What is the noise whitening process? I came across this process when working on OFDM in wireless communication. It's mentioned if we have two copies of a signal resulted from SIMO system (Single Rx Multiple Tx), we can process the noise whitening, after the FFT, in order to improve the quality of the signal. 

What does mean the noise whitening, and what's its process? 

Here is an example,  in the paper.

After taking the DFT in OFDM, we supposed to get frequency response, so how w[k] is obtained?
Consider a WSS (wide sense stationary) discrete-time random process (RP) with i.i.d. samples $X[n,s]$ whose auto-correlation sequence (ACF function) is $\phi_{XX}[m]$. We call a random process as white-noise if its ACF is the following:

$$ \phi_{XX}[m] = \begin{cases} 
{\sigma_X^2 ~~~~~, \text{ for } m=0 \\ 0 ~~~~~~~~, \text{ otherwise} }\end{cases} $$ 

This also means that the RP is uncorrelated. If a RP does not have this property then it's a colored noise. And it means its samples are correlated.

When a RP is colored, it may be possible to find an LTI filter which will try to remove the correlation between the samples of the noise and hence make it whitened. Such a filter is called either as a decorrelator or equivalently as whitening filter.

It's best described in the context of AR-p (Auto-Regressive) random processes generation through all pole filtering, where the whitening filter will be the inverse of that all-pole AR filter which generates the colored noise from an input white noise.