Assuming the short 3.87mm wavelength is a quarter wave or half wave dipole, that gives either 1.935 Ghz or 3.872 Ghz to excite them.
You're off by 10. A 3.87mm quarter-wave monopole is *19.35* GHz, not 1.935 GHz. Guess how many standards run at 19 GHz and would significantly radiate from such an antenna? Hint: pretty much none.
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Also how short would the radiation distance be for a ~20 GHz signal without a power amp? Like, even with a perfect lossless antenna, that's not going to be above the noise floor an inch from the radiation source.
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