The Doppler shift is the consequence of the movement of the transmitter and receiver relative to each other. It is depends on the difference of the speed between the transmitter and the receiver. Specifically, fd= +-v fc/c, where v is the relative velocity, fc the carrier frequency and c is the speed of light in free space. So , if both the transmitter and receiver are fixed , which means v=0 and fd=zero. The presence of the doppler shift results in the socalled coherence time of the channel:
For more information about the coherence time please follow the link:http://www.ni.com/white-paper/14911/en/
There is also Doppler shift if the signal bounces off a moving object before reaching the receiver. This is how moving target indication (MTI) radar works.
If your transmitter and receiver are not moving, and the signal goes from one to the other directly, there will be no Doppler shift. The mean Doppler shift will be zero.
You can get Doppler shift from antenna vibration. The mean of this will be zero.