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The mutual coupling will have the greatest effects on input impedance. The coupling will be least for certain spacings of the elements. The mutual impedance can be broken into real and imaginary parts that cycle and decline as the separation increases. They are out of phase by about a quarter wave.
At a quarter wave the mutual impedance is 30 -j40. at a half it is -12 -j30. At 1.1 wave it is 10 +j10.
I dont think that nec or any other code accounts for the mismatch occurring when scanning the antenna beam (scan blindness). I suggest you to read the papers of Pozar (and others) on the scan blindness phenomena and make your own code neglecting coupling. If it is not too strong (<25dB) in practice most people neglects the coupling effects. Of course you should address and confirm that couplings are low enough
I agree with you that if couplings can be taken into account the fabricated antenna would be much more similar to the synthesized one.
However take into account the following
1) an antenna design with low sidelobes requires many elements in the array, and if the coupling terms are considered, the problem maybe almost imposible to solve (just in terms of computing resources)
2) in a low sidelobe antenna the excitation errors/uncertainties maybe much more important than coupling terms
3) ideally the synthesis should be done with embedded element patterns (measured to be realistic), which already account for the effect of the coupling, estructure, edge effects,..., although unfortunately implies that you have to build the antenna before
4) many text books (antenna handbook by Lo, microwave scanning antennas by Hansen,...) already include element excitations for low sidelobe array which do not account for coupling and are good starting points for the synthesis
I agree with you that it is better include the couplings, but there are many more effects that should be also taken into account that it is almost impossible to cope all of them. I'm afraid that we still have to wait for a software tool which definitely solves all our problems.
Here is one method of reducing coupling. Start with a pair of elements and phase and space them so that there is a null in the plane of the elements. Use these element pairs as new elements in an array. Since the element pairs do not put energy in the direction of the others, they will couple less.
If you have a two dimensional array, you do pairs of pairs to get the nulls in all directions of the plane before building up the whole antenna array.
I must say that it is the most important thing to know coupling coefficent in designing a lower sidelobe antenna. Let me tell you what I have done before. We need not conside all element in you simulation, just two of them, change the position of elements, you can get their coupling coefficent. then you can synthisis an antenna distribution according taylor or other distribution function. we built a conformal array with -40 db sidelobe some years ago, measurment proves this way is possible.