To be more explicit:
1- Down UFO.
2- Disassemble it.
3- Depending on the type of UFO, there is a chance you get an Alien Detection item. Larger UFOs tend to yield more stuff. This is defined in one of the .ufo files.
4- Research Alien Materials, if you haven't already.
5- Research Alien Detection.
Then you can build an Advanced Radar building in a base. It is not an 'upgrade' in the RTS sense, but a new building (and one that does not require the original radar building to operate).
You can work out (and modify, if you like) the research tree by poking in the .ufo files -- the dependencies are there, not hardcoded in some .c file.