Power amplifier for very low input power and high gain

What type of power amplifier good for amplification signal with very low input power about -120dBm and high gain about 30dB?
It is used in GNSS receiver.

GNSS satellite system use CDMA modulation, so the circuit needs a linear amplification.
At this low output power level (+10dBm) the amplifier efficiency probably is not such important, so a Class-A Power Amplifier would be a good option getting good linearity and high gain.

Well, with output power +10dBm do you mean that power gain have to be 110dB?
My input power is very small, it is -120dBm.

That would give output of -90dBm.
-120 +30 = -90
No, it must be 130dB.
The difference between +10 and -120 is 130

Yes, I was mistaken.
For design such a low output power, is there a procedure to do it? I tried to do it as the way to design a normal power amplifier but because Pout is very low and therefore Rload from the formula Pout = Vdd^2/(2RLoad) is very very large about tens giga ohms.

Right calculation but wrong formula.

I don't know why it is wrong?
Assuming that the output voltage swings between 0 and 2Vdd and it is a sinusoidal.
=> P = Vrms^2/Rload = (Vdd/sqrt(2))^2/Rload = Vdd^2/(2Rload).

But load impedance for RF amplifiers will be usually 50 ohm, maybe 100 or 200 ohm in special cases.

Yes, the load resistance that I calculated is the one we get after impedance transformation network.
For example, with 50 ohms load we can make it up to 10 Gohms with impedance transfomation network.

I fear, you need to learn quite a bit about RF engineering to proceed with the problem.