# Comparison between FMCW radar modulation techniques

In designing a Frequency modulated continuous wave (FMCW) radar system for target detection, there is a possibility of choosing the modulation technique amongst triangle or saw-tooth modulation. What are the parameter which make the base for the selection.

Comparison between these two modulation techniques for FMCW radar will be appreciated?

• I don't know enough for a good answer, but using matched filters, you can get twice the range of triangle, with same PRF. You can have a filter for the up slope and a filter for the down slope, so you'll get update at every pulse repetition, but you'll have twice the time between two similar pulses. Commented Apr 19, 2016 at 15:18
• I believe @AndrejaKo is correct, except you don't need a matched filter. You use a homodyne architecture (mix TX and RX together). Then use a low-pass filter to filter out the sum frequency (which is GHz) and keep the difference frequency (which, depending on the slope of the chirp, may be audio frequency). There may be something a bit funny happening at the point where the slope inflects from positive to negative. Processing may be easier with the sawtooth for that reason. Commented Apr 20, 2016 at 4:26
• You say range, velocity and angle detection. This type of radar gives range, no problem. Velocity? well, if you process a series of chirps, you can calculate doppler, and from that, you can estimate the range rate (change in range with respect to change in time). But if the target is not moving directly toward or away from the radar, you are not getting actual velocity. I don't know what angle you think you can measure, but this type of radar does not normally allow any type of angular measure. Commented Apr 20, 2016 at 4:29
• Thanks for your input. But I know both are capable of providing range by mixing it with the tx signal and then taking fourier transform. About velocity yes for sure we need to have multiple sweeps to obtain the velocity (exception is the case of triangular where we can find the velocity from even on single complete sweep using up and down chirp). My question is more related to comparison between the choice, on which basis we should choose between two (as I can get all range velocity parameters from both modulation). Hope that question is now more clearer. Commented Apr 20, 2016 at 6:49
• @mkeith yes doppler velocity provides range rate or (radial velocity) but we can by using techniques of DOA find the angle of arrival and Tracking algorithms for velocity tracking. Commented Apr 20, 2016 at 6:51

Assuming your receiver is a "homodyne architecture (mix TX and RX together)" as stated by mkeith, the two methods (sawtooth vs triangular) will be identical assuming your scene is stationary during the measurement period. The low-pass filtered mixer output will then always be proportional to the range of the scatterers, regardless of a up or down sweep. With a I/Q receiver you should be able to distinguish between a negative and positive beat, but I can't see any benefit. Only generating a up-sweep (sawtooth) will most likely be easier to implement, but that depends entirely on the hardware.

For moving targets, we need to distinguish between 2 cases.

1. Slow moving targets
2. Fast moving targets

where 'fast' and 'slow' is relative to the sweep-time. For a sufficiently slow moving target, the doppler shift will be negligible and you can approximate it as stationary. You can find the velocity of a slow moving object by comparing the data from multiple sweeps, again the triangular vs sawtooth makes no difference.

I belive the intention of the triangular waveform is that you can now solve the ambiguity caused by a fast-moving object. In a FMCW radar, a moving target may seem indistinguishable from a stationary one. One traditional then introduces the triangular waveform to solve this ambiguity, see e.g. this open access article, especially figure 1.

Note that this only works for a single moving target, when you have multiple moving targets stuff gets more complicated so thread carefully.

In summary: In choosing between the two waveforms, there is a special case with a fast moving object where the triangular waveform may aid in extracting velocity (or should I say: radial relative velocity between the radar and reflector) depending on the velocity and chirp-rate. But for all other cases, the distinction is mute.

I hope that helped, let me know if I should clarify any of the points.