time-domain dual of Doppler spread:

```text
Tc ≈ 1/fm
Tc ≈ 9/(16π fm) ≈ 0.179/fm   (correlation 0.5)
Tc ≈ √(9/(16π)) / fm = 0.423/fm  (common rule)
fm = v/λ (maximum Doppler shift)
```

**Significance:**
- If symbol period Ts < Tc: **slow fading**, channel constant over a symbol.
- If Ts > Tc: **fast fading**, the channel changes within a symbol and the signal is distorted.
- It sets the time spacing for time diversity and interleaving depth, and how often channel estimates must be updated.

**Example:** v = 60 mph (26.82 m/s), fc = 1900 MHz → fm = 169.8 Hz, Tc = 0.423/169.8 ≈ 2.5 ms. A symbol rate above about 1/Tc = 400 symbols/s avoids distortion from motion.

## Check yourself

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

1. Coherence bandwidth is inversely related to:
   A. Symbol rate
   B. Mobile speed
   C. Doppler spread
   D. RMS delay spread
   Answer: D. Bc ~ 1/(5 sigma_tau) for 0.5 correlation. (Key point: Coherence bandwidth)

2. If signal bandwidth exceeds Bc, the channel is:
   A. Flat fading
   B. Distortionless
   C. Slow fading
   D. Frequency selective with ISI
   Answer: D. Equalizers, RAKE or OFDM are needed. (Key point: Bs vs Bc)

3. Coherence time is approximately:
   A. Equal to delay spread
   B. 1/fm, inversely related to Doppler shift
   C. Independent of speed
   D. Proportional to fm
   Answer: B. Tc is the time-domain dual of Doppler spread. (Key point: Coherence time)

4. If symbol period exceeds Tc, the channel is:
   A. Fast fading
   B. Slow fading
   C. Static
   D. Flat only
   Answer: A. The channel changes within a symbol, causing distortion. (Key point: Ts vs Tc)

## Close variants set in other exams

- [Coherence bandwidth/time and types of fading](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acoherence-significance-fading-types) — 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
- [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
- [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
- [Short note: Doppler spread and coherence time](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adoppler-spread-coherence-time-note) — 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×