If you ask is something is hard on a FPGA then it will be very hard. Everything is hard on FPGA unless you have the code hanging around from earlier, what you can do in seconds on a CPU you will spend days on to do on a FPGA. Even getting the data in and out of the chip is a huge problem compared to a PC or a microcontroller.
What about searching for linear feedback registers with specific properties. A modern PC is about the same speed (200MHz) as a FPGA when running a simple LFSR but a FPGA can run many at the same time.
A proper radio is going to take months or years unless you have very special skills.