I Read many papers on signal processing for pulsed and FMCW radars, taking the FMCW type, the signal processing start after mixing the received and transmitted signal, the result of this operation is a signal called FMCW beat signal. We apply 2D-FFT to extract targets from the beat signal then we apply a detection algorithm to recognize true targets and reject others. I read also from some papers that they use a tool called ambiguity function, I don't know where this function is situated in fmcw signal processing flowchart or this function is just with pulsed radar! My question is : What's the role of ambiguity function in radar signal processing? and when we should use it?
The Ambiguity Function is just a name for 2D Correlator.
It is known that given a shifted 1D Signal the optimal estimator for the shift (Range in RADAR / LIDAR, etc...) it the correlation with the signal.
What if our signal had 2 parameters and both are shifted?
In the case of RADAR we have a shift of the signal due to the range (Time Shift) and due to velocity (Frequency Shift - Doppler Effect).
So how would you solve this?
Well, correlation with the transmitted signal shifted on both parameters.
The result of this operation is the Ambiguity Function which is a grid (Discrete) saying the correlation value between the received signal and a shifted (In both parameters) transmitted signal.