# Automotive Pulse Doppler Maximum unambiguous range?

I am trying to calculate the maximum unambiguous range for FMCW automotive radar.

In automotive, the pulse repetition rate (Tp) is typically 50 - 60ms. My equation is as follows:

where c is the speed of light. This becomes

Have I done the above correctly? 7 million metres seems wrong. Is it different as automotive is using FMCW?

Looking here

For example, a given radar with a linear frequency shift with a duration of 1 ms, can provide a maximum unambiguous range of less than 150 km theoretically. This value results from the remaining necessarily overlap of the transmission signal with the echo signal (see Figure 1) to get enough time for measuring a difference frequency. Most this range can never be achieved due to low power of the transmitter. Thus always remains enough time for a measurement of the difference frequency.

This suggests my calculation is correct but for FMCW the chirp duration is used (in the example 1ms), as answered by Neil_UK

• What is the Tp ? The range depends on the frequency of the pulse signal. Aug 16 '17 at 12:18
• I think you are using the wrong formula or units. wx.db.erau.edu/faculty/mullerb/Wx365/Doppler_formulas/…
– Bort
Aug 16 '17 at 12:35
• Why does 7e6 meters sound wrong ? I think it makes sense as that is the time (50 ms) it takes for light to travel 7e6 meters. You'd need a target 7e6 / 2 meters away to interfere with the next pulse which comes 50 ms later. It means the pulses rep. rate could be much faster than 50 ms before it affects the unamb. range. Aug 16 '17 at 12:37
• @Bort Your link is for a Doppler type radar. This is not a Doppler type radar as that can only measure speed differences, not distance. Aug 16 '17 at 12:39
• here is a typical doppler range map Perhaps you're thinking that range and unambiguous range are the same. They're not ! The unambiguous range is the range that you can purely theoretically measure unambiguously, assuming you can measure all reflections and all signals, there's no noise for example. The range is the actual distance which is usable with this radar. It is limited by transmit power, noise etc. You can only have an unamb. range problem if the unamb. range is smaller that the range. Aug 16 '17 at 13:12

It depends how the radar is working. If it times the difference between transmission and reception of the pulse, then the correct unambiguous range is given by taking 50mS as the time of flight, and doing the appropriate thing with $c$, which gives you 7500km.