power waves and scattering matrix
However from what I understand, in the more general case it is
possible to assume a normalization impedance different from that
characteristic of the transmission line connected to the considered
port.

That doesn't sound useful or right.
If you don't use the same impedance of the transmission line (\$Z_0\$) you can't properly define reflections based on reflection coefficient (\$\Gamma\$): -
$$\Gamma = \dfrac{Z_L - Z_0}{Z_L + Z_0}$$
And this means you can't define standing wave ratio: -
$$SWR = \dfrac{1 + |\Gamma|}{1 - |\Gamma|}$$
And you can't define return loss: -
$$RL = -20\log_{10}(|\Gamma|)$$
I'm at a loss to think how using a non-\$Z_0\$ value has any significant use or merit. I've been wrong before of course!