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I want to work on co-frequency and co-time blind signals separation or carrier-in-carrier signal separation project. In articles published under the heading of blind separation of these signals, it is always assumed that one of the signals is known and the other signal is obtained by using that. I couldn't find an article in which both signals were unknown and separated. This has confused me. Is there anyone who has worked on this and guided me? Is there anyone who has worked on this and guided me?

In telecommunications, Raise-Cosine pulse shaping is used to send information, which according to the Fourier series is a set of sinusoidal and cosine signals. Patent articles indicate that carrier-in-carrier separation is done by using adaptive filter. In this way, the received signal (which is the sum of the first and second signals) enters the filter with one of them and by subtracting it from the received signal, another signal is obtained. Some articles have also pointed out that if the power difference between the two signals is significant, the second signal is obtained by using a trick.

However, various articles have suggested that if the power difference between the two signals is 0 dB, it is possible to obtain both signals blindly and without any of them. Is such a claim true?

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  • $\begingroup$ You have so little knowledge of your thesis topic that you have to start by asking how to construct the signals that are the subject of your thesis? This is worse than the more common "Do my homework for me" questions. At least those type of questions state the problem to be solved whereas this seems to be a "Write my thesis on this topic for me" request! $\endgroup$ Apr 16, 2020 at 16:38
  • $\begingroup$ -1 because this is too broad to post here. Assuming you've read some papers or done some work, is there something specific you're confused about? $\endgroup$
    – Engineer
    Apr 18, 2020 at 12:04
  • $\begingroup$ If you have multiple inputs then it's possible to do source separation assuming some differences in transmission location. That said blind source separation still requires knowing some quality of the signal or signals involved. You can arbitrarily decompose a signal into a sum of two signals anyway you want... $\endgroup$ Apr 19, 2020 at 17:22

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In general this is not an easy task, you would need to have "some" information about the signals (as I illustrate in the example below)

You will have to model the signal sources. Let us say you know that the signal you want to separate out is a sinusoid in white gaussian noise. But you don't know the frequency of the sinusoid and you also do not know the variance of white gaussian noise. The signal model would look like: $$ y(n) = ACos(\omega_on) + w(n)$$ where $\omega_o$ is the unknown frequency and $w(n)$ are samples of IID gaussian noise with mean 0 but unknown varainace $\sigma^2$.

The first task is to estimate these parameters by observing $N$ samples of the signal. Once this is done, the presence or absence of the signal can de decided by a generalized likelihood ratio test (GLRT). You could google it to get more information on how that is done or refer to the book Fundamentals of Estimation/Detection Theory by Stephen M Kay.

Also, once you have estimated $\omega_o$ and $\sigma^2$, you can use an appropriate tool of choice. For ex: the FFT of sinusoidal signal will have distinct peak at $\omega_0$ and $-\omega_o$. Then by just considering the frequency bin corresponding to $\omega_o$ you can do an IFFT to get the time domain sinusoidal signal. Infact for this particular signal model, you could detect the amplitude of the sinusoid as well by looking at FFT. You could ofcourse try to estimate the amplitude of sinusoid as well as part and make it part of the GLRT, but it may not be trivial.

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  • $\begingroup$ -1 because the post is asking about multiple signals. Single sinusoid in noise is chapter 1 of any estimation text and likely not what they're interested in $\endgroup$
    – Engineer
    Apr 18, 2020 at 12:06
  • $\begingroup$ @Engineer I am looking at the experience of the questionee from his question, clearly he is not much into estimation. He is thinking in other terms, if I plunder him with math (as I see people do here with new users) it doesn't help much in my opinion. He will comment if he is looking for more information on the same lines as this approach, then I can add details more. It is very easy for me to add another cosine there describe a vector parameter detection problem , but I don't think that helps him at first . $\endgroup$ Apr 18, 2020 at 12:17
  • $\begingroup$ By the way, GLRT can never be chapter 1 of any estimation/detection book. If it is, better not read that. $\endgroup$ Apr 18, 2020 at 12:19
  • $\begingroup$ That's true, I said estimate parameters of sinusoid in noise is the basics....also, how would you use GLRT to estimate parameters? $\endgroup$
    – Engineer
    Apr 18, 2020 at 12:45
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    $\begingroup$ GLRT is used for detection, so once you have the estiamted parameters, you could put it in the likelihood ratio to decide, whether the sinusoid is present or not. I have made it more explicit in the answer now after seeing the confusion. When I refer to GLRT it assumes that an estimation will happen as a part of it otherwise it's a simple LRT $\endgroup$ Apr 18, 2020 at 12:53

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