"BFO model":
What I understand is that there are two ways for the Doppler compensation from the aircraft unit:
- "hearing" a [constinuously?] transmitted signal from the satellite which frequency is known: from the difference between the supposed frequency and the received one, the shift of frequency to emit is computed,
or
- computing the necessary shift from the flight speed and direction, knowing the theoretical position of the satellite. From what the radial speed between the aircraft and the theoretical position of the satellite is computed has not been, IMHO, stated (GPS and/or ADIRU). What is admitted about this is that this compensation is faulty because the satellite is not in this position (north of it all the time of the flight) and because it moves.
It has been said that the first way was using a whole canal to do that, and so is not "economical" and MH370 used the second way which is not asking for a pilot frequency.
Without correction, the radio signal uses a larger bandwidth, so this correction allows much more canals inside the same band width.
Another thought: IMHO, people using precise BFOs values to guess a flightpath are surevaluating these data: or you take the option of a single direction and a single speed value after the [supposed] turn to south (that is, aircraft on AP), and you don't need BFOs to find a flightpath, or you presume changes in direction, speed and possibly flight level, and you can find such a large bunch of possible flightpathes that you can cross the 7th arc from Sumatra to something like 40S 70E, and flying a hundred miles more after fuel exhaustion (IFF the last ping was generated by fuel exhaustion, APU starting, ..., and not from the "same something" which made the system reboot at 18:25:xx).