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I detail the relationship below, but if this isn't at all clear, please proceed to the bottom with related links, references and background information that should further help this all make sense.

Doppler Spread is not avoided, but equalized in the receiver assuming a sufficiently long cyclic prefix to capture the related delay spread, and that the resulting fading is reduced to flat fading due to the relatively long OFDM symbols so that a "single tap equalizer" is essentially used on each bin in the receiver. So to answer this post specifically, the key requirement is the length of the CP exceeds the expected delay spread, and the bandwidth of each subcarrier is less than the coherence bandwidth of the channel.

I detail the relationship between ICI and frequency offset below, but if this isn't at all clear, please proceed to the bottom with related links, references and background information that should further help this all make sense.

As Marcus mentioned in the comments under the original question, this is complicated with lots to understand. Thankfully, the framework is already here with other posts to at least pursue Marcus' suggestion: start with understanding the simpler case of a fixed frequency offset (due to Doppler from a fixed velocity between transmitter and receiver as well as the inevitable frequency offset between independent transmitter and receiver clocks). The result of this will both be easier to show and best introduce the relationship between frequency offset and Intercarrier Interference (ICI) with OFDM modulation.

As Marcus mentioned in the comments under the original question, this is complicated with lots to understand. Thankfully, the framework is already here with other posts to at least pursue Marcus' suggestion: start with understanding the simpler case of a fixed frequency offset (due to Doppler from a fixed velocity between transmitter and receiver as well as the inevitable frequency offset between independent transmitter and receiver clocks). The result of this will both be easier to show and best introduce the relationship between frequency offset and Intercarrier Interference (ICI) with OFDM modulation. I close with the further details to consider when going from "ICI" to "Doppler Spread".

With the signal component reduced according to:

To understand how this then results in ICI, we note as further detailed in the references below that each bin of the DFT has a frequency response given by the Dirichlet Kernel (approaching a Sinc function as the number of DFT bins gets large, and can be described as an "aliased Sinc function"). The Dirichlet Kernel has a magnitude that is given as:

(Since we will be doing power combining due to the assumption of independent and changing data in each sub-carrier, we need only be concerned with the magnitude response).

With the signal power component reduced according to:

This is the expected SNR due to the effects of ICI alone at a frequency offset $k$, where $k$ is the normalized frequency in units of the subcarrier spacing. (For example if we had a subcarrier spacing of 78.125 KHz, and a frequency offset of 100 Hz, $k = 100/78125 = 1.28E-3$).

To understand how this then results in ICI, we will use the magnitude response of each bin in the DFT. We note as further detailed in the references below that each bin of the DFT has a magnitude frequency response given by the Dirichlet Kernel (approaching a Sinc function as the number of DFT bins gets large, and can be described as an "aliased Sinc function"). The Dirichlet Kernel has a magnitude that is given as: