Short version: compensating for doppler distortion in FM coded pulses is done using complicated magic, ehm, digital signal processing.
Long version: here's an IEEE paper on the topic: http://ecs.syr.edu/faculty/sarkar/pdf/2007_IEEE_Radar_297.pdf
For the mathematically inclined, Bassem Mahafza's books ("Radar Systems Analysis and Design Using Matlab" and "Matlab Simulations for Radar Systems Design") do a quite good job explaining these phenomena.