Optical Transmission Systems based on the Nonlinear Fourier Transformation

Solitons are stable pulse shapes, which propagate linearly and maintain their shape despite the highly nonlinear fiber optical channel. A challenge in the use of these signal pulses in optical data transmission is to multiplex them with high efficiency. One way to multiplex many solitons is the nonlinear Fourier transform (NFT). With the help of the NFT, signal spectra can be calculated which propagate linearly through a nonlinear channel. Thus, in perspective, it is possible to perform linear transmissions even in highly nonlinear regions with high signal power levels. The NFT decomposes a signal into a dispersive and a solitonic part. The dispersive part is similar to spectra of the conventional linear Fourier transform and dominates especially at low signal powers. As soon as the total power of a signal exceeds a certain limit, solitons arise. A disadvantage of solitons generated digitally by the NFT is their complex shape due to, for example, high electrical bandwidths or a poor peak-to-average power ratio. In the course of this work, a scalable system architecture of a photonic integrated circuit based on a silicon chip was designed, which allows to multiplex several simple solitons tightly together to push the complex electrical generation of higher order solitons into the optical domain. This photonic integrated circuit was subsequently designed and fabricated by the Institute of Integrated Photonics at RWTH Aachen University. Using this novel system architecture and additional equalization concepts designed in this work, soliton transmissions with up to four channels could be successfully realized over more than 5000 km with a very high spectral efficiency of 0.5 b/s/Hz in the soliton range

A survey on fiber nonlinearity compensation for 400 Gbps and beyond optical communication systems

Optical communication systems represent the backbone of modern communication networks. Since their deployment, different fiber technologies have been used to deal with optical fiber impairments such as dispersion-shifted fibers and dispersion-compensation fibers. In recent years, thanks to the introduction of coherent detection based systems, fiber impairments can be mitigated using digital signal processing (DSP) algorithms. Coherent systems are used in the current 100 Gbps wavelength-division multiplexing (WDM) standard technology. They allow the increase of spectral efficiency by using multi-level modulation formats, and are combined with DSP techniques to combat the linear fiber distortions. In addition to linear impairments, the next generation 400 Gbps/1 Tbps WDM systems are also more affected by the fiber nonlinearity due to the Kerr effect. At high input power, the fiber nonlinear effects become more important and their compensation is required to improve the transmission performance. Several approaches have been proposed to deal with the fiber nonlinearity. In this paper, after a brief description of the Kerr-induced nonlinear effects, a survey on the fiber nonlinearity compensation (NLC) techniques is provided. We focus on the well-known NLC techniques and discuss their performance, as well as their implementation and complexity. An extension of the inter-subcarrier nonlinear interference canceler approach is also proposed. A performance evaluation of the well-known NLC techniques and the proposed approach is provided in the context of Nyquist and super-Nyquist superchannel systems.Comment: Accepted in the IEEE Communications Surveys and Tutorial

Experimental Demonstration of Dual-Polarization NFDM Transmission With b-Modulation

Dual-polarization nonlinear frequency-division multiplexing (DP-NFDM) transmission has been intensively investigated recently due to its potential of doubling the capacity in comparison with single-polarization NFDM systems. However, up to now, due to many challenges in design and practical implementation, the demonstrated data rates of DP-NFDM transmission systems in experiments are still much lower than the record data rate of single-polarization NFDM transmissions (125 Gb/s). In this letter, by employing the concept of b-modulation and developing effective digital signal processing (DSP), we have experimentally demonstrated for the first time a high-capacity DP-NFDM transmission system, achieving a net data rate of 220 Gb/s with a spectral efficiency (SE) of 4 bits/s/Hz

Digital electronic predistortion for optical communications

The distortion of optical signals has long been an issue limiting the performance of communication systems. With the increase of transmission speeds the effects of distortion are becoming more prominent. Because of this, the use of methods known from digital signal processing (DSP) are being introduced to compensate for them. Applying DSP to improve optical signals has been limited by a discrepancy in digital signal processing speeds and optical transmission speeds. However high speed Field Programmable Gate Arrays (FPGA) which are sufficiently fast have now become available making DSP experiments without costly ASIC implementation possible for optical transmission experiments. This thesis focuses on Look Up Table (LUT) based digital Electronic Predistortion (EPD) for optical transmission. Because it is only one out of many possible implementations of EPD, it has to be placed in context with other EPD techniques and other distortion combating techniques in general, especially since it is possible to combine the different techniques. Building an actual transmitter means that compromises and decisions have to be made in the design and implementation of an EPD based system. These are based on balancing the desire to achieve optimal performance with technological and economic limitations. This is partly done using optical simulations to asses the performance. This thesis describes a novel experimental transmitter that has been built as part of this research applying LUT based EPD to an optical signal. The experimental transmitter consists of a digital design (using a hardware description language) for a pair of FPGAs and an analogue optical/electronic setup including two standard DAC integrated circuits. The DSP in the transmitter compensated for both chromatic dispersion and self phase modulation. We achieved transmission of 10.7 Gb/s non-return-to-zero (NRZ) signals with a +4 dBm launch power over 450 km keeping the required optical-signal-to-noise-ratio (OSNR) for a bit-error-rate of 2x10^{-3} below 11 dB. In doing so we showed experimentally, for the first time, that nonlinear effects can be compensated with this approach and that the combination of FPGA-DAC is a viable approach for an experimental setup

Achievable information rates for nonlinear frequency division multiplexed fibre optic systems

Fibre optic infrastructure is critical to meet the high data rate and long-distance communication requirements of modern networks. Recent developments in wireless communication technologies, such as 5G and 6G, offer the potential for ultra-high data rates and low-latency communication within a single cell. However, to extend this high performance to the backbone network, the data rate of the fibre optics connection between wireless base stations may become a bottleneck due to the capacity crunch phenomena induced by the signal dependent Kerr nonlinear effect. To address this, the nonlinear Fourier transform (NFT) is proposed as a solution to resolve the Kerr nonlinearity and linearise the nonlinear evolution of time domain pulses in the nonlinear frequency domain (NFD) for a lossless and noiseless fibre. Nonlinear frequency division multiplexing (NFDM), which encodes information on NFD using the discrete and continuous spectra revealed by NFT, is also proposed. However, implementing such signalling in an optical amplifier noise-perturbed fibre results in complicated, signal-dependent noise in NFD, the signal-dependent statistics and unknown model of which make estimating the capacity of such a system an open problem. In this thesis, the solitonic part of the NFD, the discrete spectrum is first studied. Modulating the information in the amplitude of soliton pulse, the maximum time-scaled mutual information is estimated. Such a definition allows us to directly incorporate the dependence of soliton pulse width to its amplitude into capacity formulation. The commonly used memoryless channel model based on noncentral chi-squared distribution is initially considered. Applying a variance normalising transform, this channel is approximated by a unit-variance additive white Gaussian noise (AWGN) model. Based on a numerical capacity analysis of the approximated AWGN channel, a general form of capacity-approaching input distributions is determined. These optimal distributions are discrete comprising a mass point at zero (off symbol) and a finite number of mass points almost uniformly distributed away from zero. Using this general form of input distributions, a novel closed-form approximation of the capacity is determined showing a good match to numerical results. A mismatch capacity bounds are developed based on split-step simulations of the nonlinear Schr$\rm \ddot{o}$dinger equation considering both single soliton and soliton sequence transmissions. This relaxes the initial assumption of memoryless channel to show the impact of both inter-soliton interaction and Gordon-Haus effects. Our results show that the inter-soliton interaction effect becomes increasingly significant at higher soliton amplitudes and would be the dominant impairment compared to the timing jitter induced by the Gordon-Haus effect. Next, the intrinsic soliton interaction, Gordon Haus effect and their coupled perturbation on the soliton system are visualised. The feasibility of employing an artificial neural network to resolve the inter-soliton interaction, which is the dominant impairment in higher power regimes, is investigated. A method is suggested to improve the achievable information rate of an amplitude modulated soliton communication system using a classification neural network against the inter-soliton interaction. Significant gain is demonstrated not only over the eigenvalue estimation of nonlinear Fourier transform, but also the continuous spectrum and eigenvalue correlation assisted detection scheme in the literature. Lastly, for the nonsolitonic radiation of the NFT, the continuous spectrum is exploited. An approximate channel model is proposed for direct signalling on the continuous spectrum of a NFDM communication system, describing the effect of noise and nonlinearity at the receiver. The optimal input distribution that maximises the mutual information of the proposed approximated channel under peak amplitude constraint is then studied. We present that, considering the input-dependency of the noise, the conventional amplitude-constrained constellation designs can be shaped geometrically to provide significant mutual information gains. However, it is observed that further probabilistic shaping and constellation size optimisation can only provide limited additional gains beyond the best geometrically shaped counterparts, the 64 amplitude phase shift keying. Then, an approximated channel model that neglects the correlation between subcarriers is proposed for the matched filtered signalling system, based on which the input constellation is shaped geometrically. We demonstrate that, although the inter-subcarrier interference in the filtered system is not included in the channel model, shaping of the matched filtered system can provide promising gains in mismatch capacity over the unfiltered scenario

Anwendung von maschinellem Lernen in der optischen Nachrichtenübertragungstechnik

Aufgrund des zunehmenden Datenverkehrs wird erwartet, dass die optischen Netze zukünftig mit höheren Systemkapazitäten betrieben werden. Dazu wird bspw. die kohärente Übertragung eingesetzt, bei der das Modulationsformat erhöht werden kann, erforder jedoch ein größeres SNR. Um dies zu erreichen, wird die optische Signalleistung erhöht, wodurch die Datenübertragung durch die nichtlinearen Beeinträchtigungen gestört wird. Der Schwerpunkt dieser Arbeit liegt auf der Entwicklung von Modellen des maschinellen Lernens, die auf diese nichtlineare Signalverschlechterung reagieren. Es wird die Support-Vector-Machine (SVM) implementiert und als klassifizierende Entscheidungsmaschine verwendet. Die Ergebnisse zeigen, dass die SVM eine verbesserte Kompensation sowohl der nichtlinearen Fasereffekte als auch der Verzerrungen der optischen Systemkomponenten ermöglicht. Das Prinzip von EONs bietet eine Technologie zur effizienten Nutzung der verfügbaren Ressourcen, die von der optischen Faser bereitgestellt werden. Ein Schlüsselelement der Technologie ist der bandbreitenvariable Transponder, der bspw. die Anpassung des Modulationsformats oder des Codierungsschemas an die aktuellen Verbindungsbedingungen ermöglicht. Um eine optimale Ressourcenauslastung zu gewährleisten wird der Einsatz von Algorithmen des Reinforcement Learnings untersucht. Die Ergebnisse zeigen, dass der RL-Algorithmus in der Lage ist, sich an unbekannte Link-Bedingungen anzupassen, während vergleichbare heuristische Ansätze wie der genetische Algorithmus für jedes Szenario neu trainiert werden müssen