AOA board(DWM1002) two antenna distance only 2.0154cm, why no half of wavelength 2.31cm?

That is essentially correct. You carefully measure the system performance and then model it. Maybe it behaves precise enough that a formula works with perhaps a minor fudge factor, as Decawave has done with their PDoA kit. Or maybe you fit a polynomial. Or, since this system has relatively few distinct outputs due to relatively coarse precision, just a lookup table.

The key is that the data has to have a one to one correspondence. If the curve has a dip where that isn’t true, then you have a problem since one input maps to more than one output, now you have ambiguity. The antenna non idealism can easily create that.

Yes, and that was a major effort which ultimately lead to the creation of our antenna positioner along the way since that level of testing is required. We now have an antenna which produces an amazingly flat phase response over arrival angle, while at the same time having a uniform and efficient gain pattern. This is not easy to achieve.

Mike Ciholas, President, Ciholas, Inc
3700 Bell Road, Newburgh, IN 47630 USA
mikec@ciholas.com
+1 812 962 9408