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Is it possible to calculate the SNR from finite duration time-domain samples that contain the received signal, $y(t)$, where:

$$ y(t) = x(t) + n(t) $$ and $x(t) =$ transmitted signal, and $n(t) =$ AWGN noise

The signal $y(t)$ is complex baseband, filtered and resampled at Nyquist. The question here is, can the $\mathbb{E}\big[n(t)\big]$ be calculated from the finite number of samples that contain the energy of the signal?

note: this question addresses how to do it if you have periods of time where the signal is not transmitting: SNR calculation

Engineer
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BigBrownBear00
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  • Do you have any assumptions about $x(t)$ or $n(t)$? – Engineer Sep 02 '20 at 14:41
  • @Engineer not particularly? What did you have in mind? – BigBrownBear00 Sep 02 '20 at 15:10
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    For this kind of question, we need to use some a priori information in order to separate (at least partly) the signal from the noise. Ideally, we know the signal. If not, we may know it corresponds to a given finite alphabet, or that the signal bandwidth is limited. – Damien Sep 02 '20 at 15:57
  • Yes the signal bandwidth is limited. The following are known about the signal are: duration, bandwidth, start time of signal, and sample rate. No a-priori symbols/pilots/preamble to use for this question. – BigBrownBear00 Sep 02 '20 at 16:04
  • Do you know if $n(t)$ is zero mean noise? – Engineer Sep 02 '20 at 17:31
  • @Engineer I'm not sure if it's zero mean b/c there is a receiver with AGC. That would change the mean of the noise figure right? – BigBrownBear00 Sep 02 '20 at 18:07

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