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I am trying to design a simple FMCW radar for the ideal case. Below are steps I planned.

  1. Transmit signal, Tx = cos(T)
  2. receive signal, Rx = cos(R)
  3. Mix transmitted signal and received signal, Sx1 = cos(T) * cos(R) = 0.5 * {cos(T+R) * cos(T-R)}
  4. Apply Low Pass filter, Sx2 = cos(T-R) (I won't consider 0.5 because what I need is phase and frequency)
  5. Apply FFT (Fast Fourier Transform) to get beat frequency to calculate range and velocity of the target.

In the process, I have a problem with step 5.

enter image description here After mixing the transmitted signal and received signal, LPF is applied to get only the difference of two frequencies. And then FFT is applied to extract beat frequency. However, in sawtooth chirp, there are two values. f_b (frequency difference in T_valid region) and B - f_b (frequency difference in t_d region. Assume B is bandwidth.). The value we need here is f_b. Since we don't know t_d yet, how do I apply FFT over T_valid?

enter image description here Similar question. I want to extract the up beat frequency and the down beat frequency. However, there are regions where beat frequency is not constant. I'll call this region T_invalid. If I include T_invalid region in FFT, I won't be able to get the constant value I need. How do I apply FFT over only the T_valid region?

DONG CHAN LEE
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  • What is the application? – user57037 Jan 29 '21 at 04:37
  • @mkeith Sorry, but what do you mean by application? I want to get beat frequency and finally get range and velocity of an object. To get beat frequency, I need to do FFT over from tau to T. Let tau = 2*R/c and T = sweep time. But the problem is, since I don't know the range (because the range is what I'm trying to find out) I don't know tau. Then from when to T do I use FFT? – DONG CHAN LEE Jan 29 '21 at 04:46
  • What is the target? What will be done with the information about the target? – user57037 Jan 29 '21 at 04:50
  • @mkeith I want to design radar for a self-driving car. Suppose there's a random target in front of the car and the radar should calculate the distance and the relative velocity of the target with the beat frequency extracted from FFT. – DONG CHAN LEE Jan 29 '21 at 04:57
  • @mkeith So I am trying to find a way to apply FFT to get the beat frequency. But if you see the first figure, Tc is sweep time and if I apply FFT over the whole Tc, there are two beat frequencies, fb and B - fb. And fb is the only one I need. So I wanna know what I can do to get only the value fb. – DONG CHAN LEE Jan 29 '21 at 05:04
  • What is the source for the graphics? Can you provide a reference (edit it into the original question)? We have to make sure that the site is OK from a copyright perspective. If you are the original creator, then please add a note saying so. – user57037 Jan 29 '21 at 16:25
  • @mkeith I edited my question and uploaded the graphic I drew. Also added some more explanation. – DONG CHAN LEE Feb 01 '21 at 01:18
  • It is pretty complicated. I mean, you can just adjust your sample window so that you only sample during Tvalid. You can also apply gating to transmit and receive waveforms so that the range is restricted (range gating). But this depends on many details. I really think you should read some textbooks about FMCW (aka linear FM homodyne) radar imaging. Also, I don't see any advantage to using triangular waveform. I think you should use sawtooth waveform to save trouble. – user57037 Feb 01 '21 at 02:03
  • Do you know about the relationship between chirp bandwidth and downrange resolution? Alias free range? There are a lot of tradeoffs that need to be considered at system design time. – user57037 Feb 01 '21 at 02:08
  • @mkeith thank you for your comments! Can you please recommend me a book that covers basic principles of FMCW radar signal processing? – DONG CHAN LEE Feb 01 '21 at 09:52

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Look into windowed FFTs, basically you make the sweep long compared to the maximum range, then pick the middle bit, window to minimise lobes in whatever way makes sense for your use case, and run the fft.

FFT window functions were for a while the easy way to get your name on a paper, Blackman appears to have been particularly prolific.

Dan Mills
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