Frequency-domain equalization supported by training-aided 2 × 2 multi-input multi-output channel estimation (CE) is proposed for coherent optical transmission systems. In particular, novel training sequence (TS) schemes based on a constant amplitude zero auto-correlation code, efficient CE algorithms and equalizer-tap updating solutions are derived from the theoretical linear fiber channel model and investigated through simulations. The robustness of the proposed methods is demonstrated with respect to the main degrading optical propagation effects, such as amplified spontaneous emission noise, chromatic dispersion, polarization-mode dispersion, polarization-dependent loss, time misalignment between received and reference TS, frequency offset between transmitter and receiver lasers, as well as dynamic state of polarization rotation.