The approach is to divide the GPR system into its component functional parts, and do a search for those
parts, instead of searching for the system itself which did not turn up a lot of useful information. That's why I listed those 5 things in my last post. So taking number 1, the signal generator, there is a simple circuit you could build at: http://www.holmea.demon.co.uk/Avalanche/Avalanche.htm
It looks like a well written article and the circuit looks like it will work. There are ways to speed up the pulse by adding step recovery diodes, optimizing the device type, etc., to get the spectrum into the GHz range. This article is instructive also because he was building it for use as a Time Domain Reflectometer (TDR). This shows the similarity between a TDR and ground penetrating radar. The TDR includes a very fast scope to look at the reflections in the time domain. In fact if you attach a TDR to an antenna matched to the ground, and look for reflections. you have about 90 percent of the GPR hardware built.