Let's have an FMCW radar sensor. I arrange the raw data in a matrix format with MXN dimensions, where M represents the number of time samples per chirp and N represents the total number of chirps. Now, after taking the FFT across each column, what do we get? Is it a range-time plot or a range doppler? I am confused after seeing many representations of the radar data plot. For example, range-time, range-doppler, time-doppler, and velocity-time plots. What are they, and how can I obtain each of them?
Hello Ritesh,
Returns from an FMCW radar are shifted in frequency due to two effects: (i) the range delay and (ii) Doppler shift from moving targets. For typical parameters, the range delay frequency is much greater than the Doppler shift (often by a few orders of magnitude). Therefore, the phase of returning samples changes rapidly due to the range delay but the phase due to the Doppler shift changes over a much longer timescale. This allows us to make a useful approximation when the duration of the chirp is short (as is often the case for automotive radars that repeat the chirp many times within a beam dwell time).
Let us consider, as you say, M samples per chirp and N chirps, giving a total of M * N samples. We can designate the samples as xm,n where the index m refers to the sample number (m=0,1,2...(M-1)) and n refers to the chirp number (n=0,1,2,...(N-1)).
The M samples taken over an individual chirp (say, for example, the nth chirp, i.e. samples xm=0,1,2,...(M-1),n) exhibit a phase gradient due mainly to the range delay. If we assume the phase variation due to the Doppler to be negligibly small over the duration of the chirp then we can say that any phase variation in the M samples taken during each chirp is due to the range delay. An FFT of these M samples yields a frequency, fR, that is indicative of range, where:
Range = c*fR /(2K), where K = B/T and is the gradient of the chirp [Hz per second], B is the total chirp bandwidth and T is the duration of the chirp.
Hence the FFT of the M samples is a frequency plot that scales to a RANGE plot.
If we now consider any one of these samples (say, for example, the mth sample) across all N chirps (xm,n=0,1,2,...(N-1)), they will have a reasonably consistent phase due to the range delay because the samples are all drawn from the same position within the chirp, but they will now exhibit a slower rate of change of phase due to their Doppler shift. The slower rate of change of phase is evident over the longer timescale of N chirps. The Doppler induced phase gradient is due to a small variation in range (in the order of the wavelength) over the timescale of the N chirps. An FFT of consistent samples across the N chirps will therefore yield the Doppler shift frequency, fd, from which we can deduce the radial velocity, Vr, of the target as:
Vr = lambda*fd / 2 where lambda is the wavelength.
Hence the FFT of the N samples is a Doppler frequency plot that scales to a (RADIAL) VELOCITY plot.
The 2-dimensional FFT of your array is therefore a RANGE-VELOCITY plot (after suitable scaling).
Note that the approximation that the Doppler induced phase variation during a single chirp is negligibly small does break down in some radar applications, i.e. those using a long chirp duration and/or where high target velocities can be encountered. In that case we can resolve the range delay frequency and the Doppler frequency over two chirps; an up ramp and a down ramp, giving a triangular frequency modulation.
I hope this helps.
Best regards,
Clive Alabaster
Director & Consultant
White Horse Radar Limited
www.whitehorseradar.co.uk
After taking the FFT across each column of the raw data matrix, we obtain a range-doppler plot. The range-doppler plot shows the range and Doppler shift of the targets in the radar scene. Specifically, the range is represented along the horizontal axis, and the Doppler shift is represented along the vertical axis.To obtain a range-time plot, we need to perform an additional processing step called range compression. Range compression involves applying a matched filter to the received signals to remove the spreading effect of the transmitted signal. After range compression, the resulting data can be plotted as a range-time plot, which shows the distance to each target as a function of time. Similarly, to obtain a velocity-time plot, we need to perform a Doppler processing step. Doppler processing involves extracting the velocity information of the targets from the Doppler shift in the received signals. After Doppler processing, the resulting data can be plotted as a velocity-time plot, which shows the velocity of each target as a function of time. Finally, to obtain a time-doppler plot, we need to perform a two-dimensional FFT on the raw data matrix. The resulting data can be plotted as a time-doppler plot, which shows the time and frequency (Doppler) information of the targets in the radar scene.
In summary, the different types of radar data plots (range-time, range-doppler, time-doppler, and velocity-time plots) can be obtained from the raw data matrix by applying different processing steps.
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