Sequential Number-Theoretic Optimization for High-Dimensional Channel Equalization in Coherent Optical PDM Systems

Polarization-division multiplexing (PDM) in coherent optical communications enhances system capacity but is vulnerable to various channel distortions including transmitter and receiver in-phase/quadrature (IQ) mismatch, rotation of state of polarization (RSOP), frequency offset (FO) and phase noise (PN), which significantly degrade the system performance. To address these challenges, we propose a novel approach using sequential number-theoretic optimization (SNTO) for the joint estimation of these distortions. We further introduce a decision-aided scheme with a window-split structure to accurately track and compensate for time-varying RSOP and PN, thereby implementing signal detection. Through comprehensive mean squared error (MSE) and bit error rate (BER) analysis under different signal-to-noise ratio (SNR) conditions and varying RSOP speeds, our method demonstrates high precision and effectiveness. The SNTO-based algorithm maintains robust performance with superior estimation accuracy and resilience against ultra-fast RSOP. This work introduces an innovative solution for high-dimensional channel equalization in coherent optical PDM systems with not only effectiveness but also robustness.