# Advice on generating stable FMCW waveform

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.

$$T_P$$ 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

Note

• What do you mean "every period"? Do you mean from pulse to pulse? – Envidia Feb 19 at 2:31
• Please see this answer in case what I have worked out there is helpful to you: dsp.stackexchange.com/questions/66541/… 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 at 5:05
• @Envidia: I mean period of the triangular modulation waveform – not_fogarty Feb 19 at 13:50
• @DanBoschen: Thanks! I'll take a look shortly – not_fogarty Feb 19 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 at 21:15