I'm confused how the Doppler shift is measured in the case of the continuously modulated frequency? It seems both range and Doppler shift are encoded in the reflected signal - how are they separated?
Edit: or is it the case that a full period of the reflected signal must be detected first before Doppler can be calculated?
You're thinking sawtooth VCO frequency variation because its the simplest way to teach how distance ranging works with FMCW
The "real world" radars usually use a triangle wave. If no movement, the delta on rising and falling parts of the triangle are the same. A doppler will shift the height so to speak so the delta output instead of being constant (distance) will have a square wave look to it and the height of that sq wave will be the doppler component.
So pseudocode looks something like figure out the average delta when the triangle modulation is going up, then average when its going down, and the average of the averages is the distance and the difference of the averages is the doppler.
Note that "real radars" and "military radars" use wildly more interesting modulation schemes. Sawtooths and triangles were cutting edge in 1950 not so much anymore. Imagine if you generated a known pseudo-random or crypto-generated digital signal and transmitted that and the remembered what you transmitted for awhile and correlated your known previous values with what you rx a little later; now that was cutting edge in the 60s/70s and thats quite hard to jam compared to legacy methods.
Also I "know" the NWS WSR-88 weather radars transmit some really cool and interesting waveforms for weather experiments although I don't have the details.
Edited: Its too early in the morning for me to think about this, I may have the above backwards. The general concept, anyway, is the rate of change of your triangle wave is way faster than the change in movement, and over the very short term of a couple cycles of the triangle modulation, the returned freq from doppler is a "constant" offset high or low added to the shift from distance. Now during the upslope of a triangle the returned signal will lag and return a lower/negative voltage and during the downslope of a triangle the returned signal will lag and return a higher/positive voltage from the past. So yeah I'm sleepy and I got it backwards above; leaving for the LOLs.
Edited x2: Ugh I'm sleepy. This is like parody leetcode for EEs. Just do a numerical simulation using small simple numbers of modulating a FMCW with a triangle wave (not sawtooth...) and it'll all eventually make sense.
"Modulation can be turned off on alternate scans to identify velocity using unmodulated carrier frequency shift. This allows range and velocity to be found with just one radar set."
Doppler is measured across multiple chirps or pulses. So doppler is not really encoded in the same signal used for range. Relative motion induces a phase rotation across multiple chirps, which can be coherently combined with a Fourier transform.
Edit: or is it the case that a full period of the reflected signal must be detected first before Doppler can be calculated?