For a course that i'm taking im asked a question about the ambiguity function of a FMCW radar. However i have not found a good source for reading about this so don't quite understand it.

I get given the following cuts:

Doppler and delay cut of the ambiguity function

I understand it in the following way: If there are 2 targets, i cannot distinguish between them if they have a delay larger than +- 0.2 us or +- 20 kHz doppler shift?

Do these cuts also say something about the waveform? Would for instance the width (ie from -0.2us to 0.2us = 0.4 us) be equal to 1 / B, the bandwidth of the FMCW radar? And for the other cut would the width (-20 to 20 kHz = 40 kHz) then be the 1/T, the pulse time? thus resulting in ~2.5MHz bandwidth and 25 us pulse width?

I tried recreating these cuts in matlab but didnt have any success in doing so so far. Any good sources for reading about it would also be appreciated !

Thank you :)

  • $\begingroup$ I think you have it backwards - you can't resolve targets with a delays less than 20 us, and you can't resolve targets with less than 20 kHz Doppler shift. This is assuming you're using the null as your resolution figure. $\endgroup$
    – David
    Commented Apr 25, 2023 at 13:25

1 Answer 1


You may start with an easier model, were you have a single parameter.
Think of transmitting and receiving a reflection of a known signal.

The model is parameterized by the delay of the reception of the signal.
A good way to estimate the delay is using the matched filter.
If you analyze the performance of the accuracy of the estimation you will see it depends on the "sharpness" of the signal. Formally, its bandwidth. It also depends on the SNR, but let's assume it is set for all signals to evaluate.

The ambiguity function is extension of this to 2 parameters.
We still have the delay, which is limited by the same property of the signal.
Yet we also have the Doppler shift which is a property relative velocity.


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