I have a question about I/Q signals in Doppler radar, but I couldn't find a solution for this.
As far as I understand, the received signal at receiver side will be down-converted by mixing it with the transmit signal (direct conversion). And in order to generate I/Q signals, the received signal is also mixed with a 90degree phase shift of the transmit signal.
I have read several papers, and all of them say that
$$I(t) = \cos(\phi(t))$$ $$Q(t) = \sin(\phi(t))$$
My question is: where is the Doppler frequency component (assume having a moving target, for simplicity I ignore their amplitudes). I expected to see something like:
$$I(t) = \cos(f_D 2\pi t + \phi(t))$$ $$Q(t) = \sin(f_D 2\pi t + \phi(t))$$
Why the Doppler frequency does no more remain in the IQ signals?