Hi, all. Most radar systems are TDD (pulsed) in nature. There is a small TX window, followed by a RX window.
For radar TWTA, there is a "Pulse off Noise Power Density" specification. I include a Pulse TWTA application note from Amplifier Research. Inside, it quotes a pulse off noise power spectral density of -140dBm/Hz (Note for phase noise is usually in dBc/Hz). It is this pulse off noise that will leak to the RX input, via the circulator.
Assuming a circulator with 20 dB isolation, the TX noise (TX off state) leaking to the RX will be -140dBm -20dB, i.e. -160dBm in 1 Hz bandwidth.
This may seem trivial, but with modern radar signal processing bandwidth down to 1 Hz, the amount of RX input noise floor tolerable may be in similar range. So care must be exercised to ensure the pulse -off noise spectral density ( other important TWTA spec includes NF, pulse off isolation etc) to ensure the TX leakage signal to RX is acceptable.
Hope this will clarify the air.