On Fiber Nonlinearity Mitigation via 4D Geometric Shaping for Next-Generation Single-Span Systems

Four-dimensional (4D) constellations are optimized using geometric shaping (GS) with orthant symmetry (OS) over realistic optical channel models targeting next-generation single-span systems. The optical fiber is modeled via the Manakov equation and is implemented using the split-step Fourier method (SSFM) in a Monte-Carlo based approach. Additional noise sources and losses are added making the link model relevant in practice. Constellations are optimized for different cardinalities, forward error correction code rates, and symbol rates. The SSFM-optimized constellations are reported to offer up to 4% in reach increase with respect to conventional quadrature amplitude modulation (QAM). Comparisons against existing additive white Gaussian noise (AWGN)-optimized constellations show that SSFM-optimized constellations with OS generally negligibly outperform AWGN-optimized counterparts. This somewhat unexpected result leads to the conclusion that AWGN-optimized constellations are a good choice for realistic single-span optical links.