What is the current state of research on Autonomous Air Traffic Control?
Do you mean air to air? Or were you thinking of a ground system? What sort of traffic density?

If the former there are a number of concepts within the big medernisation programs like US NextGen, EU SESAR, Australian OneSky or Japan's CARATS programs.

ICAO has a global roadmap running to 2040.

VHF datalink mode 2 is up and running now, higher bandwidth satcom comming (Inmarsat SB-S/ Iris). VOIP likely to have some interesting latency effects in airspaces eith high R/T loads.

Significant global safety spectrum, ITU, regulatory, standardisation and other institutional and political challenges stand before a cool tech idea.  

For spectrum look within current band allocations.

Aviation is generally incremental. Bear in mind thst your tech needs to be robust, globally portable.

If you can develop a regulstir accepted method to assure AI or ML apps then this would be a fertlle and lucrative area.