Most software defined radio peripherals involve a FPGA. In designing a SDR peripheral, I would like to know whether its possible to design a GNU Radio Compatible SDR hardware peripheral without any FPGAs. i.e. Directly sending the output from the ADCs to a PC via USB. If possible, I think My interest to eliminate FPGAs (at some other cost) is because FPGA soldering, design is a difficult process that is not properly explained by most vendors. If there is a way I could eliminate them from my design it will be great. My interest is to design something similar to this.
In the above image I found from TI, is it possible that we directly connect the output of the ADC to the to the PC via some sort of a USB connection? Perhaps, transmission is possible this way as well.
I would also like to know the exact purpose(s) of using FPGAs in SDR peripheral designs. Im sure there may be many. But I would like to know the most imperative ones.
UPDATE:
As suggested by Neil_UK in the answers section, if the limitation is not being able to transmit the raw ADC samples via a USB interface to the PC due to slowness in USB speed, What would be the highest practical bandwidth that we could have in a system that directly connects the ADC to a USB? perhaps a USB 3.0? is it only the bandwidth that will be limited by this decision? What other fundamental features would go missing if SDRs were desiged this way? (provided its not required to operate on signals e.g. demodulate them)