Non linearity : IP3 / 1 dB compression relation

Hi,
I used to work with GaAs circuit (pHemt) and I use the "rule" that IP3 is 8 to 12 dB higher than 1 dB compression point.
I am not expert with non linearity effect so I have many question :

1) This "~10 dB" rule is valid for all GaAs circuit ? Amplifier but also Mixer, Phase shifter, switchs ?
Is cold pHemt are used this rule still good ?

2) And for other process : SiGe , GaN, SOI,... ?
What are the relationship ?

Thank you

It is essentially approx. 9.6dB that comes from mathematical relationships between P1dB and OIP3 ( In fact first order and third order distortion effects).
But in practice it varies as you said 8-12dB because of higher order nonlinear effects.That number above has been extracted based on the first order nonlinearities assumption.
This is independent from device type which you intend to use.It's general approximation.
You can find lot of information about that on the Internet. ( how it's obtained, where coming from etc.)

For any amplifier (GaAs, CMOS, BJT, SiGe, etc) the 10dB difference rule between IP3 and P1dB is valid ONLY if the amplifier has proper bias termination and filtering at frequency equal to f2-f1 in a two-tone test.

I have used EpHEMT for my design of LNA. I am getting IIP3 as 39 dBm and P1 dB compression point as 20 dBm. I have designed LNA with Single transistor and feedback. P1 dB compression point is measured with respect to output power.

Is it compulsory the difference between IIP3 and P1 dB compression approximately 8 -12 dB, even the single pHEMT transistor with feedback and two or three pHEMT transistors with feedback.

No, it's not compulsory.I designed a wideband amplifier that works 30-1200MHz with feedback using GaAs pHEMT years ago, and it had 24dBm P1dB and 41dBm OIP3.So the difference was 17dB.
But it's acceptable because while OIP3 measurement is done memory effects impact this.( Lower and Higher sidebands may be different and you takes the worst one etc.)It's also frequency depended.