The meaning of Cross and Auto Correlation Matrices
The cross-correlation between i and f is maximum when f has the same shape than i but can be shifted in time.

I believe that this is what you want here:
You want your feedback f to look like your input signal i but since it has propagated in your circuit it can be shifted in time.

So when you are trying to adjust the shape of f to the one of i i.e. i(t) ~ f(t-T), basically what you want is to adjust f such as i*i ~i*f.