UWB signals - upconvertion and downconversion question

Hi,

Assuming one generates a UWB signal through a pulse generator.

This UWB signal will have a 0 (DC) - fMax signal bandwidth which normally gets upconverted to a higher carrier fC through the use of mixers. After that it's sent through UWB antennas/etc. So the signal bandwidth that is sent will be fC to fC + fMax for example...

Once received the signal is downconverted through a mixer back to its original 0 - fMax bandwidth where it is processed.

One question that comes up is -- the signal that is propagating has specific frequency components in the fC to fC + fMax band. It has different wavelengths/etc. and might exhibit different propagation characteristics than the signal which was 0 - fMax. As such, once downconverted back to its original bandwidth, how does this signal retain any information of the medium it was transmitted through?

Any good references that explain this for UWB and through math or through example?

Thanks!