Suppose we have a monostatic radar system, with only one target crossing at a speed $v$ at the main lobe of the antenna. The Doppler frequency for this case will be given by

$
f\_d = \frac{2v}{\lambda} = \frac{2v \cdot f}{c}
$

With $f$ being the carrier frequency of the received signal. However, if we downconvert, $f = 0$, which would give a $f\_d = 0$, which does not sound right to me. So, how does downconversion affect the Doppler signature?