Spherical wave modeling of MIMO channels has become important for future 5G networks. The reason is near field communication scenarios with massive MIMO. some work is done my METIS on this including array of linear antennas. I was wondering as to how to model mimo channel in near field with array of dual or multipolarized antennas.
I am likely not the best one to answer this question, but I'll give my two cents. Sorry if I have not fully understood your question. For one polarized antenna as reference, I guess one could use vector spherical harmonics (VSH) to model the signal energy at a destination point. The signal energy is nothing but the transmit-receiver antenna gain times the channel coefficient/attenuation. Other alternative is to use the scalar spherical harmonics to model the vertical and horizontal waves independently. Since you are in the near field, I think you can disregard any polarization changes. Also, in the near-field there are no multiple scatterers, so the best approach would be a geometrical modeling. I think that the near-field modeling is similar to the far-field case, except that you have to consider the geometry of the system and you have to be more careful with the properties of translation/rotation of the spherical harmonics. If the antenna array is not complex (e.g. ULA), then the MIMO channel modeling becomes straightforward.
If by "model", you're really meaning "simulate", then it sounds like you're referring to the boundary array technique for creating a near-field over-the-air RF environment that looks as though it came from the far field. (See http://www.ets-lindgren.com/pdf/MW_0810_Foegelle.pdf.) The techniques described here are primarily around testing the performance of MIMO handsets and other small electronic devices where the size and spacing of antennas is a challenge. On the base station side, it's much easier to work with larger antenna spacings and produce good uncorrelated antennas without having to worry about the platform interactions seen on the mobile device.
Massive MIMO isn't going to change much about the mobile side testing, but is going to be a testing challenge for evaluating the base station antenna performance. The antenna design can no longer be easily isolated from the electronics package, and will likely be an integrated arrangement where self interference and other issues seen in mobile devices will also crop up. The boundary array approach will still be possible for evaluating this type of device, but will need to be scaled up to address the larger physical size (not the total number of MIMO antennas) of the base station MIMO array.
The boundary array works under the same Nyquist rules as near-to-far-field conversion. In the latter case, the near field must be sampled with sufficient resolution (e.g. > 2 samples per wavelength around the circumference of the DUT) to accurately predict the far field. In the boundary array, the probes around the boundary of the test volume must be arrayed at sufficient resolution to recreate the near field as though it came from the far field. The larger the DUT antenna spacing becomes, the finer the boundary array resolution required to keep the DUT from being able to resolve the individual elements in the array.
The real question is, what's a massive MIMO array going to look like? If one were to envision an array of 7 antennas spaced at half a wavelength around the perimeter of a circle with one in the center, you'd have an 8 antenna array with all antennas at 0.5 wavelength spacing or better, which should result in a nicely uncorrelated system, The overall physical dimension of such a MIMO array would be just over a wavelength and thus a sixteen position boundary array should still be more than sufficient to test such a device. Similar scales can be expected as you go up, since the arrays will likely be volumetric in nature. It's only if you try for a linear MIMO array that the boundary array has to become huge to be able to handle the narrow beams produced by such an array.
This is obviously a very new area, but something I've been looking at for a while. The other side of the question of course is what exactly does this test look like (what do you want to know about the base station?). And since the multi-user scenario offered by massive MIMO will require many reference device connections at the other end of the system, the channel emulation resources required to connect all of the mobile stations to the system may exceed that needed to run the boundary array!
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