Compensation of fibre impairments in coherent optical systems

Tese de mestrado integrado. Engenharia Electrotécnica e de Computadores. Faculdade de Engenharia. Universidade do Porto. 201

Polarization-dependent nonlinear effects in coherent detection systems

In the last decades the demand for data capacity has increased exponentially. Optical Coherent Detection, firstly proposed at the end of the 1980s to improve receiver sensitivity, has proved as one of the most powerful techniques to increase the optical communication spectral efficiency and so the total per channel capacity. Indeed, thanks to the recent advances in digital signal processing (DSP) and high speed electronics, the DSP-based coherent detection in optical networks expedited the use of polarization division multiplexing (PDM) as a cost-effective way of doubling system capacity. Furthermore, coherent detection presents many others advantages with respect to direct detection such as the use of multilevel optical modulation formats like N-PSK and N-QAM and compensating linear propagation effects in the electrical domain as chromatic dispersion, polarization mode dispersion (PMD) and optical filtering. On the other hand, transmission reach of WDM systems is a major concern for the deployment of such a solution and is usually mainly limited by cross-nonlinear effects. In WDM transmission systems, the cross-nonlinearities make neighboring channels interact depending on their power and state of polarization (SOP). The last is of particular concern in PDM systems since they are more sensitive to a new kind of distortion that has been generally referred to as cross-polarization modulation (XPolM) as a way to distinguish it from the well known cross-phase modulation (XPM). At the beginning of our research activity in 2009, despite the growing interest and the number of publications on XPolM, many of its features were still unknown. For example, in Sept. 2009 Winter et al. provided a model that successfully measured the degree of polarization degradation in presence of XPolM, but it was still not clear when the bit error rate (BER) is dominated by XPolM and how XPolM relates to the other relevant nonlinear effects, such as XPM and self-phase modulation (SPM). With the investigations presented in this thesis we want to fill the gap, by providing a systematic simulation study of system performance where each nonlinear effect acts individually. Furthermore, thanks to the possibility in Optilux software to take into account separately the nonlinear terms of the propagation equation, we add some new piece of knowledge about XPolM. We quantify the XPolM-induced penalty as a function of transmission parameters such as the channel power, spacing and state of polarization (SOP). We also clarify the role of the Viterbi and Viterbi-based carrier phase estimator in mitigation of XPM and XPolM. We focused our investigation mainly on PDM-quadrature phase shift keying (QPSK) modulation format. The thesis is organized as follows. In the first chapter the principal impairments for long haul transmissions are briefly recalled. They are divided into linear and nonlinear effects, according to whether they are independent of the signal power or not. The first group is composed of fiber attenuation, chromatic dispersion and polarization mode dispersion. The second group is composed of nonlinear polarization-independent effects: such as SPM and XPM. Other linear effects such as polarization dependent loss and nonlinear effects as intra channel cross phase modulation, four wave mixing, nonlinear phase noise and non elastic scattering effects (stimulated Raman and Brillouin scattering) are not included in our discussion, while the XPolM is discussed at length in Ch. 3. The second chapter discusses the joint use of PDM and the coherent detection, as a solution to increase the transmission capacity. We also discuss a new technique, namely mode division multiplexing (MDM), to further increase the transmission capacity thanks to the joint use with PDM and coherent detection. In Ch.3, after the definition of the XPolM term in the propagation equation, we show the polarization rotation and the PDM-QPSK constellation distortion induced by XPolM as a function of the rotation axis orientation. We perform such analysis both mathematically and by simulation. In Ch. 4 we show when the bit error rate (BER) of a PDM-QPSK channel is dominated by XPolM, through a massive use of simulation in a wide range of system setups. We analyze different pulse shapes, transmission links and transmission fibers in both hybrid (PDM-QPSK -- OOK) and homogeneous systems (PDM-QPSK). Furthermore we clarify the role of channel power, spacing, state of polarization (SOP) and Viterbi and Viterbi-based carrier phase estimator on the XPM- and XPolM-induced penalty. In the last part of the chapter we quantify the nonlinear penalty in a PDM-BPSK transmission system, showing the average performance and its fluctuation induced by the transmission sequences and SOPs. In Ch. 5 we compare different optical methods to improve the resilience of coherent 112-Gb/s PDM-QPSK WDM transmissions against cross-channel nonlinearities. Such methods consist of increasing the line group velocity dispersion (GVD), or the line PMD, or inserting in-line XPM suppressors, which are passive devices that introduce different delays on adjacent channels at specific points of the line. In Ch. 6 we summarize the experimental results obtained during the research activity at Alcatel-Lucent Bell-Labs France on MDM. In such an activity we employ a mode converter based on a liquid-crystal on silicon (LCOS) spatial modulator and a prototype few mode fiber (FMF). Last but not least, in the Appendix we discuss three different rules to correctly simulate the cross-nonlinearities, showing also some artifacts that can arise with a non-correct setting of some numerical parameters, such as the nonlinear step of Split-Step Fourier method, the sequence length and the sequence type

Contribution à l'étude des systèmes de transmission optique utilisant le format de modulation QPSK

La demande constante de capacité et la saturation prévue de la fibre monomode ont conduit récemment à des avances technologiques qui ont complètement changé le paysage des télécommunications à fibre optique. Le progrès le plus important était la mise en œuvre d'une détection cohérente à l'aide d'électronique rapide. Cela a permis pas seulement l'utilisation de formats de modulation qui promettent une utilisation plus efficace de la bande passante, mais aussi l utilisation des algorithmes adaptés pour combattre la dégradation du signal optique due à la propagation. Cette thèse a commencé un peu après le début de cette ère du cohérent et son principal objectif était de revoir les effets physiques de la propagation dans des systèmes de transmission terrestres, utilisant le format de modulation QPSK (Quadrature Phase Shift Keying). Le manuscrit est divisé en deux parties. La première partie est consacrée à une étude sur les séquences des données qui doivent être utilisés dans les simulations numériques, lorsqu un format de modulation avancée est impliqué. La propagation, et en particulier l'interaction entre la dispersion chromatique et les non-linéarités, introduisent une interférence inter-symbole (ISI). Vu que cet ISI dépend de l enchainement des données transmises, il est évident que le choix de la séquence a une influence sur la qualité estimée du canal. Etant donné que des séquences aléatoires infinies ne sont pas pratiquement réalisables, nous utilisons souvent des séquences pseudo-aléatoires (PR), i.e. des séquences déterministes de longueur finie, avec des statistiques équilibrés, qui semblent être aléatoires. Dans la première partie, nous décrivons la méthode de génération de séquences PR avec M. niveaux (M> 2) et nous détaillons leurs propriétés. En outre, nous proposons des outils numériques pour caractériser les séquences non pseudo-aléatoires qu on utilise souvent dans des simulations, ou parfois aussi dans des expériences au laboratoire. Enfin, nous présentons les résultats de simulations qui permettent de quantifier la nécessité d'utiliser des séquences PR en fonction des paramètres du système. Après avoir établi les séquences finies "les plus adaptées", dans la seconde partie du manuscrit, nous nous concentrons sur l'étude de la propagation, dans le contexte d'un système de transmission QPSK et en supposant une gestion de dispersion et un type de fibre variables. Plus précisément, nous étudions numériquement les statistiques de signaux dégradés dus à l'interaction de la dispersion chromatique avec les effets non linéaires, en négligeant tout effet de polarisation ou inter-canaux, aussi que le bruit des amplificateurs. Dans ce contexte, nous étions intéressés à déterminer si certaines lois empiriques développées pour les systèmes OOK, sont valable dans le cas d'une modulation QPSK, tels que le critère de la phase non-linéaire cumulée ( NL) ou des lois qui permettent une optimisation de la gestion de dispersion. Ensuite, nous révélons l'importance de la rotation de la constellation du signal initial, comme un paramètre qui peut fournir des informations pour la post-optimisation de notre système. Nous discutons également autour du fait que la forme de la constellation dépend de la gestion de dispersion et concernant les constellations nous concluons qu'il y en a généralement 3 types, avec: (1) une variance de phase supérieure à la variance d'amplitude (2) une variance d'amplitude supérieure à la variance de phase et (3) avec le signal ayant une constellation qui ressemble à la constellation d un signal sous l'influence d'un bruit blanc gaussien additif. Enfin, nous fournissons une explication phénoménologique des formes des constellations révélant le fait que des sous-séquences différentes conduisent à un type différent de dégradation et nous utilisons ces informations pour définir un paramètre qui quantifie le bénéfice potentiel d'un algorithme de correction du type MAP(Maximum A Posteriori Probability)The constant demand for capacity increase, together with the foreseen saturation of the single-mode optical fiber, paved the way to technological breakthroughs that have completely changed the landscape of fiber-optic telecommunications. The most important advance was, undeniably, the practical implementation of a coherent detection with the help of high-speed electronics. This has, first, enabled the use of advanced modulation formats that allowed for a more efficient use of the fiber bandwidth, compared to the classical On-Off Keying, while adapted algorithms could not be used in order to mitigate the optical signal degradation. This thesis began a little after the advent of coherent detection and its main objective was to revisit the propagation effects in optical transmission systems using "Quadrature phase shift keying" (QPSK) modulation in the context of terrestrial systems, i.e. for transmission distances of up to about 2000 km. The manuscript is divided into two parts. The first part is dedicated to a study on the data sequences that need to be used in numerical simulations, when advanced modulation is involved. Fiber propagation, and in particular the interplay between chromatic dispersion and nonlinearities, usually introduce a nonlinear inter-symbol interference (ISI) to the transmitted signal. Since this ISI depends on the actual transmitted data pattern, it is obvious that the choice of the sequence used in our numerical simulations will have a direct influence on the estimated channel quality. Since, an infinite length, random sequence is impractical; we very commonly use pseudorandom" (PR) sequences, i.e. finite-length, deterministic sequences with balanced pattern statistics that seem to be random. In the first part we describe the method of generating M-level (with M>2) pseudorandom sequences and we detail their properties. In addition, we propose numerical tools to characterize the non-pseudorandom sequences that we use in numerical simulations, or we are sometimes forced to use in laboratory experiments. Finally, we present results of numerical simulations that quantify the necessity to use PR sequences as a function of our system parameters. After having established the fairest possible finite sequences, in the second part of the manuscript, we focus on the study of the nonlinear propagation, in the context of a transmission system using QPSK modulation and assuming a variable dispersion management and fiber type. Specifically, we numerically study the signal statistics due to the interplay of chromatic dispersion and nonlinear effects, neglecting all polarization or multi-wavelength effects and the amplifier noise. In this context, we were first interested in determining whether some empirical laws developed for OOK systems, can be also used in the case of QPSK modulation, such as the criterion of cumulative nonlinear phase ( NL) or laws that allow for a quick optimization of the dispersion management. Next we reveal the importance of a global phase rotation added to the initial signal constellation, as a parameter that can provide interesting information for the post-optimization of our system. We also discuss the fact that the constellation shape critically depends on the applied dispersion management, while there are generally 3 types of constellations, concerning the complex signal statistics: (1) the phase variance is higher than the amplitude variance (2) the amplitude variance is higher than the phase variance and (3) the received signal constellation resembles to a constellation of a signal under the influence of just an Additive White Gaussian Noise. Finally, we provide a phenomenological explanation of the constellations shapes revealing the fact that different data sub-sequences suffer from a different kind of signal degradation, while we also use this information to define a parameter that quantifies the potential benefit from a MAP (Maximum A Posteriori probability) correction algorithmEVRY-INT (912282302) / SudocSudocFranceF

Forward Error Correction in Memoryless Optical Modulation

The unprecedented growth in demand for digital media has led to an all-time high in society’s demand for information. This demand will in all likelihood continue to grow as technology such as 3D television service, on-demand video and peer-to-peer networking continue to become more common place. The large amount of information required is currently transmitted optically using a wavelength division multiplexing (WDM) network structure. The need to increase the capacity of the existing WDM network infrastructure efficiently is essential to continue to provide new high bandwidth services to end-users, while at the same time minimizing network providers’ costs. In WDM systems the key to reducing the cost per transported information bit is to effectively share all optical components. These components must operate within the same wavelength limited window; therefore it is necessary to place the WDM channels as close together as possible. At the same time, the correct modulation format must be selected in order to create flexible, cost-effective, high-capacity optical networks. This thesis presents a detailed comparison of Differential Quadrature Phase Shift Keying (DQPSK) to other modulation formats. This comparison is implemented through a series of simulations in which the bit error rate of various modulation formats are compared both with and without the presence of forward error correction techniques. Based off of these simulation results, the top performing modulation formats are placed into a multiplexed simulation to assess their overall robustness in the face of multiple filtering impairments