If we have a non-linear function $f$, that is applied to input $x$, we have then the output $y=f(x)$
Using Bussgang decomposition we can linearize this nonlinearity and express $y$ as $y=Bx+ η$,
Where B could be found as per the below formula below:
$B= \frac{E(yx^{*})}{E(|x|^2)}$
We can use input pilots at the beginning, so assume we we know $x,y$ and we get $B$, from the just above formula.
Then we obtain $\eta= y-Bx$, and this was for the training phase.
But now for the testing , I already have $B$ that I obtained previously from the training phase, but I don’t have $\eta$ nor $x$, so how can I find back the input $x$?
