If you use simultaneous excitation, you get F-parameters, which are equivalent to S-parameters, but each F-port is a combination of S-ports.

Thanks Malcolm White for the response. Yes you are right.

For example, for two ports we have 4 S-parameters and 2 F-parameters but in that case, my question is how do I interpret those 2 F-parameters? Are those Return Loss(+taken into account for Mutual Coupling) or Insertion Loss((+taken into account for Mutual Coupling)?

The F parameters give the total complex signal at the combination of output ports specified for the specified combination of input ports.

Try it out for a Y combiner/splitter with ports 1, 2, 3 with simultaneous input to ports 1 and 2 and see what you get.

I think if the inputs are in phase F[(1 0deg) (1 0deg), 3) will be (2, 0 deg), but I'm not sure of the normalisation, so it might be (1, 0 deg)

F[(1 0deg) (1 0deg), (1 0deg) (1 0deg)) will be 0

F[(1 0deg) (1 180deg), 3) will be 0

F[(1 0deg) (1 180deg), (1 0deg) (1 0deg)) will be (1, 180 deg) I think, but try it.

Thanks very much, sir for the response Malcolm White

I have a clearer idea about the F parameters now.