FMCW radar: understanding of doppler fft

Question

I am using fmcw radar to find out distance and speed of moving objects using stm32l476 microcontroller. I transmit the modulation signal as sawtooth waveform and I read the recieved signal in the digital form using ADC function available. Then, I copy this recieved ADC data into fft_in array(converting it into float32_t)(fft_in array size = 512). After copying this fft_in array, I apply fft on this array and process it for finding out range of the object. Until here everything works fine.

Now, in order to find velocity of the object, first, I copy this arrays(fft_in) as rows of the matrix for 64 chirps(Matrix size[64][512]). Then, I take Peak range bin column and apply fft for this column array. So while processing this column array by applying fft, its length reduce to half[32 elements]. Then finding out peak value bin multiplied by frequnecy resolution gives the phase differnce 'w' from which velocity can be calculated as "𝐯=𝛌𝛚/𝟒𝛑𝐓 𝐜".

while running this algorithm, I find that when object is stationery, I get peak value at 22th element(out of 32 elements). what does this imply?

I have sampling frequency for ADC as 24502hz. So per bin value for range estimation is 47.8566hz (24502/512).

I have 64 chirps and Tc is 0.006325s. So 1/0.006325 gives 158.10Hz.What would be per velocity bin resolution, Is it 2.47Hz(158.10/64)? I have bit confusion in this concept.How does 2nd fft works for finding out velocity in fmcw radar?

Answer 1

Infineon has excellent resources on this topic, see this FAQ for the basics: https://www.infineon.com/dgdl/Infineon-Radar%20FAQ-PI-v02_00-EN.pdf?fileId=5546d46266f85d6301671c76d2a00614

If you want to know more details, check out the P2G Software User Manual: https://www.infineon.com/dgdl/Infineon-P2G_Software_User_Manual-UserManual-v01_01-EN.pdf?fileId=5546d4627762291e017769040a233324 (Chapter 4)

There is even the software available with all the algorithms (including FMCW). How to get the software with the "Infineon Toolbox" is described here: https://www.mouser.com/pdfdocs/Infineon_Position2Go_QS.pdf

Some hints from me:

• I suggest applying a window function before the fft https://en.wikipedia.org/wiki/Window_function and remove the mean.
• Read about frequency mixers https://en.wikipedia.org/wiki/Frequency_mixer