[bisrig]

I know that this doesn't directly address the question you're asking, but to give an idea of the order of magnitude of the effect: the Doppler shift in frequency rounds to f_carrier * 2v/c. In the case of anything with "reasonable" speed, 2v/c is going to be very small (~10e-6 for Mach 1), and thus you would be talking about very minute differences between the transmitted and received pulse in terms of either overall pulse length or number of wavefronts received vs. sent (for what it's worth my intuition is that the pulse length actually shortens, but either way it's not measurable by the receiver).