I have used PSA4-5043+ without problems; I was surprised to achieve noise figure of < 0.5 dB over band.
I observed, however, that some 3V regulators like LP2950CZ-3 generated oscillations and disturbed the operation of those nice LNAs. I had to connect a 10 uF capacitor across the LP terminals to get a clean 3V output.
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The spectrum peaks shown in your picture apparently come from external sources and the ADG device. If you need a clean spectrum, you must use a suitable band-pass filter BEFORE the PSA LNA, and enclose the circuits before it to prevent external FM and local TV signals from getting into PSA. Remember, it is an extremely low noise device. The more sensitive you make the receiver front-end, the more vulnerable it is to interference.