To start with, the output of the VCO isn't a simple sine wave. If you look closer at the datasheet, you'll see a plot of harmonic amplitudes vs tuning voltage.
Yes, just noticed it. This is a diagram from MITs ISM band synthetic aperture radar. The theory here is:
A FMCW (here up-chirp) is generated using a ramp generator as the input of the VCO. So, at an instant Tx frequency might be lets say 2 GHz. This Tx signal is reflected off of a target and received by the Rx antenna. Some time
t passed during the period transmitted signal reached the target and got reflected. During the time
t the transmit signal has changed from 2 GHz to lets say 2.00004 GHz (because the signal is ramping) so now if we mix (down converte) the current Tx signal 2.00004 GHz and received signal 2 GHz we get an IF of 40 kHz which can be easily sampled and processed. Here IF will contain the distance information. Greater IF means greater target distance. For direction of motion of the target CW is transmitted and then received Doppler shifted signal is mixed with the CW and IF determines if it is moving towards or away.
For harmonics we will have the following conditions when mixed (I don't know if I am doing this correct)
1) Harmonic frequencies of Tx at an instant
t will get mixed with received signal (which was fundamental Tx at some instant <
t) and produce Ghz signal which will not be picked up by the Preamp of the processing system.
No worries [Harmonics mixing with fundamental frequency] i.e. 4.00008-2 = 2.00008 GHz
2)Harmonic frequencies of Tx at an instant
t will mix with the reflected Harmonics transmitted at some instant prior to
t which will produce imaginary targets at twice the distance of the real target.
[Harmonics mixing with themselves] i.e 4.00008-4 = 80KHz
So, how do you solve the imaginary target problem?
Add a filter which lets in 2-3 GHz signal?