At 1.6 GHz with 160 dB of gain makes it really difficult to isolate the high power stages from the input. Any conductor will radiate some power, and with that much gain, a tiny bit of leakage will be louder than the signals from the GPS satellites that are 20,000 km away.
I would have expected a superhetrodyne receiver with two frequency shifts so that any unintended radiation from the sections where the signal is more powerful will be well away from the GPS frequencies.
I've had GPS active antennas oscillate with 20 - 30 dB of gain when the output of the antenna amplifier radiates and the antenna picks it up. I really don't think that it's possible to isolate against 100 dBs of gain.