How does ICA handle inevitable delays in signals? 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! 

Thanks
One of the most successful uses of ICA has been in the study of electrophysiology (i.e. brain activity), principally EEG (Electroencephalography) and MEG (Magnetoencephalography). They are used to remove artefacts (such as electrical impulses caused by muscle movements (eye blinks etc)) without the need for reference channels. In this application the spatial separations between sensors is minute compared with the propagation speed of the waves, and as such the assumptions of ICA effectively hold. 

For fMRI, which relies on blood flow in the brain, the temporal delay issue is more significant. One approach, taken in the paper Latency (in)sensitive ICA. Group independent component analysis of fMRI data in the temporal frequency domain by Calhoun et al (2003) attempted to solve this problem by making estimates of the time delay in each voxel, and then using this as prior information in a modified ICA. Maybe something like this could be applied in your domain?