A bit confused by the thermal noise spectrum: people say thermal noise is white, i.e., it has same amplitude (power) through the whole frequency spectrum. But it's also said that thermal noise has Gaussian distribution. Isn't this a conflict? Thanks for clarifying this issue.
you did not get it.
AWGN is absolutely white in frequency domain, it does NOT conform to Gaussian distribution.
(in Actually case, noise power will not be infinte and thermal noise is no longer white while the frequency continues to increase, which is the infomation I tried to convey to you)