Practicality of the assumption of i.i.d. for Rayleigh channels I would like to understand how far the assumption of having i.i.d. is accurate/valid (from the practical point of view) when an OFDM system is working in Rayleigh channels. Is this means the channel has to encounter flat and slow fading? If not, under what conditions, the assumption of i.i.d. can be considered practically acceptable?

Any hints?
I am a little late but I post my answer anyway so that someone having the same question will find it interesting and discuss.

The discrete baseband multipath channel can be modeled as a FIR, i.e. 
$$y[n] = \sum_{l=0}^{L-1} x[n-l] h_l + w[n]$$
where $L$ is the number of channel taps. $L$ depends on the relation between the bandwidth of basis waveform and the delay spread of channel.

The term "Rayleigh fading" channel implies that the channel taps $h_l$ can be modeled as i.i.d circular symmetric Gaussian complex random variables because :


$h_l$ is the sum of a large number of small independent circular symmetric random variables, each random variable is channel of a physical path. This the rich scattering assumption, which is typically vaid for urban environment.
there is not a particular path having gain much significant than others. Otherwise, we have Rician fading.


Let me call this random variables "Rayleigh".

With a sufficient cyclic prefix ("sufficient" means greater than delay spread, thus OFDM receiver captures all delayed versions of OFDM symbol, proof can be found at single-tap OFDM regardless subcarrier spacing), the demodulated data at subcarrier $k$ is
$$z[k] = x[k] \times \sum_{l=0}^{L-1}h_l e^{-j2\pi \frac{l}{N} k} = x[k] \times H[k]$$
where $N$ is DFT size.

The channel taps $h_l$ are i.i.d circular symmetric Gaussian random variables, $H[k]$ are circular symmetric Gaussian random variables, but they are in general not iid.

As pointed out by Maximilian Matthé in the comment, the covariance matrix is   $F \mathrm{diag}(\vec{p}_0) F^H$ where $\vec{p}_0$ is Power Delay Profile zero-padded to size $N$. The frequency bins at $k = u \times N/L, u \in \mathbb{N}$ are independent, if $N/L$ is integer. Other ones are sinc-interpolated thus they are correlated. Note that $N/L \times \Delta f = 1 / L T_s \approx 1/\tau_m$ can be seen as coherence bandwidth.