frequency shift of about 890 kHz (supposing my math is correct)
$$\begin{align}
\Delta f_\text{Doppler} &= f_0 \frac vc\\
&=800\cdot 10^6\,\text{Hz}\frac{3.4\cdot10^2\frac{\text m}{\text s}}{3\cdot 10^8\frac{\text m}{\text s}}\\
&\approx 800\cdot 10^6\,\text{Hz}\cdot 1.13\cdot 10^{-6}\\
&\approx 906 \,\text{Hz}
\end{align}$$
So, your shift expectation is off by a factor of 1000.
Supposing we don't have to worry about interference, how should I go about correcting this frequency shift? I was thinking about using an FLL or a PLL, but I'm not sure where whether these could support such important shifts.
You can design the bandwidth of your PLL or FLL to accomodate any shift. It just gets a bit tricky keeping other signals out of the observation.
Even your ~ MHz shift isn't all that much to deal with. Normal observers will simply have a larger bandwidth than just necessary to observe your communication signal, anyways, and need
- to have frequency correction anyways, since no two clocks / frequency generators are perfectly identical, physically (and if someone says "I've built this communication system. For now, I neglected synchronization needs", you know that they omitted the hard part)
- When knowing what your communication signals look like, it's often not that hard to find them in the spectrum.
- When you observe a communication partner for a while, you can easily write down a Doppler rate, i.e. the rate at which the Doppler shift changes. From that, you can predict future shifts and make your detection even easier (typical Kalman-Filter application)
