I am currently reading up on and teaching myself ICA from a number of good sources. (Also see this post for past context). I have the basic jist down, but there is something I am not clear about.
For a scenario where multiple signals are impinging on multiple spatial sensors, (of course, with number of sensors >= number of signals), it is inevitable that for any one sensor, all the signals arriving to it will have different delays/phase-offsets associated with them, as compared to those arriving at a different sensor.
Now, as far as I know, the signal model for ICA is a simple mixing matrix, where the total energy arriving at any one sensor is modeled as nothing but a simple linear combination of all the other signals of interest. Every sensor has a different array of linear combination coefficients associated with it. So far so good.
What I do not understand, is that inevitably there are going to in fact be some delay/phase-offset among individual signals arriving at individual sensors that differ from one another. That is, $s_1(n)$ might arrive at $sensor_1$ at some time 0s, while that same $s_1(n)$ arrives at $sensor_2$ attenuated, but also at some delay or phase difference. The way I see it this is physically inevitable.
...How can it be that this is not modeled in the mixing matrix? It seems that delays will make a huge difference. No longer are we talking about simple linear combinations anymore. How does ICA handle this? Have I missed something here?
I should also add as an addendum, if indeed ICA cannot handle delays, then what applications does it find usefulness in? Clearly spatial ones with sensors are out!