# coherence bandwidth
The frequency domain equivalent of [delay spread](Delay%20spread.md)
The characteristic of the channel.
Not affected by the signal characteristics.
[delay profile](delay%20profile.md)
## Equation
If frequency [correlation coefficient](correlation%20coefficient.md) is above 0.9, the coherence [bandwidth](Bandwidth.md) can be approximated as:
$B_c\approx \frac{1}{50\sigma_\tau}$
If the correlation is above 0.5, the coherence [bandwidth](Bandwidth.md) can be approximated by $B_c\approx \frac{1}{5\sigma_\tau}$
## What do we need to know?
The signal [bandwidth](Bandwidth.md).
We can then compare this with the coherence [bandwidth](Bandwidth.md).
$B_{signal}\ vs. B_C$

>[! note]
> If $B_{signal} << B_C$ then all frequencies within the signal are attenuated equally and we have no delay effects. This is called flat fading. Different attenuation in the frequency domain leads to different attenuation and delays in the time domain.

If $B_{signal} >>B_C$
Moving to the time domain, we get multiple copies of the same signal, with different delays and attenuation.

[Frequency selective fading](Frequency%20selective%20fading.md) implies [multipath](Multipath%20Fading.md)!
## Rough guide
The symbol bandwidth is roughly 1/symbol width in time!
## Statistical Definition
### Verbose Method
1. Find channel amplitude probability distribution function as a function of frequency
2. Find the correlation function between the two frequencies
3. Integrate over one of these frequencies to express the correlation coefficient $\rho$ in terms of the frequency separation $\Delta f$
For instance, 50% coherence bandwidth is a frequency separation such that $\rho > 0.5$.
### Simplified Explanation
Consider that within the coherence bandwidth, the channel gain is flat (easier to understand, not necessarily true!)
# References
1.
# Footnotes
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