I don't entirely understand the problem being solved, either. I've never used a noise bridge and had to google it, and I may have gotten it wrong: Is it the case that you're trying to generate noise with a spectrum extending to, say, HF or VHF in an attempt to tune an antenna?
Ordinarily, a semiconductor junction can be used as a wideband noise source. It would be very unusual to do it with a LFSR for RF use.
Incidentally, the more usual 'offline' approach to measure impedance is to use a vector network analyzer VNA); it doesn't rely on any noise source. Nowadays, they can be quite low-cost (sub-$100), e.g. see 'NanoVNA'.
If your aim is to adjust your antenna tuner all connected up, then slightly cruder non-vector methods can be used; simply, measure the reflected signal during a very short burst of transmission (done with a bridge or directional coupler type of device). Ordinarily, this would all be automated (i.e., the antenna tuner components would either be electrically adjustable or switched in rapidly using relays under microcontroller control). This is a very effective and tried-and-tested method.