I used to work for a company making current profilers. Sort of the same thing and they used piezo electric transducers.
You will need to transmit a pulse at the target. Don't really need to know the doppler shift since you are not trying to measure the speed exactly, just determine if they are running or walking. What you do need to do is measure the time of flight. This is the difference between when you transmit and receive. You do not transmit continuously, but rather in pulses when you want to detect a target.
Since this MUST be a uP design you would then compare the time against limits for walking and running by taking several reading and looking at the change in position (i.e. 1st target was 5 feet away, 2nd target was 3 feet away). This is much easier than working with doppler shifts. You just measure the difference in distance as a function of time. If transmitting every second...moved 2 ft in 1 second...moving 2ft/sec.
Now if you do want to know how fast they are moving you can sample enough times to get that too.
So, you need a ucontroller to run the thing. Memory can be in the uC. You will need a transmitter circuit, I'm guessing 12Khz is fine for that distance but there may be something off the shelf on a different freq so check around. Of course you will also need to be able to receive. That's really all you need. The rest is software.
If you wanted to get fancy you can start transmitting a digital pulse string and reading that back. That would allow you to distinguish between multiple targets in the same zone. It gets very complicated to do this kind of thing though. Most techniques are patented and closely guarded by the companies.
Sounds like a fun project. Keep us updated!