How to find phase shift and process I/Q channel
The way to do it is to correlate the received signal with the signal you sent out- likely a chirp or something.  You correlate it with the signal from antenna 1, which will give you a time (location of the cross correlation peak) and phase (phase of the complex value of the peak).  You do the same with the signal from antenna 2, getting a time and phase.  If all is right the time should be the same (or, depending on your time resolution, very, very close).  The phase difference is simply the difference of the phases of the cross correlation peaks from the two antennas.