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[URL unfurl="true"]https://www.keysight.com/ca/en/assets/7018-06743/application-notes/5952-1087.pdf[/URL]

There are many different matrices including W-parameters. Let me try to summarize the above.

[ATTACH=full]198091[/ATTACH]

The total at any point  , Vt, It

[ATTACH=full]198092[/ATTACH]

The traveling waves

[ATTACH=full]198093[/ATTACH]

The formation of scattering  waves relative to impedance , Zo

[ATTACH=full]198094[/ATTACH]

The relationship to scattering parameters (S-parms)

[ATTACH=full]198095[/ATTACH]

The S-parm definitions and assumptions.

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Using admittance

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Using normalized shunt admittance.

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Converting to T parameters which are independent of the other side of a 2 port.

[ATTACH=full]198099[/ATTACH]

The use of conjugate impedance matching with flow diagrams

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The definition of delivered power 

Pdel = |a|² –|b|²

The reflection also can be inverted if the magnitude of load Z is less than Zo or non-inverted if greater than Zo.

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[ATTACH=full]198101[/ATTACH]

Ideally all interfaces should be conjugally matched.

If for some reason an interface path cannot be transformed efficiently which end do you match for Zo of the path to maximize output power?

1. The source? 

2. the one which is higher?  (source or load)  for no reflection ...

3. The RMS median of both ?

RMS of both ends.  Zo = sqrt (Zsource ²+ Zload ²)

e.g. sqrt( 100²+20²) = 102 

e.g. without reactance factors or using s-parms for simplicity, Zs= 100 to Z.ant=20 ohm suggestions a path impedance of 102 ohms which seems to suggest and 2).

The simple answer is if we assume the PA input has zero reflections then s22 does not matter. 

[ATTACH=full]198102[/ATTACH]