I have seen such projects - real LTE PHY algorithms are much more complex than stuff in 3GPP. You can write something 3GPP compliant in some simplified cases, but it would be totally useless in real network.

Secondly you don't really want to use FPGA for majority DSP processing in LTE PHY. Design cycles on FPGA are too slow and HLS techniques are still not trusted. Beside that x86+fpga are some kind of specialized stuff - you could just put a PCIe accelerator with some major wireless SoC.