Phased Array Toolbox: Target's reflection Phase information alters across range-bin border. Why ?

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Andreas Schwager on 18 Jun 2015
Edited: Honglei Chen on 22 Jun 2015
The Phased Array Toolbox includes the 'FMCWExample.m'. The code below is this example slightly modified in order to derive the phase information where the target is located. It is expected that the phase of the reflected signal equals zero if the target is located at distances of integer multiples of lambda/2. If target is located at car_dist = 256*lambda; it outputs: Target in 0.996713m Phase of target: -0.1637° Bin: 1
If target is located at car_dist = 257*lambda; it outputs: Target in 1.000606m Phase of target: -0.65452° Bin: 2
Why does the phase changes if target moves across a range bin border?

Honglei Chen on 19 Jun 2015
I believe this is due to some discontinuity in the dechirped signal. For example, when the signal is at first range bin, then the first sample in the dechirped signal is 0. If in your program, you do
xr = xr(2:end);
before passing it through fft, the phase angle becomes 0. Similar result is obtained if for the signal arriving in second range bin, I do
xr = xr(3:end);
before taking the FFT.
This being said, is there any particular reason you are looking at the phase angle? The range information is recovered from frequency so I'm wondering what you plan to use the phase angle for. Thanks.
Honglei Chen on 22 Jun 2015
Hi Andrea, what I mean is that you insert
xr = xr(2:end);
into your code before taking fft to see the effect. I agree that FFT is always done on the entire xr array, I'm simply trying to show that it matches the theory if we remove the discontinuities. I think in theory FMCW is considered as no particular starting and ending point so the mixed signal is a perfect sinusoid. However, in real application, the chirp has to stop at a given time and then retransmitted. So there are discontinuities at the start/stop of the sweeps. Looks to me that those discontinuities is the cause of the phases we saw. If we can find a way to suppress these discontinuities, then I would expect the phase to be closer to the theoretical result.