TY - GEN

T1 - Computing continuous nonlinear fourier spectrum of optical signal with artificial neural networks

AU - Sedov, Egor

AU - Prilepsky, Jaroslaw

AU - Chekhovskoy, Igor

AU - Turitsyn, Sergei

N1 - This work was supported by the RSF grant 17-72-30006 (ES, ST), by the grant of the President of the RF MK-677.2020.9 (IC), by the EPSRC grant TRANSNET (ES, ST), Leverhulme Trust project RPG-2018-063 (JP, SK). Publisher Copyright: © 2021 IEEE.

PY - 2021/6

Y1 - 2021/6

N2 - Nonlinear Fourier transform (NFT) (also known in the mathematical and nonlinear science community as the inverse scattering transform [1] ) has recently attracted a great deal of attention in the context of optical transmission in fiber channels [2] , that can be approximated by the nonlinear Schrodinger equation. Within the NFT-based¨ transmission approach, we modulate the parameters of the nonlinear spectrum (NS) and generate the respective information signal in time domain using inverse NFT. Both discrete and continuous parts of NS can be used, here we focus on the continuous spectrum only. Then, the signal is launched into the fiber, and at the receiver we apply direct NFT to the received signal's to retrieve the information encoded in NS. In this work we demonstrate that the high-accuracy computation of the continuous NS can be performed by using artificial neural networks (NN). The NS of a given localized signal q ( t ) containing no solitonic (discrete) components is represented by the continuous complex-valued function r ( ξ ) (the reflection coefficient) of the real spectral parameter ξ , where the latter plays the role of nonlinear frequency. The signals in our work have been specifically pre-selected to ensure that they contain no discrete spectrum. In the time domain, considered (normalized) symbol is given as the sum of independent sub-carriers [3] : $q(t) = \frac{1}{Q}\sum\nolimits_{k = 1}^M {{C_k}} {e^{i{\omega _k}t}}f(t)$ where M is a number of frequency channels, ω k is a carrier frequency of the k -th channel, C k corresponds to the digital data in k -th channel, and T defines the symbol interval; f ( t ) is the return-to-zero carrier support waveform. To assess the quality of NN prediction, we use the following formula for the relative error: $\eta (\xi ) = \frac{{\left\langle {\left| {{r_{predicted{\text{ }}}}(\xi ) - {r_{actual{\text{ }}}}(\xi )} \right|} \right\rangle }}{{\left\langle {\left| {{r_{actual{\text{ }}}}(\xi )} \right|} \right\rangle }}$ , where 〈•〉 denotes the mean over the spectral interval, the "predicted"and "actual"indices refer to the NN-predicted and precomputed values of the reflection coefficient r ( ξ ), respectively.

AB - Nonlinear Fourier transform (NFT) (also known in the mathematical and nonlinear science community as the inverse scattering transform [1] ) has recently attracted a great deal of attention in the context of optical transmission in fiber channels [2] , that can be approximated by the nonlinear Schrodinger equation. Within the NFT-based¨ transmission approach, we modulate the parameters of the nonlinear spectrum (NS) and generate the respective information signal in time domain using inverse NFT. Both discrete and continuous parts of NS can be used, here we focus on the continuous spectrum only. Then, the signal is launched into the fiber, and at the receiver we apply direct NFT to the received signal's to retrieve the information encoded in NS. In this work we demonstrate that the high-accuracy computation of the continuous NS can be performed by using artificial neural networks (NN). The NS of a given localized signal q ( t ) containing no solitonic (discrete) components is represented by the continuous complex-valued function r ( ξ ) (the reflection coefficient) of the real spectral parameter ξ , where the latter plays the role of nonlinear frequency. The signals in our work have been specifically pre-selected to ensure that they contain no discrete spectrum. In the time domain, considered (normalized) symbol is given as the sum of independent sub-carriers [3] : $q(t) = \frac{1}{Q}\sum\nolimits_{k = 1}^M {{C_k}} {e^{i{\omega _k}t}}f(t)$ where M is a number of frequency channels, ω k is a carrier frequency of the k -th channel, C k corresponds to the digital data in k -th channel, and T defines the symbol interval; f ( t ) is the return-to-zero carrier support waveform. To assess the quality of NN prediction, we use the following formula for the relative error: $\eta (\xi ) = \frac{{\left\langle {\left| {{r_{predicted{\text{ }}}}(\xi ) - {r_{actual{\text{ }}}}(\xi )} \right|} \right\rangle }}{{\left\langle {\left| {{r_{actual{\text{ }}}}(\xi )} \right|} \right\rangle }}$ , where 〈•〉 denotes the mean over the spectral interval, the "predicted"and "actual"indices refer to the NN-predicted and precomputed values of the reflection coefficient r ( ξ ), respectively.

UR - http://www.scopus.com/inward/record.url?scp=85119250551&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=47524830

U2 - 10.1109/CLEO/Europe-EQEC52157.2021.9541637

DO - 10.1109/CLEO/Europe-EQEC52157.2021.9541637

M3 - Conference contribution

AN - SCOPUS:85119250551

T3 - 2021 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2021

BT - 2021 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2021

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2021 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2021

Y2 - 21 June 2021 through 25 June 2021

ER -