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[oneginee]

I am struggling to understand what should be the goal for s11, s12, s22, s21 scattering parameters in a receiving (only, not transmitting) antenna array made of two antennas.

First let me take a step back and consider one antenna only. Then the only parameter is s11. In order to minimize loss from impedance mismatch we need to achieve s11=0. This can be done by antenna geometry design or using a discrete elements matching network.

In the two antennas case mutual coupling between the two antennas will be significant in practical cases (certainly for 0.5 lambda spacing and still at spacing an order of magnitude bigger). That means s12 and s21 are non zero and you have to live with that. That is fine. Now assuming you have some degrees of freedom in antenna geometry design to change s11 (but spacing between antennas is fixed), and you can use matching networks, how do you achieve impedance matching at both ports ?

I assume {s11=0, s22=0} isn't the correct answer anymore ? (or is it)
What relation between s11 and s12 should be satisfied (assuming s11=s22 and s12=s21) ?

How to look at this problem ?