Ideally this would be just signal a simple A-to-D (Analog to Digital) conversion then at the antenna a D-to-A conversion. That's not tractable however. The limitations of digital hardware prevent the reception of radio signals between 10 kHz and 2.4 GHz. That's not a small piece of RF real estate. One of the first software radios was an American military project named SpeakEasy. Of course things being what they are, there is also a competing open source project as well.
Speakeasy had Two phases:
1. A radio for the U.S. Army to operate between 2Mhz and 2Ghz. It was to operate with both VHF, FM, QAM, SSB and Combat Voice and data channels. In 1997 an operable version was demonstrated at a big brass hoe-down called Force XXI.
2. Same as above but more quickly reconfigurable for different bands and standards. 15 months into the project they had a working demo which was sent into production with a reduced 4 MHz to 400 MHz range.
So that's the excitement, they were a dream 10 years ago and now are a reality ...sort of. It's an interesting progression and I've never seen a working model myself but the GNU makes for interesting reading even if the optimistic parts read like sci-fi.