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 0.003625s. 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

It seems your procedure is correct but I do not understand why you lost half of the samples (64 to 32). Max velocity with no ambiguity will have phase difference equal to pi ($\omega = \pi$), so $V_{max} = \frac{\lambda}{4Tc}$.

So, you know sample 64 is equivalent to $\frac{\lambda}{4Tc}$ meanwhile sample 1 is equivalent to $-\frac{\lambda}{4Tc}$ or the opposite. Using this information you can calculate your velocity bin and calculate any velocity.

Second FFT works the same way it works for pulsed radar. You are studying phase difference between two consecutives chirps.

Good reference: https://training.ti.com/intro-mmwave-sensing-fmcw-radars-module-3-velocity-estimation