Phase noise in probabilistic shaping DP-CS-NFDM systems: modeling and low-complexity estimation

This Letter investigates the phase noise estimation (PNE) problem in probabilistic shaping (PS) dual-polarization continuous spectrum nonlinear frequency division multiplexing (DP-CS-NFDM) systems. Firstly, a rigorous phase noise model in the nonlinear Fourier domain establishes the structure of intra-burst impairment, consisting of a common phase rotation on the ideal nonlinear Fourier coefficient plus an additive signal-coupled perturbation. This finding motivates a low-complexity per-burst PNE scheme. Secondly, we propose a QPSK-partitioning and decision-aided (QP-DA) scheme, which integrates QPSK-partitioning with a decision-aided mechanism to counteract the performance degradation of conventional PNE induced by PS. Finally, the experimental validations on a 40 GHz PS DP-CS-NFDM system demonstrate that the proposed QP-DA scheme achieves a 187-km extension in transmission reach and a 475-kHz improvement in laser linewidth tolerance over the blind phase search (BPS) benchmark, yielding a computational complexity of merely 8.4% relative to BPS.