Fast/Slow Fading: How are doppler shift and coherence time related?

In the literature I've read that fast fading happens if the bit duration is larger than the coherence time of the channel.

The coherence time of a channel is proportional to $$\frac{1}{f_{Doppler}}$$. So coherence time and doppler spread are related somehow. Why do frequency shifts determine the time span for which the channel coefficients are constant, e.g. is there any physical meaning of this relation? Is there any intuitive explanation?

Here's an intuitive explanation.

Imagine a communication system (wireless) in a static environment (maybe picture the inside of a closed warehouse). There will be an amount of fading, but it is static: it never changes, because the channel doesn't change.

For the channel to change, the multipath scenario must change, and that means that objects must move around (it can be the reflectors/scatterers, the antennas, or both). If they move relatively slowly, you have "slow" fading; if they move relatively quickly, the fading becomes "fast".

Now, whenever you mix waves and moving objects, you get Doppler shifts. Furthermore, the faster the movement, the higher the Doppler. In consequence, you can measure how fast the channel is changing by either measuring how fast the objects are moving, or by how large the Doppler is.

Since the Doppler shift is easy to quantify, it is the preferred way to measure how fast a fading channel is changing.

• Thank you. But is the fast changing of a channel caused by the movement or by the doppler shift itself? If I move with my mobile device around and I have a magical tool which can compensate the doppler shift to zero, so that I get v>0 but f_doppler=0. Would I get a coherence time equal to zero or isn't it directly coupled to the doppler shift? Commented Aug 25, 2020 at 13:49
• They are closely interrelated. Movement causes Doppler, and Doppler implies movement. Now, the receiver is obviously unaware of scatters/reflectors moving; the effect that the receiver perceives is Doppler only. If you could magically revert the Doppler shifts in the signal, you could convert a fast fading channel into a slow fading one (the coherence time would be large).
– MBaz
Commented Aug 25, 2020 at 15:43