For wide bandwidth modulation formats this is a bit of a pain since you need a very wideband, high current, power supply. so they are doing an A/theta modulator but trying to simplify the bias control on the PA to avoid that.
No, they're doing something more complicated than A/theta modulation (aka envelope tracking aka envelope elimination and restorataion aka ...). They are doing an outphasing amplifier which splits the original signal into two constant amplitude variable phase signals which will reproduce the original signal when they are recombined, but they are adding some envelope tracking elements to further improve efficiency since wideband combiners will absorb the differential section of the input signals as loss.
What I'm not clear on is why they are doing this when they have a predistortion loop anyway. a pure predistortion loop should be able to achieve very similar results without any need for the PA bias adjust. you can also do it with 1 PA instead of two.
A predistorter doesn't have much of anything to do with PA efficiency (the point of this MIT research), PD's are for linearity. High efficiency PA topologies typically take a hit to linearity. Fancy techniques like outphasing and envelope tracking are better than some but they still reduce linearity. Poor linearity means increased distortion. Distortion increases error rates in digital transmissions, and it also leads to signal leaking into adjacent signal bands, which isn't allowed in the tight cellular spectral environment. So they put a PD in there to linearize things a bit further. That's probably why they are using discrete bias levels instead of continuously variable - they can optimize their PD loop to work best in these four well-characterized states which gets most of the efficiency gain while making the linearization easier.
I don't know, looks like somebody's thesis to me. Doesn't look like it's particular practical. Also, first rule of looking at schemes like this. How much of that power they saved is being used in the more complicated digital circuitry. That's the reason you don't see PD loops in cell phones. It's a wash, you spend so much power analyzing the signal to do PD that you burn up the savings . Now if you have a 10W transmitter, PD makes lots of sense.
These are not fundamental limitations. It's making more and more sense as digital processing and DSP chips get faster, cheaper, and lower power. The point of research is to try to push the state of the art and it may not be "practical" when the research paper is hot off the press. If it's good enough then it will be practical some time down the road, and if it isn't good enough then it will be left aside as a lesson learned. Apparently the researchers think its good enough to found a startup company, so they're either foolish or they understand it better than you. Time will tell.