In microwave circuits described by scattering parameters, it is advantageous to regard noise as noise waves . The noise characteristics of an n-port is then defined completely by one outgoing noise wave at each port (see 2-port example in fig. 2.1) and the correlation between these noise sources. Therefore, mathematically, you can characterize a noisy n-port by its scattering matrix and its noise wave correlation matrix .
Where is the time average of and is the conjugate complex of . Noise correlation matrices are hermitian matrices because the following equations hold.
Where Im is the imaginary part of and is the magnitude of .