Can I implement a FM Radio Rx on the the Spartan 3E kit?
Starting Problems I am facing-
How do I interface the Antenna with the Spartan 3E kit?
Implementing the A/D converter.
Mirics has a nice chipset for FM SDR that includes the RF front-end, tuner and A/D and exports I/Q samples over USB.
Here's a nice discussion about the part: http://www.reddit.com/r/RTLSDR/comments/2yjhvr/information_on_mirics_chipset_for_general_sdr/
I understand that this product uses the Mirics chip, but I have no experience with it myself: http://sdrplay.com/
You should be able to connect this box to the Spartan FPGA board via USB using their provided drivers for Linux.