Statistical properties of nonlinear distortion of a polarization-multiplexed OFDM signal in long-haul fiber links

We investigate nonlinear transmission regimes of a polarization-multiplexed 16-quadrature amplitude modulation (PDM-16-QAM) orthogonal frequency-division multiplexed (OFDM) signal in a long-haul optical link. We study the dependence between the strength of nonlinear distortion and statistical properties of a PDM-OFDM signal. We also consider the constellation shaping-based solutions that allow to significantly reduce the bit error rate (up to three to 12 times at the cost of 5%-20% signal redundancy) and propose a method to analytically optimize the symbol distribution for higher-order modulation formats using only the initial signal.