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The versions of NEC that the public can afford and be allowed to use only have wires and lumped impedances (no surfaces). You are going to have trouble with the coaxial structure. My only suggestion is to approximate the outer conductors of the coax with many parallel wires runnning the length and connected by perpendicualr wires (like hoops around the circumfrence) at the ends and possibly several points down the length.
Another problem with NEC is wires too close together. This may keep the coax from being accurately modeled.
You may be stuck having to use some more complex 3D type simulator.
It looks like there is a phase reversal problem with the null down the center. I assume that the physical measurements say that there is no null.
Your NEC model does not have the connection of the center of each element to the reflecting plane. First put those in and rerun the simulation.
If you still have the null problem, try simulating a subset of the driven elements and first use just one of the four driven elements. Look for the null. If it is there this is your problem Next do two elements that are end to end. Look for the null. If it is there, reverse the phase of one of the driving voltage generators.
Your suggestions help me to realise that I made mistake in process of modelling. I created a lower pair of dipoles as reflection of the upper pair. If you reflect dipoles, they are rotated as well and this is not appropriate way in this case.
TRANSLATE option must be used instead REFLECT option, in SuperNEC. Now, radiation pattern is similar as it is in Kathrein catalogue. The only problem seems to be gain issue, because gain value it is about 2 dBd lower then it is noticed in the catalogue.
You might try putting more grid lines in the sheet to see if the lost 2 dB of gain comes back. Another thing to check is if the reflecting sheet is the same size as the one in your simulation. You might try an experiment where in your simulation you increase the size of the reflector. Finally, measure your physical antenna and the commercial one. They may have been overoptimistic in selecting numbers to put on their data sheet.