1：Experimental Design and Method Selection:

The study introduces a system model for uncoded MCF transmission with phase noise comprising common laser phase noise and core- and polarization-specific phase drifts. A pilot-aided CPE algorithm is developed for this model to evaluate joint-channel and per-channel CPE strategies.

2：Sample Selection and Data Sources:

Monte Carlo simulations and MCF transmission experiments are conducted to assess phase-noise tolerances and compare strategies in terms of power efficiency, information rate, and laser-linewidth requirements.

3：List of Experimental Equipment and Materials:

The experimental setup included 3 synchronized recirculating loops running through 3 adjacent cores of a 7-core, 53.7 km, weakly-coupled, single-mode, homogeneous MCF. An external cavity laser (ECL) with 100 kHz linewidth was used as a light source and shared for all cores at the transmitter, while a separate 100 kHz ECL acted as an LO at the receiver.

4：7 km, weakly-coupled, single-mode, homogeneous MCF. An external cavity laser (ECL) with 100 kHz linewidth was used as a light source and shared for all cores at the transmitter, while a separate 100 kHz ECL acted as an LO at the receiver. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: Transmission of DP-QPSK, DP-16QAM, and DP-64QAM was carried out at 20 GBd. All detected signals were simultaneously digitized in a 12-channel oscilloscope operating at 80 GS/s for offline DSP.

5：Data Analysis Methods:

Performance is assessed by estimating BER or achievable information rate (AIR) for different pilot overheads, laser linewidth and symbol duration products, and SNRs per bit.