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My first inclination when thinking about the Cocktail Party Problem would be to use adaptive beamforming to isolate different signals, but this does not seem to be how the problem is commonly thought about. Indeed, basic ICA assumes the signals all arrive at the sensor array at the same time (instantaneous mixing), and breaks down when there are significant delays (see this question for example).

So what is the relationship between these two approaches? Could they be combined in some way? I know there may not be a definitive answer to this right now, so partial answers/insights are welcome.

Second question: What defines a delay that is too big for ICA to handle? Is it relative to the sample rate, or the wavelength?

Edit for question 2

I assume ICA will break for a delay of $\lambda /2$ ($\lambda$ is the wavelength), but will ICA work for delays significantly less than that, or is a 1 sample delay between two sensors enough to foil ICA? How brittle is it?

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  • $\begingroup$ What's ICA in this context? $\endgroup$
    – Ben
    Commented May 12, 2022 at 20:57
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    $\begingroup$ @Ben, my apologies, it's Independent Component Analysis. I'll make that clear in the question. Thanks for pointing that out! $\endgroup$
    – Gillespie
    Commented May 12, 2022 at 21:25

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For question 1, Could they be combined in some way?, a couple of pointers:

For question 2, What defines a delay that is too big. I think little answer can be provided without infomration on source, signals's dynamics, etc. A couple of references:

With that, do you have the possibility to reframe the question with more hypotheses? (nature of the array, expected delays, etc.)

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    $\begingroup$ Thanks for the answer Laurent! I'll look more carefully at those references when I get time. I don't have a specific array geometry in mind, so the question is a little more general. If the signal delay between two array elements is $\lambda /2$, I know ICA will fail. The question is, does it fail for delays significantly less than that. I don't know enough about the precise assumptions of the ICA model to say if a 1 sample delay breaks it, or if you need delays on the order of the wavelength to break it. $\endgroup$
    – Gillespie
    Commented Aug 29, 2022 at 13:10

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