Optical Communication based on Nonlinear Fouriertransformation
Final Report Abstract
Today, optical communication systems face a major challenge due to the rapidly growing demand for transmission capacity. This is limited by the nonlinear properties of the optical fiber, which are described by the model of the nonlinear Schrödinger equation for one or by the Manakov equations for both polarizations. A powerful mathematical tool for solving these nonlinear differential equations is the nonlinear Fourier transform (NFT). The NFT converts the input signal into a non-linear spectrum consisting of a continuous and a discrete component. The propagation of information in the nonlinear channel is then described by a simple phase rotation, since the eigenvalues are invariant. In this project, the eigenvalues of the discrete spectrum are used as information carriers. Optimized algorithms and suitable modulation methods have been developed. The technological requirement is the coherent transmission technology that allows the generation and detection of the optical field in the complex plane. An analog coherent transmission system was implemented for the experimental investigations. The transmission channel is a recirculating fiber loop. The arrangement of the amplifiers is optimized so that there is a minimal variation of optical power along the link. When using forward pumped Raman amplifiers, a novel process of interaction between signal and pump waves was identified and investigated in detail in cooperation with the Krummrich group. It is a type of modulation instability that creates new spectral components up to the GHz range in the receiver. Therefore, only backward pumped Raman amplifiers can be used in the fiber loop. With the transmission system, 2 eigenvalues with 10 bits/symbol in both polarizations were successfully transmitted over 1600 km. The modulated discrete eigenvalues that propagate through the noisy system are correlated at the receiver. Equalization and compensation for influences of noise were a focus. A novel approach is the use of joint detection when receiving transmitted eigenvalues. The range when transmitting 4ASK-8PSK signals has been increased by 120 km. Significantly better results were achieved with nonlinear equalizers. In particular, the use of a neural network was realized together with the Pachnicke group. This meant that the transmission range of an 8 Gbit/s signal could be increased by 2000 km to a distance of 5000 km. These were record values in 2022. A contribution was made to understanding how noise couples the nonlinear Fourier coefficients along the fiber and how these can be compensated for with suitable equalizers.
Publications
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Joint detection equalization on nonlinear Fourier transform based optical communication. 45th European Conference on Optical Communication (ECOC 2019), 369 (4 pp.)-369 (4 pp.). Institution of Engineering and Technology.
Chan, K.; Leibrich, J.; Geisler, A. & Schaeffer, C.G.
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Neural Networks based Equalization of Experimental Transmission using the Nonlinear Fourier Transformation. 2020 European Conference on Optical Communications (ECOC), 1-4. IEEE.
Koch, Jonas; Chan, Ken; Kuhl, Sebastian; Schaeffer, Christian G. & Pachnicke, Stephan
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On the Evolution of Noise in Multiple-Span Transmission With Forward Pumped Raman Amplifiers. Journal of Lightwave Technology, 39(10), 3177-3186.
Krummrich, Peter M.; Geisler, Alexander; Jeurink, Steffen & Schaeffer, Christian G.
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Signal Processing Techniques for Optical Transmission Based on Eigenvalue Communication. IEEE Journal of Selected Topics in Quantum Electronics, 27(3), 1-14.
Koch, Jonas; Chan, Ken; Schaeffer, Christian G. & Pachnicke, Stephan
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Experimental Investigation of Information Transmission Using the Nonlinear Fourier Transformation. Dissertation Fakultät ET, Helmut-Schmidt-Universität Hamburg / UniBwH
Geisler, Alexander
