impedance matching with a rectangular waveguide

good morning dears
need for emergency help !!!!!
I want to reach out an impedance matching between microstrip line (characterisitc imedance Zo) and rectangular waveguide ,actually is a SIW,
through a microstrip step discontinuity transition with characterisitc imedance Z1, (see the attached figure), actually I spend a lot of my time without being able to find the appropriate Z1 impedance. so I have some questions and I will be thankfull if you answear me :

1- For impedance matching, I take input impedance of rectangular waveguide as a load impedance , is this correct or not ?

2- To calculate input impedance of rectangular waveguide using hfss, I use the expression :
Zin = Z11-(Z12*Z21/(Z22+ZL)) where ZL=50 Ohm. is this correct ? if not is there any method to find Zin ?

Check this paper:
"New Design Procedure to Determine the Taper Transition for Impedance Matching Between Microstrip Line and SIW Component"

From my experience if substrate is too thick, then it was difficult to have good matching between microstrip and SIW, maybe someone can comment on why is that.

I recommend to use GCPW line to SIW transition, much better bandwidth:

Look for theirs GCPW to SIW transition picture.
It may be simplified: insets may be non-triangular, just inset with the same width as GCPW line gap.
Optimization is done by altering inset length and inset inclination angle.

In the attached document check equation (11) to find the SIW impedance.