A textbook definition of S parameters is; the reflected signal at port 1 = S11 x a1 + S12 x a2. This is a combination of the signal applied to and reflected from port 1, added to any signal at port 2 multiplied by the reverse isolation S12. The output signal at port 2 = S21 x a1 + S22 x a2, which is a combination of the signal applied to port 1 and the gain parameter S21, and any signal applied to port multiplied by the output reflection parameter S22.