I'm looking for the method to calculate theoretical similarity of two random noises $x$ and $y$ with mean $0$ and standard deviation $1$, I've got also $12500$ samples of signal, sampled $2.5$ Ga/s.
Due to my idea I wanted calculate the probability that the two noises have coherence $$C_{xy}(f)=\frac{|G(f)_{xy}|^2}{G(f)_{xx}G(f)_{yy}}$$ higher than $0.5$ in frequency range $2$-$20\mathrm{MHz}$? I wanted to compare it with experimental result. I found probably the answer to my question: Statistical significance of coherence values. How to do this for my signal? How $\alpha$ coefficient in this link was calculated?