How could I add ~ 1 GHz frequency voltage noise of random intensity to a circuit?
You can buy commercial RF noise generator (I've used one made by "Noise Com").

Or you can grab a noise generator off of eBay like https://www.ebay.com/itm/172241109978.

To couple the signal in, use a choke in series with the DC supply and a capacitor to couple the noise signal in.