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

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

Characterization and design of coherent optical OFDM transmission systems based on Hartley Transform

Nowadays, due to huge deployment of optical transport networks, a continuous increase towards higher data rates up to 100 Gb/s and beyond is observed. Furthermore, an evolution of the current optical networks is forecasted, acquiring new functionalities, e.g. elastic spectrum assignment for the optical signals. The target for these new challenges in transmission is to find techniques ready to deal with a growth of demand for bandwidth continuously asked by network operators, for whom the standard systems do not meet the new functionalities while higher rates are being set up. A solution for covering all of those needs is to adapt techniques capable to deal with such enormous data rates, and ensuring the same high efficiency for long distances and mitigate the optical impairments accumulated along the transmission path. Additionally, these transmission techniques are expected to provide some degree of flexibility, in order to enhance the network flexibility. A promising technology that can fully cope with those requires is the coherent optical orthogonal frequency division multiplexing (CO-OFDM). CO-OFDM provides several advantages, namely high sensitivity and spectral efficiency, simple integration and possibility to fully recover a signal in phase, amplitude and polarization. These systems are composed by digital signal processing (DSP) blocks that easily process data and can equalize and compensate the main impairments, providing high tolerance for dispersion effects. However, CO-OFDM systems are not free from drawbacks. Their high peak-to-average power ratio (PAPR) reduce their tolerance to nonlinearities. Furthermore, CO-OFDM systems are sensitive to any frequency shift and phase offset. Hence, a constant envelope optical OFDM (CE-OFDM) is proposed for significantly reducing the PAPR and solving high sensitivity to nonlinear impairments. It consists in a phase modulated discrete multi-tone signal, which is coherently detected at the receiver side. An alternative transform, the discrete Hartley transform, is proposed to speed up calculations in the DSP and eliminate the need to have a Hermitian symmetry. The optical CE-OFDM by its unique flexibility and rate scalability turns out as a great technology applicable to different configurations, ranging from access to core networks. In case of access solutions, several cases are investigated. First, the optical CE-OFDM is applied for radio access network signals delivery by means of a wavelength division multiplexing (WDM) overlay in deployed access architecture. A decomposed radio access network is deployed over an existing standard passive optical network (PON), capable to avoid interference and cross talks with access signals between network clients. The system exhibited narrow channel spacing, while reducing losses fed into the access equipment path. Next, a full duplex 10 Gb/s bidirectional PON transmission over a single wavelength with RSOA based ONU is investigated. The key point of that system is the upstream transmission, which is achieved re-modulating the phase of a downstream intensity modulated signal after proper saturation. The reported sensitivity performances show a power budget matching the PON standards and an OSNR easy to reach on non-amplified PON. Next, a flexible metropolitan area network of up to 100km with traffic add/drop using WDM is investigated. There the narrowing effect of the optical filters is studied. Finally, an elastic upgrade of the existing Telefonica model of the Spanish national core network is proposed. For that, the transceiver architecture is proposed to be operated featuring polarization multiplexing. Respect to the existing fixed grid, the flexible approach (enabled by the CE-OFDM transceiver) results into reduced bandwidth occupancy and low OSNR requirement.Hoy en día, debido al gran despliegue de las redes de ópticas de transporte, se espera un aumento continuado hacia mayores velocidades de datos, hasta 100 Gb/s y más allá. Por otra parte, la evolución que se prevé para las redes ópticas actuales, incluye la adquisición de nuevas funcionalidades, por ejemplo, la asignación del espectro de forma elástica para las señales ópticas. Por tanto, el claro desafío en cuanto a las tecnologías de transmisión es encontrar técnicas preparadas para hacer frente a un crecimiento de la demanda de ancho de banda; demanda que continuamente se incrementa por parte de los operadores de red, para quienes los sistemas estándar no se acaban de ajustar a las nuevas funcionalidades que esperan para la red. Una solución para cubrir todas estas necesidades es la adaptación de técnicas capaces de hacer frente a estas velocidades de datos enormes, y garantizar el mismo nivel de eficiencia para las largas distancias y mitigar las deficiencias ópticas acumuladas a lo largo de la ruta de transmisión. Además, se espera que estas técnicas de transmisión puedan proporcionar cierto grado de flexibilidad, a fin de mejorar y hacer más eficiente la gestión de la red. Una tecnología prometedora que puede hacer frente a estos requisitos es lo que se llama multiplexación por división de frecuencias ortogonales, combinado con la detección óptica coherente (CO-OFDM). CO-OFDM ofrece varias ventajas, entre otras: alta sensibilidad y eficiencia espectral y, sobre todo, la posibilidad de recuperar por completo de una señal en fase, la amplitud y la polarización. Estos sistemas están compuestos por bloques de procesado de señales digitales (DSP) que permiten detectar los datos fácilmente así como también compensar las principales degradaciones, proporcionando alta tolerancia a los efectos de dispersión. Sin embargo, los sistemas CO-OFDM no están exentos de inconvenientes. Su alta relación de potencia de pico a potencia media (PAPR) reduce sensiblemente la tolerancia no linealidades. Por otra parte, los sistemas CO-OFDM son sensibles a cualquier cambio de frecuencia y desplazamiento de fase. Por tanto, se propone un sistema OFDM de envolvente constante (CE-OFDM) para reducir significativamente la PAPR y solucionar la alta sensibilidad a las degradaciones no lineales. Consiste en una señal OFDM modulada en fase, que se detecta coherentemente en el receptor. Una transformada alternativa, la transformada discreta de Hartley, se propone para acelerar los cálculos en el DSP. El sistema CE-OFDM por su flexibilidad y escalabilidad única, resulta una tecnología aplicable a diferentes escenarios, que van desde las redes de acceso hasta las redes troncales. En el caso de las soluciones de acceso, se investigan varios casos. En primer lugar, el CE-OFDM aplica para el desarrollo y soporte de datos de una red radio, reutilizando una red óptica de acceso ya desplegada. A continuación, se investiga la transmisión bidireccional dúplex a 10 Gb / s sobre una sola longitud de onda empleando un RSOA a las unidades de usuario. El punto clave de este sistema es la transmisión en sentido ascendente, que se consigue re-modulando la fase de una señal de intensidad modulada después de saturar de forma adecuada. A continuación, se estudia una red de área metropolitana flexible de hasta 100 km. Concretamente el efecto de concatenación de filtros ópticos es el objetivo de este estudio. Finalmente, se propone una actualización elástica del modelo de Telefónica I+D para la red troncal española. Por ello, se propone operar el CE-OFDM en multiplexación de polarización. Los resultados muestran que esta combinación reduce sensiblemente el empleo de ancho de banda esto como los requisitos de los enlaces transmisión, reduciendo también los costes tanto de desarrollo como de operación y mantenimiento de la red.Avui dia, a causa del gran desplegament de les xarxes de òptiques de transport, s'espera un augment continuat cap a majors velocitats de dades, fins a 100 Gb/s i més enllà. D'altra banda, l'evolució que es preveu per a les xarxes òptiques actuals, inclou l'adquisició de noves funcionalitats, per exemple, assignació de l'espectre de forma elàstica per als senyals òptics. Per tant, el clar desafiament pel que fa a les tecnologies de transmissió és trobar tècniques preparades per fer front a un creixement de la demanda d'ample de banda; demanda que contínuament es fa per part dels operadors de xarxa, per als qui els sistemes estàndard no s'acaben d'ajustar a les noves funcionalitats que esperen per a la xarxa. Una solució per a cobrir totes aquestes necessitats és l'adaptació de tècniques capaces de fer front a aquestes velocitats de dades enormes, i garantir el mateix nivell d'eficiència per a les llargues distàncies i mitigar les deficiències òptiques acumulades al llarg de la ruta de transmissió. A més, s'espera que aquestes tècniques de transmissió puguin proporcionar cert grau de flexibilitat, per tal de millorar i tornar més eficient la gestió de la xarxa. Una tecnologia prometedora que pot fer front a aquests requisits és el que s'anomena multiplexació per divisió de freqüències ortogonals, combinat amb la detecció òptica coherent (CO-OFDM). CO-OFDM ofereix diversos avantatges, entre altres: alta sensibilitat i eficiència espectral i, sobretot, la possibilitat de recuperar per complet d'una senyal en fase, l'amplitud i la polarització. Aquests sistemes estan compostos per blocs de processament de senyals digitals (DSP) que permeten detectar les dades fàcilment així com també compensar les principals degradacions, proporcionant alta tolerància pels efectes de dispersió. No obstant això, els sistemes CO-OFDM no estan exempts d'inconvenients. La seva alta relació de potència de pic a potència mitjana (PAPR) redueix sensiblement la tolerància a no linealitats. D'altra banda, els sistemes de CO-OFDM són sensibles a qualsevol canvi de freqüència i desplaçament de fase. Per tant, es proposa un sistema OFDM d'envolvent constant (CE-OFDM) per a reduir significativament la PAPR i solucionar l'alta sensibilitat a les degradacions no lineals. Consisteix en un senyal OFDM modulat en fase, que es detecta coherentment en el receptor. Una transformada alternativa, la transformada discreta d'Hartley, es proposa accelerar els càlculs en el DSP. El sistema CE-OFDM per la seva flexibilitat i escalabilitat única, resulta una tecnologia aplicable a diferents escenaris, que van des de les xarxes d'accés fins a les xarxes troncals. En el cas de les solucions d'accés, s'investiguen diversos casos. En primer lloc, el CE-OFDM s'aplica per al desplegament i suport de dades d'una xarxa radio, reutilitzant una xarxa òptica d'accés ja desplegada. A continuació, s'investiga la transmissió bidireccional dúplex a 10 Gb/s sobre una sola longitud d'ona emprant un RSOA a les unitats d'usuari. El punt clau d'aquest sistema és la transmissió en sentit ascendent, que s'aconsegueix re-modulant la fase d'un senyal d'intensitat modulada després de saturar-la de forma adequada. A continuació, s'estudia una xarxa d'àrea metropolitana flexible de fins a 100 km. Concretament l'efecte de concatenació de filtres òptics és l'objectiu d'aquest estudi. Finalment, es proposa una actualització elàstica del model de Telefónica I+D per a la xarxa troncal espanyola. Per això, es proposa operar el CE-OFDM en multiplexació de polarització. Els resultats mostren que aquesta combinació redueix sensiblement l'ocupació d'ample de banda això com també els requisits dels enllaços transmissió, reduint també els costos tant de desplegament com d'operació i manteniment de la xarxa

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

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