Performance of Probabilistic Shaping Coherent Channels in Hybrid Systems

We present the performance comparison of probabilistically shaped 64QAM with uniform 16/32QAM in hybrid systems. The results show that the PS signal can increase the maximum reach and is more tolerant to strong nonlinear interference. Nevertheless, when the nonlinear interference is weak, uniform formats can provide higher performance

Advanced Modulation Techniques for Flexible Optical Transceivers: The Rate/Reach Tradeoff

This tutorial paper reviews advanced modulation techniques that have been proposed in the literature for the implementation of flexible (or reconfigurable) transceivers, which are fundamental building blocks of next-generation software-defined optical networks. Using a common reference multi-span propagation system scenario, the performance of transceivers employing standard quadrature amplitude modulation with variable-rate forward error correction, probabilistic constellation-shaping, and time-domain hybrid formats is assessed, highlighting the achievable flexibility in terms of continuous tradeoff between transmission rate and distance. The combination of these techniques with sub-carrier multiplexing, which enables an increase of the fiber nonlinearity tolerance thanks to the optimization of the symbol rate per sub-carrier, is also discussed

On the Probabilistic Shaping and Geometric Shaping in Optical Communication Systems

We introduce and compare typical shaping schemes suitable for optical communications. The geometrically shaped-quadrature amplitude modulation (GS-QAM) formats are characterized by the non-equidistant spacing of constellation points, transmitted uniformly, and applied to improve system capacity. On the other hand, the well-known constant composition distribution matcher (CCDM) is applied for the generation of probabilistically shaped QAM (PS-QAM) formats. Mutual information (MI) is used as a metric to analyze the performances of regular/GS/PS-MQAM formats. In a linear amplified spontaneous emission noise limited region, it can be proved by the numerical simulation that MI performances of the GS-8/16QAM are always better than regular 8/16QAM and PS-8/16QAM; the largest shaping gains can be separately reached by PS-32QAM and GS-32QAM. We continue with the experimental demonstration on the 16QAM-based transmission system, and find that GS-16QAM generally has the best MI performance. We also find that the modulation-dependent nonlinear noises of the GS-8/16/32QAM are comparable to that of the regular 8/16/32QAM and generally lower than PS-8/16/32QAM. By using the enhanced Gaussian noise model, we observe that the GS-8/16QAM formats have better performances than regular 8/16QAM and PS-8/16QAM over multi-span transmission. Meanwhile, PS-32QAM formats provide superior performance over a relatively long transmission distance.MURI Program, Office of Naval Research (ONR) [N00014-13-1-0627]Open access journal.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Polarization-ring-switching for nonlinearity-tolerant geometrically-shaped four-dimensional formats maximizing generalized mutual information

In this paper, a new four-dimensional 64-ary polarization ring switching (4D-64PRS) modulation format with a spectral efficiency of 6 bit/4D-sym is introduced. The format is designed by maximizing the generalized mutual information (GMI) and by imposing a constant-modulus on the 4D structure. The proposed format yields an improved performance with respect to state-of-the-art geometrically shaped modulation formats for bit-interleaved coded modulation systems at the same spectral efficiency. Unlike previously published results, the coordinates of the constellation points and the binary labeling of the constellation are jointly optimized. When compared with polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM), gains of up to 0.7 dB in signal-to-noise ratio are observed in the additive white Gaussian noise (AWGN) channel. For a long-haul nonlinear optical fiber system of 8,000 km, gains of up to 0.27 bit/4D-sym (5.5% data capacity increase) are observed. These gains translate into a reach increase of approximately 16% (1,100 km). The proposed modulation format is also shown to be more tolerant to nonlinearities than PM-8QAM. Results with LDPC codes are also presented, which confirm the gains predicted by the GMI.Comment: 12 pages, 12 figure

Joint Superchannel Digital Signal Processing for Effective Inter-Channel Interference Cancellation

Modern optical communication systems transmit multiple frequency channels, each operating very close to its theoretical limit. The total bandwidth can reach 10 THz limited by the optical amplifiers. Maximizing spectral efficiency, the throughput per bandwidth is thus crucial. Replacing independent lasers with an optical frequency comb can enable very dense packing by overcoming relative drifts. However, to date, interference from non-ideal spectral shaping prevents exploiting the full potential of frequency combs. Here, we demonstrate comb-enabled multi-channel digital signal processing, which overcomes these limitations. Each channel is detected using an independent coherent receiver and processed at two samples-per-symbol. By accounting for the unique comb stability and exploiting aliasing in the design of the dynamic equalizer, we show that the optimal spectral shape changes, resulting in a higher signal-to-noise ratio that pushes the optimal symbol rate towards and even above the channel spacing, resulting in the first example of frequency-domain super-Nyquist transmission with multi-channel detection for optical systems. The scheme is verified both in back-to-back configuration and in single span transmission of a 21 channel superchannel originating from a 25 GHz-spaced frequency comb. By jointly processing three wavelength channels at a time, we achieve spectral efficiency beyond what is possible with independent channels. At the same time, one significantly relaxes the hardware requirements on digital-to-analog resolution and bandwidth, as well as filter tap numbers. Our results show that comb-enabled multi-channel processing can overcome the limitations of classical dense wavelength division multiplexing systems, enabling tighter spacing to make better use of the available spectrum in optical communications

Equalização digital para sistemas de transmissão ópticos coerentes

This thesis focus on the digital equalization of fiber impairments for coherent optical transmission systems. New efficient and low-complexity equalization and mitigation techniques that counteract fiber nonlinear impairments are proposed and the tradeoff between performance and complexity is numerically assessed and experimentally demonstrated in metro and long-haul 400G superchannels-based transmission systems. Digital backpropagation (DBP) based on low-complexity split-step Fourier method and Volterra series nonlinear equalizers are experimentally assessed in an uniform superchannel system. In contrast with standard DBP methods, these techniques prove to be able to be implemented with larger step-sizes, consequently requiring a reduced number of multiplications, and still achieve a significant reach extension over linear equalization techniques. Moreover, given its structure, the complexity of the proposed Volterra-based DBP approach can be easily adjusted by changing the nonlinear filter dimension according to the system requirements, thus providing a higher flexibility to the nonlinear equalization block. A frequency-hybrid superchannel envisioning near-future flexible networks is then proposed as a way to increase the system bit-rate granularity. The problematic of the power-ratio between superchannel carriers is addressed and optimized for linear and nonlinear operation regimes using three distinct FEC paradigms. Applying a single FEC to the entire superchannel has a simpler implementation and is found to be a more robust approach, tolerating larger uncertainties on the system parameters optimization. We also investigate the performance gain provided by the application of different DBP techniques in frequency-hybrid superchannel systems, and its implications on the optimum power-ratio. It is shown that the application of DBP can be restricted to the carrier transporting the higher cardinality QAM format, since the DBP benefit on the other carriers is negligible, which might bring a substantially complexity reduction of the DBP technique applied to the superchannel.A presente tese foca-se na equalização digital das distorções da fibra para sistemas óticos de transmissão coerente. São propostas novas técnicas eficientes e de baixa complexidade para a equalização e mitigação das distorções não lineares da fibra, e o compromisso entre desempenho e complexidade é testado numericamente e demonstrado experimental em sistemas de transmissão metro e longa distância baseados em supercanais 400G. A propagação digital inversa baseada no método de split-step Fourier e equalizadores não lineares de séries de Volterra de baixa complexidade são testadas experimentalmente num sistema baseado em supercanais uniformes. Ao contrário dos métodos convencionais utilizados, estas técnicas podem ser implementadas utilizando menos interações e ainda extender o alcance do sistema face às técnicas de equalização linear. Para além disso, a complexidade do método baseado em Volterra pode ser facilmente ajustada alterando a dimensão do filtro não linear de acordo com os requisitos do sistema, concedendo assim maior flexibilidade ao bloco de equalização não linear. Tendo em vista as futuras redes flexı́veis, um supercanal hı́brido na frequência é proposto de modo a aumentar a granularidade da taxa de transmissão do sistema. A problemática da relação de potência entre as portadoras do supercanal é abordada e optimizada em regimes de operação linear e não linear utilizando paradigmas diferentes de códigos correctores de erros. A aplicação de um único código corrector de erros à totalidade do supercanal mostra ser a abordagem mais robusta, tolerando maiores incertezas na optimização dos parâmetros do sistema. O ganho de desempenho dado pela aplicação de diferentes técnicas de propagação digital inversa em sistemas de supercanais hı́bridos na frequência é tamém analizado, assim como as suas implicações na relação óptima de potência. Mostra-se que esta pode ser restringida à portadora que transporta o formato de modulação de ordem mais elevada, uma vez que o benefı́cio trazido pelas restantes portadotas é negligenciável, permitindo reduzir significativamente a complexidade do algoritmo aplicado.Programa Doutoral em Telecomunicaçõe

Overhead-optimization of pilot-based digital signal processing for flexible high spectral efficiency transmission

We present a low-complexity fully pilot-based digital signal processing (DSP) chain designed for high spectral efficiency optical transmission systems. We study the performance of the individual pilot algorithms in simulations before demonstrating transmission of a 51 724 Gbaud PM-64QAM superchannel over distances reaching 1000 km. We present an overhead optimization technique using the system achievable information rate to find the optimal balance between increased performance and throughput reduction from adding additional DSP pilots. Using the optimal overhead of 2.4%, we report 9.3 (8.3) bits/s/Hz spectral efficiency, or equivalently 11.9 (10.6) Tb/s superchannel throughput, after 480 (960) km of transmission over 80 km spans with EDFA-only amplification. Moreover, we show that the optimum overhead depends only weakly on transmission distance, concluding that back-to-back optimization is sufficient for all studied distances. Our results show that pilot-based DSP combined with overhead optimization can increase the robustness and performance of systems using advanced modulation formats while still maintaining state-of-the-art spectral efficiency and multi-Tb/s throughput

High Spectral Efficiency Fiber-Optic Transmission Systems Using Pilot Tones

Modern fiber-optic communication systems combine state-of-the-art components with powerful digital signal processing (DSP) to maximize the system spectral efficiency (SE). Systems rely on wavelength-division multiplexing, including superchannel transmission, to enable transmission over the available bandwidth which reaches about 10 THz when accounting for the so-called C and L bands. A superchannel is a set of densely packed wavelength channels viewed as a single unit. By treating the channels together, they can be packed more closely than what is normally feasible and sharing of resources among the channels within the superchannel can be considered. In this thesis we focus on the special case of superchannels formed using coherent optical frequency combs. A frequency comb is a multi-wavelength light source and comb-based superchannels consists of channels which are modulated on lines originating from a common comb. Frequency combs have phase-locked carriers, meaning that in contrast to the standard case of independent lasers, the channels within a comb-based superchannel are locked on a frequency grid. Moreover, it implies that the carrier offsets originating from a non-ideal laser source are shared among all comb lines.Shared carrier offsets can be exploited to reduce the complexity of the DSP used to effectively recover the data. A frequency comb is fully characterized by knowing the state of two of its lines, meaning that if this information is transferred to the receiver, one could compensate carrier offsets for all wavelength channels within the superchannel. By transmission of optical pilot tones, self-homodyne detection of a 50x20Gbaud PM-64QAM superchannel is demonstrated with 4% spectral overhead. While two tones are required to fully phase-lock two combs, a single tone is enough to enable significant relaxation of the DSP-requirements while at the same time requiring minimal additional complexity compared to standard intradyne systems. Superchannel transmission using a single shared pilot tone is demonstrated by transmission of a 51x24Gbaud PM-128QAM superchannel with a resulting SE of 10.3bits/s/Hz. The single pilot scheme is also evaluated for distances up to 1000km showing high robustness to both noise and fiber nonlinearities. Finally, the high gain low overhead combination of the single pilot-tone scheme was used in a record demonstration reaching a SE of 11.5bits/s/Hz for fully loaded C-band transmission