0

I am trying to derive parameters for a triangular FMCW waveform such that the phase of the signal has consistency from one period to the next. Perhaps this is arbitrary and feel free to tell me so, but I have a bistatic FMCW system and as such I will be implementing a delay and freq offset calibration procedure on start up to sync the Tx and Rx sides.

So I wish to set my triangle FMCW period, FMCW bandwidth, and sample rate such that the resulting time domain output is clean and steady, however for some reason I'm not doing well with deriving it via some simple trig.

$$ \cos(2\pi f_0 t + \pi Rt^2) \\ \text{where } R=\frac{B}{T_p} $$ so at $t=0$ the argument is also $0$, so I would think I need to solve for a value of $T_p$ such that when $t=T_p$, the argument is equal to some large multiple of $2\pi$ while keeping in mind the sample rate should yield a whole number of samples per period.

This approach has not been working however, and I'm at a loss of what the issue is.

For additional info

$T_P$ is half of the full period of the triangular modulation waveform

for current parameters I have set

$$ sample rate = 8M\\ B = 1.6M \\ Tp = 1.25ms \\ $$

EDIT: Images to illustrate point

enter image description here

enter image description here

Note

not_fogarty
  • 1
  • 2
  • What do you mean "every period"? Do you mean from pulse to pulse? – Envidia Feb 19 '21 at 02:31
  • Please see this answer in case what I have worked out there is helpful to you: https://dsp.stackexchange.com/questions/66541/how-can-i-plot-the-frequency-response-on-a-bode-diagram-with-fast-fourier-transf/66545#66545 It is a discrete time FMCW chirp with end sample blanking and transition windowing to minimize the discontinuity from chirp to chirp while maximizing flat frequency coverage over the chirp range. – Dan Boschen Feb 19 '21 at 05:05
  • @Envidia: I mean period of the triangular modulation waveform – not_fogarty Feb 19 '21 at 13:50
  • @DanBoschen: Thanks! I'll take a look shortly – not_fogarty Feb 19 '21 at 13:51
  • @DanBoschen I've puzzled over this link you sent and not sure I'm fully grasping how to implement this. To reiterate my problem: I'm trying to produce an FMCW waveform that is consistent across periods (or pulses) in phase. One primary reason is it's a bistatic radar I will be using heterodyne correlation scheme on incoming signal. It'll be best if I can loop a recorded FMCW signal that syncs nicely from end to end without discontinuity – not_fogarty Feb 22 '21 at 21:15
  • @not_fogarty I see, and yes the link isn't specific to that -- you want phase coherence from chirp to chirp. An NCO would be useful for this implementation since you can control / sync phase easily, assuming you sync carrier phase to start of sweep as well (I think that may imply an integer relationship between your carrier and sweep rate--- but even if not you could track the phase rotation and offset in the NCO at the start of the sweep) Have you considered that? – Dan Boschen Feb 22 '21 at 21:17
  • Yeah That's what I figured as well but it when looking at time domain plot it still wants to drift slowly but surely. think I'm missing a minor piece of the puzzle. Haven't used NCO's before so that's a good thing to consider in future, unfortunately they don't look to be available in GNU Radio – not_fogarty Feb 22 '21 at 21:43

0 Answers0