Gaussian noise with different SNR levels are usually used in research works to simulate a realistic environment. How can researchers guarantee that Gaussian noise can simulate the reality of a System?
Answer
Gaussian is a very good assumption for every process or system that's subject to the Central Limit Theorem. See http://en.wikipedia.org/wiki/Central_limit_theorem
What this means is that when gaussian random variables are added, the result is gaussian (so you can apply similar statistics after the addition as were before), and besides that, when any random variables (that have finite variance, so Cauchy r.v. does not apply) are added, they tend to become more gaussian in their p.d.f. as you add 'em up.
What's also very cool about the "normalized" gaussian function, $e^{-\pi t^2}$ is that its Fourier transform is exactly the same: $$\mathcal{F}\left\{e^{-\pi t^2}\right\}=e^{-\pi f^2}$$ that sometimes makes the math fun and easy. Regarding the gaussian p.d.f., that means the corresponding characteristic function is also gaussian. And when you add random variables, you convolve their p.d.f.'s and that means you multiply their characteristic functions. When you multiply two gaussians, what then do you get?
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