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Hi, what kind of antenna parameters do you want to test?
I think if you just want to measure the return loss (S11) or VSWR, then Network Analyzer is the only equipment you need. You just need to calibrate 1-port measurement of VNA, and then directly connect the VNA to your antenna, and read the S11 or VSWR from VNA.
If you want to measure the radiation pattern or Gain/directivity/efficiency, I think you need a Anechoic Chamber, a standard (reference) antenna and a motor to move the antennas... That need more sophisticated setup and maybe you can find some useful information from google.
For the S11, keep in mind that proximity effects will affect the antenna patterns and thus the impedance (this depends on antenna type, frequency, etc.).
For the patterns, gain, directivity, etc there are some 4 different techniques (freespace/open-range or chamber, reflection range / open or chamber, compact range w corrections for reflections). ARRL has some good articles on this.
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