I don't understand how to get function Ui(t) in Equation (1) from this article.
I can convert S21 data to time domain data with time domain option of VNA.
I suppose I can get Ui(t) from this time domain data.
But I don't know the detailed means.
You can export thr s12 ampltude and phase (in matlab for exemple), one sample for position of the antenna, and then you can use the FFT on complex S12 data.