  In this theoretical work, the DSP-perceived channel in optical coherent
communications is first simplified, based on which we categorize linear MIMO
equalizers into four classes according to their reference locations. The entire
channel inverse can be represented by a complex conjugate-dependent system,
coinciding with the widely linear equalization theory. Suboptimally removing FO
dynamics, relatively static channel inverses parameterized with common device
and channel parameters are presented for monitoring or calibration purposes.
