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

Abstract

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Analytical Model of Nonlinear Fiber Propagation for General Dual-Polarization Four-Dimensional Modulation Format

“…Substituting the spectrum of transmitted periodic signal (9) in (8), we obtain the PSD of received NLI, which is dealt with in Appendix B. Therefore, the η ss,XCI = (η x ss,XCI , η y ss,XCI ) for x polarization can be written as…”

“…The process of deriving the Manakov solution is similar to [24]. The solution after N s spans is expressed as (8), where the µ(f 1 , f 2 , f, N s , L s ) can be expressed as…”

“…III. Substituting the spectrum of the transmitted periodic signal ( 9) in (8), for instance, we obtain the x component,…”

“…Performing joint shaping over multiple dimensions (e.g., time slots, wavelengths, and spatial dimensions) to achieve large performance gains has recently received interest in the literature for both the additive white Gaussian noise (AWGN) [4], [5] and the optical fiber channel [5]- [8]. When constellation shaping tailored to the AWGN channel is used in the nonlinear optical channel, however, a performance penalty is introduced.…”

Geometrically shaped multi-dimensional modulation formats designed by deep learning

“…The state-of-art AE is expected to effectively design modulation formats that combine GS and MD with optimized SNR receiver sensitivity. Recently, it has been reported that the GS-MD modulation formats has higher receiver sensitivity with the AE [9].…”