Osmocom Cellular Network Infrastructure
osmocom.org
osmocom.org
But yes, this is already possible, in fact, Osmocom has a fully open baseband running on certain phone chipsets.
- srsLTE (https://www.srslte.com/)
- OpenAirInterface (https://www.openairinterface.org/)
I've successfully used srsENB as a base station, largely to generate "model" LTE waveforms so that I could then decode them and verify my understanding. srsLTE is quite well written code-wise and is actively improving/growing. Seems to have a supportive single company and community behind it.
OpenAirInterface is more geared towards 5G research and is a lot more ad-hoc in terms of documentation and capabilities.