Since a UWB signal is noise-like, you cannot measure any phase shift. However, you can measure time delay (in your case 6 ns which may not be too precise as the fastest logic I know of ECLiPSE is 100 ps reaction time.
If you do use a single frequency signal, you can do what was done around 1920-1930 and known as a Radio Altimeter. A swept frequency signal was beamed to the ground and the return signal was mixed with a low power version of the transmitted signal. The time delay and the sweep rate an the distance would cause an audio tone output from the mixing. The audio frequency was related to the altitude.
As William Shakespeare (a few hundred years ago), Who was quoting King Solomon (a few thousand years ago), who was quoting who knows who, said "There is nothing new under the sun."