FMCW Radar Working Logic Help
I'm not sure that you understand the basic operation of the FMCW radar.  

As soon as the transmitter sends out its signal, this signal is shifting in frequency at a particular rate, in Hz per Second.  The radar receiver will see no returns until the transmitter signal bounces off a target and returns to the antenna.  There will be a speed-of-light time delay, so the received signal will be at a different frequency than the signal currently being sent (the difference being Hz per Second times the round-trip delay).  The receiver mixes this return signal with the currently-transmitted signal to get the difference signal.  The reflected signal will be continuously received for the duration of the transmission, and for a stationary target the difference between the TX and RX frequencies will be constant.  You can perform your FFT of this difference over the full duration of the transmit signal. Different targets at different distances will give other difference signals, and the FFT can resolve all these simultaneous returns.

These transmissions aren't exactly continuous, but they are much longer than traditional pulsed-radar.  Multiple chirps are sent as the antenna rotates, so you have angle as well as distance information.  The amplitude of the return will indicate the "radar cross section" (size) of the target.