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

TL;DR

This paper reviews and extends geometrically-shaped multi-dimensional modulation formats for optical communications, demonstrating significant spectral efficiency gains and improved nonlinear tolerance through innovative design and optimization techniques.

Contribution

It introduces high-efficiency 4D modulation formats based on orthant-symmetry and nonlinear interference modeling, enhancing spectral efficiency and transmission reach in optical systems.

Findings

Up to 25% increase in transmission reach for multi-span systems.

Achieved spectrum efficiencies up to 10 bits/4D-sym.

Enhanced nonlinear tolerance with 0.25 dB SNR improvement.

Abstract

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 bit/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.