between the thickness of the substrate and the radius of pro

What is the relation between the thickness of the substrate and the radius of probe in the case of probe feed to the patch antenna. i.e if the thickness is 1.6mm what should be the radius of the probe?

The radius of the probe should not be related tothe thickness of the substrate. You pick a probe radius in design and then you can use the dimension to simulate it on IE3D/FIDELITY.

I saw some simulation files and I guess they used the probe radius as half of the substrate thickness, I try like that I have better results but not the best. May be the trial and error way can help you.

There is no specific requirement that I am aware of like the 2:1 ratio you cite. I would look at insertion loss and matching as issues to be considered rather than letting the dielectric thickness drive the coax dimensions. If there was a thickness to coax dimensional requirement, what would happen as the dielectric constant changed?