Optical coherent transmission with spectral efficient modulation and detection based on the non-linear Fourier transform

该项目旨在利用基于非线性傅里叶变换(NFT)的孤子来改善光通信。这是一种全新的方法，在将信号调制到光纤上时隐含地考虑了克尔非线性。相比之下，传统方法将非线性视为需要减轻的干扰源。因此，传统的线性通信方案在覆盖范围和数据速率方面的性能受到光纤非线性的限制；增加发射功率会导致频谱效率降低，但信噪比仍有可能提高。因此，即使在进一步增加发射功率的情况下，考虑系统设计中已经存在的克尔非线性以实现通信质量的全面改善也是很有希望和直观的。本项目关注基于NFT的通信链路的可实现速率(互信息)，包括调制、信道和检测，而不是进一步考虑非线性光纤信道的理论容量。通过对由特征值和相应的频谱幅度组成的离散非线性频谱进行频谱有效调制来实现改善的传输质量。不再进一步考虑连续谱，并将其设置为零，因此仍需研究“纯”孤子脉冲。虽然孤子在过去已经得到了广泛的研究，但它们在高频谱效率的数据通信中的应用还处于起步阶段，还需要进一步研究它们的基本性质和相对于经典的基于奈奎斯特的信号的潜在优势。为了实现频谱高效调制，需要考虑不同的特征值星座以及频谱幅度的星座；特别是需要研究不同自由度对光纤时间带宽积的影响。这些自由度是星座特征值的实部和虚部，每个星座特征值的多重性和排列，以及同时传输的特征值的数量。此外，需要研究相应频谱幅度的信号点的调制(星座大小和点的排列)。此外，还需要研究噪声、非线性孤子相互作用以及其他现实世界中的缺陷对优化星座和脉冲序列的影响。最后，应在使用波分复用的光通信系统的背景下考虑为频谱效率而优化的基于NFT的传输的特性。

This project aims at improving optical communications using solitons based on the non-linear Fourier transform (NFT). It is a fundamentally new approach that implicitly takes into account the Kerr-nonlinearity when modulating signals onto the optical fiber. In contrast, conventional methods consider nonlinearities as a source of interference that needs to be mitigated. Thus, the performance of conventional linear communication schemes with respect to reach and data rates is limited by the the fiber nonlinearities; increasing launch powers results in reduced spectral efficiency although the signal-to-noise ratio may still improve. It is, thus, promising and intuitive to account for the Kerr-nonlinearity already in the system design to achieve an overall improved communication quality, even when further increasing the launch power.This project focuses on the achievable rate (mutual information) of NFT-based communication links including modulation, channel and detection; the theoretical capacity of the nonlinear optical fiber channel is not further considered. The improved transmission quality shall be achieved by spectral efficient modulation of the discrete nonlinear spectrum consisting of eigenvalues and respective spectral amplitudes. The continuous spectrum is not further considered and is set to zero, so that "pure" soliton impulses remain to be studied. Although solitons have been investigated extensively in the past, their application to data communication with high spectral efficiency is still in its beginnings; further research on their fundamental properties and potential advantages over classic "Nyquist"-based signaling is required.To achieve spectral efficient modulation, different eigenvalue constellations as well as constellations of the spectral amplitude are to be considered; in particular, the influence of the various degrees of freedom on the time-bandwidth-product along the fiber needs to be studied. Such degrees of freedom are the real and imaginary part of the eigenvalues of a constellation, the multiplicity and arrangement of the eigenvalues per constellation, and the number of concurrently transmitted eigenvalues. Moreover, the modulation of signal points of the respective spectral amplitude (constellation size and arrangement of points) needs to be investigated. Also, the influence of noise, nonlinear soliton interaction as well as other real-world imperfections on the optimized constellations and pulse sequences needs to be studied. Finally, the properties of NFT-based transmission optimized for spectral efficiency shall be considered in the context of an optical communication system using wavelength division multiplex.