Geometrically-Shaped Multi-Dimensional Modulation Formats in Coherent Optical Transmission Systems

Shaping modulation formats in multi-dimensional (MD) space is an effective approach to harvest spectral efficiency gains in both the additive white Gaussian noise (AWGN) channel and the optical fiber channel. In the first part of this paper, existing MD geometrically-shaped modulations for fiber optical communications are reviewed. It is shown that large gains can be obtained by exploiting correlation in the dimensions or/and by increasing the cardinality of the modulation format. Practical limitations and challenges are also discussed together with efficient solutions. In the second part, we extend the recently proposed four-dimensional (4D) modulation format family based on the constraint of orthant-symmetry to high spectrum efficiencies up to 10 b/4D-sym by maximizing generalized mutual information for AWGN channel. Reach increases of up to 25% for a multi-span optical fiber transmission system are reported. Lastly, with the help of a recently introduced nonlinear interference (NLI) model, an optimization for designing nonlinear-tolerant 4D modulation formats is introduced for a single-span optical fiber system. Simulation results show that the proposed NLI model-based 4D modulation format could increase the effective SNRs by 0.25 dB with respect to the AWGN channel-optimal 4D modulation format.

Automated summary

Shaping modulation formats in multi-dimensional space is an effective approach to improve spectral efficiency in both AWGN channel and optical fiber channel. The first part of the paper reviews existing MD geometrically-shaped modulations for fiber optical communications, emphasizing the gains obtained through correlation exploitation and increasing modulation format cardinality, along with discussing practical limitations and challenges with efficient solutions. The second part presents extensions to the 4D modulation format family and optimization for designing nonlinear-tolerant 4D modulation formats, resulting in significant improvements in spectrum efficiency and effective SNRs.