How to classify the movement type of a target into two categories(direct motion or else) by using a doppler radar?
If range isn’t important, sure you could do something like this with unmodulated pulses (i.e the pulsed you transmit are just sinusoids carriers with some known frequency). You would transmit the pulse and then receive it at some time delay. You could attempt to construct some sort of spectrogram or other time-frequency representation of the received signal. If the target is moving at a constant velocity, there would be a constant Doppler shift. If the target had non-constant velocity, you would be able to observe a non-constant Doppler shift.

If you cared about resolving range to the target, you would have to use a pulsed Doppler system. That would be very difficult to do with a pulsed Doppler system. Pulsed Doppler radars tend to ideally assume the target signal is moving at a constant rate, and that over the entire coherent processing interval (CPI), it doesn’t change range bins. The reason the assumption is key is because if the target shifts range bins, you will not get all of your Doppler processing gain and you’ll tend to smear out the target on the range-Doppler map, which makes detection of the target difficult if not impossible

In industry, the issue of range cell migration over a CPI for high velocity targets is pretty difficult but doable under the right circumstances. You can check out something called the keystone algorithm, that has seen some use in practice. I’d say it’d be very important to select your bandwidth and sample rate such that you don’t cause any extra apparent range migration of the target.

As for microdoppler on pulse Doppler radars , I have yet to actually see that be used in the industry I work in (defense), and that community largely treats it as computationally inefficient. With that being said, let’s say you have all the computation time in the world and you could do such a thing, sure it may reveal some characteristics. One classic example would be being able to detect the type of engine on some sort of airplane based on the microdoppler characteristics, e.g. the rotors of a helicopter or the supersonic wake of a jet.

In summary: yes, if you didn’t need range information you could analyze Doppler through using a spectrogram. Keep in mind that your RF carrier frequency will determine the Doppler shift that is apparent, so selecting an appropriate RF is pretty key for something like this.