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 $\operatorname{PRF} = 2 f_d = 2 \cdot (2 V_\max / \lambda)$.
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:
Choosing to observe $[-\frac{PRF}{2}, \frac{PRF}{2})$ we get the maximum unambiguous velocities we can observe:
$$v_{max} = \pm\frac{PRF \lambda}{4} = \pm\frac{(50 \space kHz)0.03}{4}$$ $$v_{max} = \pm 375 \space m/s$$
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:
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:
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).
