Conceptually, system noise is affected most by the noise figure of the 1st amplifier in the receive, as well as its gain. That's why LNAs are used, due to low NF (noise figure). Also, dB is waaaaay easier to do the math in.
This is off the top of my head, not a book source so take it with a grain of salt:
Each cascading amplifier in series uses the gain of the PREVIOUS amplifier, and divides its own NF by that value. So if you have amplifiers: LNA, A1, A2, A3 with associated NF NFlna, NF1, NF2, NF3, and gains Glna, G1, G2, G3 the equation for system NF is something like:
NFlna + NF1/Glna + NF2/G1 + NF3/G2 [dB]
Note, noise temperature is not included here, this is purely the recieve chain.
I would look up in the book "Satellite communications " 2nd edition by Pratt, Bostian, and Allmut, but I am not near my copy. Maybe you can find a PDF, but they explain it there quite well.
If anyone else is still looking, I checked out some reviews online and this one seems pretty highly rated. You can purchase it used for like $15 which is pretty good for a textbook: https://www.amazon.com/Satellite-Communications-Timothy-Pratt/dp/047137007X
I also found it using "less conventional" methods which I won't delve into but I'm sure you have the capabilities to research.