In literature, $V_\max = \lambda\cdot \operatorname{PRF} / 2$; should it be $V_\max = \lambda \cdot \operatorname{PRF} / 4$, which would be consistent with FMCW $V_\max = \lambda / (4 \cdot T_c)$?

This is because $\operatorname{PRF} = 2 f_d = 2 \cdot (2 V_\max / \lambda)$.

  • $\begingroup$ hi Linda, great having you back! I've edited your question to make the formulas easier to read. I think it's identical to what it was before, but it'd be nice if you checked. $\endgroup$ Commented Mar 23, 2023 at 16:51
  • 1
    $\begingroup$ Can somebody answer my question here? I am very confused the this factor of 2 difference. $\endgroup$
    – Linda
    Commented Mar 23, 2023 at 19:28
  • $\begingroup$ @Linda I posted an answer below. I can post a real example, but it will take some time as I'm running out of it these days. $\endgroup$
    – Envidia
    Commented Mar 25, 2023 at 3:41

1 Answer 1


Both are actually correct, but it depends on what Doppler $f_D$ frequencies we want to observe.

If we only want to observe positive Doppler frequencies, that is, targets with closing (approaching) radial velocities then the maximum unambiguous observable Doppler span given a pulse-repetition frequency (PRF) is

$$[0, PRF)$$

Thus the maximum observable unambiguous velocity (within one bin given the maximum frequency yielded by the DFT) when $f_D = PRF$ is

$$V_{max} = \frac{PRF\lambda}{2}$$

If we want to consider both positive and negative frequencies (we want to observe targets moving towards and away from the radar), the captured Doppler span given a PRF is now

$$[\frac{-PRF}{2}, \frac{PRF}{2})$$

In the same fashion the maximum observable unambiguous velocity when $f_D = \pm PRF/2$ is

$$V_{max} = \pm\frac{PRF\lambda}{4}$$


I think you would also benefit from viewing this answer, which goes into a little more detail. I'm also using the same parameters for the simulation.

To see the effect of our choice in defining the observed Doppler span, we assume the following:

  • Target range of 800 m and velocity of 250 (closing) m/s
  • Wavelength λ of 0.03 m
  • PRF of 50 kHz

Choosing to observe $[-\frac{PRF}{2}, \frac{PRF}{2})$ we get the maximum unambiguous velocities we can observe:

$$v_{max} = \pm\frac{PRF \lambda}{4} = \pm\frac{(50 \space kHz)0.03}{4}$$ $$v_{max} = \pm 375 \space m/s$$

enter image description here

We're able to unambiguously observe targets either moving away or towards the radar as long as the target is no faster than 375 m/s as shown in the range-Doppler map above. If the target does go beyond this limit, the target will alias. Let's say the target speeds up to 450 m/s towards the radar:

enter image description here

Performing a measurement here would give you not only a wrong value of its absolute speed, but you would perceive it as going away from you. Not good!

However if we choose to observe the Doppler span as $[0, PRF)$ then we get

$$v_{max} = \frac{PRF \lambda}{2} = \frac{(50 \space kHz)0.03}{2}$$ $$v_{max} = 750 \space m/s$$

And forming the range-Doppler map:

enter image description here

Measuring the target now will give us the correct absolute speed and direction, but we're relegated to only being able to observe positive Doppler (closing) targets, albeit with a potentially higher velocity (double in this case).


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