I’m a Tetramic user. I know almost nothing about streaming, little about lossy codecs and enough to be dangerous with Ambisionics.
I assume you'll need to interleave any transmitted channels to one file to stream.
I think you are going to need a laptop to do some computation on the mobile side.
If you are forced to use a lossy file format to accommodate data transmission bandwith limitations, best bet is to convert to your final target output (ie: stereo, 4 channel speaker feed, 5.1) before transmission to avoid problems. Lossy encoders do data reduction by leveraging human perceptual schemes, A/B-format is pure math based. Perceputal lossy schemes which sound fine to humans toss data which may be critical for A or B format conversion to your final listenable output. If you need to transmit A or B format, Look for a lossless file compression scheme which is not perceptual based. FLAC would work but may not be enough compression. Beyond that, B-format is more robust and somewhat less suseptible to odd asymetric errors than raw A-format mic output, so if your only choice is lossy transmission, you may look into doing the A-to-B format conversion prior to transmission.
Do you need height information? If not, convert from A to B format, then throw out the Z channel and you only need to transmit 3 channels (W,X,Y).
I think this is probably a good ranking order of preference-
1) Stream 4 channel A or B format losslessly compressed. If that's too data heavy, then-
2) Stream 3 channel B format without height, losslessly compressed. Still too data heavy?
3) Stream the lossy compressed, non-ambisionic final target audio output (stereo, 4 channel speaker feed, 5.1, whatever) as long as you don’t need to do additional manipulation later. Perceptual coding will not cause problems with those formats and will greatly minimize the transmitted data.
4) Stream 3 or 4 channel B-format compressed with something lossy, but it might not decode correctly.
6) Stream A-format compressed with somthing lossy but it's even more likey to have decoding problems, and strange ones.
Oh yeah, now that I think of it, there is also the old UHJ compression scheme which was used for channel reduction in the analog era. It reduces 4 B-format channels to 3, or 3 to 2 (it’s a lossy audio scheme vs. a lossy data scheme). Not sure if that is a viable option or not, or how it fits into in the digital realm.
I suggest subscribing to the sursound mailing list and querying the ambisonic heavy hitters and researchers.