I simulated the coupling between the patch antenna arrays, and I found that the coupling varies when i change the height of the air box. the difference at most by 5dB. the height of airbox change from 1/3 wavelength to one wavelength, using the rad boundary. I want to know how to get more realistic results?It's a quarter wavelength or a wavelength
Based on the Tags on your question I assume, that you use Ansys HFSS. I generally use 0.5 lambda (lowest frequency in the sweep) for my air box (distance from object to air box end). I always use a parameter to set the dimension of the box. This allows me to run a simulation, copy the trace and then verify that a larger air box does not change the result with an additional simulation. In general making your air box larger should not really affect your results after a certain threshold length. Maybe you should also check your port definition. Are you using modal or lumped ports?
Martin Obermaier is correct. HFSS help manual recommends the radiation boundary be "located at least a quarter wavelength from the radiating source", of course at the lowest frequency. Martin's suggestion of 0.5*lambda is on the safe side.
Your question is not easy because it depend on boundary condition and the mod of excitation or the model of propagation
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