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I have data blocks being received at a node which can be presumed to be Gaussian sequence, $X(m_1,sigma_1).$ In some of the blocks a separate Gaussian stream $Y(m_2,sigma_2)$ adds to the original stream and intended receiver gets a mixture.

  1. I am interested in figuring out if the block I am receiving is with or without external mix.

The issue is $m_1$ and $sigma_1$ and $m_2$ and $sigma_2$ are not known a priori. Can Gaussian Mixture Classifier help?

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This isn't really a case of a mixture, but of a random effect. One of the signals will be the "pure" gaussian sequence: $X(m_1,\sigma_1)$, the second will be the gaussian signal: $X(m_1+m_2,\sqrt{\sigma_1+\sigma_2})$.

You are adding two random inputs in the second case, not randomly selecting which sequence generates the signal (this would be a case of a mixture). Since the pure signal will have less variance than the noisy signal, you can test if a signal is getting noise by testing the variance of the signal.

A simple test would be to classify the blocks into two groups based on their variance.

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  • $\begingroup$ Replace $\sqrt{\sigma_1+\sigma_2}$ by $\sqrt{\sigma_1^2+\sigma_2^2}$. $\endgroup$ – Did Feb 26 '15 at 10:56

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