Long-haul Optical Fiber Communication Research Articles

Coherent all-optical reservoir computing for nonlinear equalization in long-haul optical fiber communication systems

Photonic reservoir computing (RC), as a promising paradigm of optical signal processing, has attracted a great deal of attention in fiber nonlinearity equalization recently. For real long-haul transmission scenarios, we propose an all-optical RC operated in a coherent scheme to mitigate the nonlinear distortion of high-speed signals. Compared with the direct decision architecture, the proposed RC can dramatically improve the Q2 factor by 2.6 dB for a single-wavelength system and 1.9 dB for a 7-channel wavelength-division multiplexing (WDM) system over 3960-km fiber transmission. Furthermore, the robustness of the coherent all-optical RC is also verified by conducting studies on different training sequences. The coherent all-optical RC shows great potential in real-time nonlinearity mitigation for long-haul fiber transmissions.

Inter-channel nonlinearity compensation in long-haul optical fiber communication using overlapped-dense LSTM network: Complexity reduction and visual understanding

The nonlinear distortion resulted from the Kerr effect in optical fibers limits the transmission capacity in long-haul optical fiber communications. In wavelength-division multiplexing (WDM) systems, the inter-channel nonlinear distortion is generally stronger than the intra-channel one, and also more difficult to be compensated, despite that there exist many reports on the nonlinearity compensation methods. Recently, recurrent neural networks have emerged as a potential solution without relying on detailed transmission link information. However, these networks often suffer from high computational complexity and lack interpretability due to their black-box nature. In this paper, we propose a novel overlapped-dense long short-term memory network (OD-LSTM). It can track the correlation of cross-phase-modulation (XPM) and consequently is capable of compensating the inter-channel nonlinear distortion. For a lower complexity, the overlapped-dense structure reduces the hidden units at time steps of different regions, since the correlation of XPM is reduced for the more distant symbols. To evaluate the effectiveness of our proposed scheme, we conduct a numerical simulation on a nine-channel WDM coherent optical transmission over a 1600-km standard single-mode fiber (SSMF) with DP-16QAM at 40 Gbaud. At the optimal optical power of −3 dBm, we observe a 0.52 dB Q-factor gain with the OD-LSTM equalizer, outperforming the digital back-propagation (DBP) with three steps per span and the Co-LSTM regressor. In terms of complexity, our proposed approach achieves a 13.5 % reduction compared to the Co-LSTM classifier, and its complexity is slightly lower than that of the ultralow complexity Co-LSTM regressor. We also discuss the visual understanding of the OD-LSTM, which provides insights into the internal mechanisms of the network.

Qualitative analysis of PMD-induced long-haul optical fiber link

Abstract This paper studies the detrimental effect of polarization mode dispersion on long-haul optical fiber communication in terms of the quality factor and bit error rate. The dispersion value is varied for different fiber lengths, specifically for long-haul communication, and the results obtained are analyzed in terms of the quality factor. The polarization mode dispersion causes pulse broadening, leading to interchannel interference. There is a need to check the occurrence and the associated effects of this dispersion. The communication range for conducting the analysis varies from 150 km to 350 km. The analysis is first conducted on varied communication fiber link length for different dispersion values, and it is observed that a fiber length of 200 km gives comparatively favorable results, as seen from the BER analysis.

Deep Learning-Aided Perturbation Model-Based Fiber Nonlinearity Compensation

Fiber nonlinearity effects cap achievable rates and ranges in long-haul optical fiber communication links. Conventional nonlinearity compensation methods, such as perturbation theory-based nonlinearity compensation (PB-NLC), attempt to compensate for the nonlinearity by approximating analytical solutions to the signal propagation over optical fibers. However, their practical usability is limited by model mismatch and the immense computational complexity associated with the analytical computation of perturbation triplets and the nonlinearity distortion field. Recently, machine learning techniques have been used to optimise parameters of PB-based approaches, which traditionally have been determined analytically from physical models. It has been claimed in the literature that the learned PB-NLC approaches have improved performance and/or reduced computational complexity over their non-learned counterparts. In this paper, we first revisit the acclaimed benefits of the learned PB-NLC approaches by carefully carrying out a comprehensive performance-complexity analysis utilizing state-of-the-art complexity reduction methods. Interestingly, our results show that least squares-based PB-NLC with clustering quantization has the best performance-complexity trade-off among the learned PB-NLC approaches. Second, we advance the state-of-the-art of learned PB-NLC by proposing and designing a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fully learned</i> structure by adopting the noiseless Manakov equation as the channel propagation model. We apply a bi-directional recurrent neural network for learning perturbation triplets that are alike those obtained from the analytical computation and are used as input features for the neural network to estimate the nonlinearity distortion field. Finally, we demonstrate through numerical simulations that our proposed fully learned approach achieves an improved performance-complexity trade-off compared to the existing learned and non-learned PB-NLC techniques.

Wideband Multichannel Nyquist-Spaced Long-Haul Optical Transmission Influenced by Enhanced Equalization Phase Noise.

Enhanced equalization phase noise (EEPN), generated from the uncompensated dispersion experienced by laser phase noises, can cause serious damage to the transmission quality of optical fiber systems. In this work, the performance of a wideband Nyquist-spaced long-haul nonlinear optical fiber communication systems suffering from EEPN is investigated and discussed through split-step numerical simulations and analytical models based on the perturbation analysis, in the cases of digital nonlinearity compensation (NLC) and electronic dispersion compensation (EDC). The efficiency and the accuracy of the analytical models were validated via simulations, considering the different symbol rates and modulation formats. The performance of the C-band transmission was comprehensively studied based on the model. Our results reveal that the growth of symbol rates and transmission distances aggravates the distortions in the C-band system.

Combined impact of SRS, FWM and ASE noise in UDWDM/DWDM long-haul communication systems using EDFAs

In this paper, the combined impact of SRS, FWM and ASE noise in center channels of 7-, 15-, 31- and 63-channel UDWDM/DWDM long-haul multi-span optical fiber communication systems using different numbers of EDFAs has been analyzed with simulations. UDWDM/DWDM systems with varying system parameters, i.e. channel input powers, channel spacing values, multi-span fiber lengths and numbers of EDFAs, have been taken into account in simulations. Comparative OSNR simulation results satisfying a minimum 23 dB OSNR criterion under the combined impact of SRS, FWM and ASE noise have been presented and evaluated. OSNR vs channel input power simulation results show that FWM becomes the most dominant effect with respect to SRS and ASE noise in UDWDM systems. Therefore, OSNR values decrease as channel input powers increase in multi-span UDWDM systems having 3.125 GHz and 6.25 GHz channel spacing values. However, both ASE noise and SRS become more dominant with respect to FWM in DWDM systems with 100 GHz channel spacing values. OSNR values increase as the channel input powers increase in those multi-span DWDM systems. Simulation results for OSNR vs channel spacing values show that OSNR values obtained in multi-span UDWDM systems increase as channel spacing values increase in the 3.125 GHz–6.25 GHz range. This is due to the decrease in FWM crosstalk, which has a dominant effect in UDWDM systems, with increasing channel spacing values in those UDWDM systems. However, OSNR values obtained in multi-span DWDM systems decrease as channel spacing values increase in the 12.5 GHz–100 GHz range. This is due to the increase in ASE noise, which has a dominant effect in DWDM systems, with increasing optical filter bandwidths of those DWDM systems. OSNR vs channel length simulation results show that OSNR values generally decrease with increasing total fiber lengths and inter-amplifier fiber lengths in both UDWDM and DWDM multi-span systems. This is due to the FWM crosstalk and the ASE noise, which become more dominant with respect to the SRS as the total fiber length and inter-amplifier fiber lengths increase. Simulation results for OSNR vs number of EDFAs show that OSNR values obtained in multi-span UDWDM systems having 3.125 GHz channel spacing values decrease with increasing numbers of EDFAs. However, OSNR values in multi-span UDWDM/DWDM systems having 6.25 GHz-100 GHz channel spacing range increase with increasing numbers of EDFAs. Simulation results provide important clues for the design and implementation of reliable long-haul UDWDM/DWDM systems.

Nonlinear Coherent Optical Systems in the Presence of Equalization Enhanced Phase Noise

Equalization enhanced phase noise (EEPN) occurs due to the interplay between laser phase noise and electronic dispersion compensation (EDC) module. It degrades significantly the performance of uncompensated long-haul coherent optical fiber communication systems. In this work, a general expression accounting for EEPN is presented based on Gaussian noise model to evaluate the performance of multi-channel optical communication systems using EDC and digital nonlinearity compensation (NLC). The nonlinear interaction between the signal and the EEPN is analyzed. Numerical simulations are carried out in nonlinear Nyquist-spaced wavelength division multiplexing (WDM) coherent transmission systems. Significant performance degradation due to EEPN in the cases of EDC and NLC are observed, with and without the consideration of transceiver (TRx) noise. The validation of the analytical approach has been done via split-step Fourier simulations. The maximum transmission distance and the laser linewidth tolerance are also estimated to provide important insights into the impact of EEPN.

Reduced sampling rate Kalman filters for carrier phase and frequency offset tracking in 200\xa0Gbps 16 QAM coherent communication system

We propose 1 state and 2 state multi-step Kalman filters (MKFs) to estimate and compensate CFO, LPN and NLPN in long-haul coherent fiber-optic communication systems. The proposed filters generate state estimates once every m symbols and therefore operate at a reduced sampling rate compared to conventional KFs that perform symbol by symbol processing. No computations are performed to obtain phase estimates of the intermediate m-1 samples; instead, the present and previous estimates are averaged and used to derotate the intermediate m-1 samples which are then demodulated to recover the transmitted symbols. This reduces the computational load on the receiver DSP. Further, in order to improve estimation accuracy, we adaptively vary the process noise covariance Q. Simulation results of 200 Gbps PDM 16 QAM system over 12 spans shows that the proposed 1 state MKF can reduce the sampling rate requirement by a factor of m = 20 with Q-factor degradation of 1.32 dB compared to single-step KF at linewidth of 100 kHz. The 2 state MKF tracks PN and CFO with a maximum step size of m=10 for a CFO of 100 MHz at linewidth of 100 kHz. We also study the dynamic performance of the proposed algorithms by applying step change to CFO. The 2 state MKF with adaptive Q is able to track a step change of 400 MHz of CFO with m = 1 and 3 with high estimation accuracy but slower convergence time compared to the non-adaptive 2 state MKF. Finally, we study the computational requirements of the proposed MKFs and show that they offer significant reduction in computations compared to single-step KF thus making the proposed filters suitable for hardware implementation.

A novel four dimensional constellation shaping with non-uniform signaling for long-haul fiber-optic communication

In this paper, a new four-dimensional (4D) constellation shaping scheme is proposed for long-haul fiber-optic system to approach the optimal performance. The scheme designs a non-uniform signaling for 4D 80-ary multisphere distribution (4D-80MD) constellation by combining constellation shaping of four dimensions with pragmatic low density parity check (LDPC) code modulation. Additionally, the design of multisphere distribution is introduced based on a bounded-energy enumerative amplitude trellis. The proposed 4D-80MD constellation has the same spectral efficiency (SE) as the conventional polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM). We study the efficiency of 4D-80MD, combined with bit-interleaved coded-modulation with iterative decoding, and demonstrate in back-to-back system that the proposed 4D-80MD outperforms PM-8QAM about 1 dB For a long-haul optical fiber system, the optimized 4D-80MD is able to achieve a reach improvement of up to 21%. The results also show increased rates and reduced non-linear noise compared with 2D shaped signal with the same SE.

Generation of Solitons:The wave of future

Very high speed and data rate optical fiber transmissions over a large distance in thousands of kilometers is turning into a reality. This paper discusses about the evolution of soliton beats along with their generation which is shown with the help of simulations carried out in Opti-system. Stable soliton pulses result from the balance between combination of both linear and non-linear effects i.e. Group Velocity Dispersion (GVD) and Self Phase Modulation (SPM) simultaneously. Thus, Long-haul optical fiber communication can be made possible now using solitons, as they provide high data conveying capacity and require less no of repeaters for transmission making them ideal waves of the future. At the end, some of the issues and challenges related with solitons and their cures have additionally been laid out.

Design of Time-Frequency Packed WDM Superchannel Transmission Systems

We consider time and frequency-packing (TFP) wavelength division-multiplexing (WDM) superchannel systems for longhaul optical fiber communication. Employing very high baud rates in conjunction with higher-order modulation formats is challenging due to practical constraints. TFP superchannels therefore become an attractive choice to facilitate high data rates with improved spectral efficiency. However, TFP introduces inter-symbol interference (ISI) and/or inter-carrier interference (ICI) that necessitate efficient interference handling techniques. Moreover, phase noise (PN) due to wide laser linewidth (LLW) may cause significant signal distortion in WDM transmission, and the presence of ISI and ICI in TFP systems further complicates carrier phase recovery (CPR). In this article, we propose a spectrally efficient TFP superchannel design equipped with powerful interference cancellation and PN mitigation techniques, targeting Terabit-per-second (Tbps) data rates. First, we propose a joint ISI and ICI channel estimation algorithm coupled with polarization-recovery and a coarse PN cancellation method. Second, we investigate two iterative CPR algorithms to mitigate the distortion due to the residual PN. Third, a combination of successive and parallel interference cancellation methods for ICI mitigation is investigated in tandem with turbo ISI equalization. The effectiveness of the proposed algorithms is demonstrated through computer simulations of a coded TFP superchannel system in the presence of linear fiber impairments, targeting a throughput of 1.2 Tbps. Numerical results suggest that the proposed TFP design offers more than 2 dB performance gains and as high as 960 km transmission distance improvement over existing competitive super-Nyquist designs. Simulation results also indicate that the proposed design exhibits excellent tolerance to high LLWs and aggressive optical filtering stemming from cascaded reconfigurable optical add-drop multiplexers in the fiber link.

Phase Noise Cancellation in Coherent Communication Systems Using a Radio Frequency Pilot Tone

Long-haul optical fiber communication employing digital signal processing (DSP)-based dispersion compensation can be distorted by the phenomenon of equalization-enhanced phase noise (EEPN), due to the reciprocities between the dispersion compensation unit and the local oscillator (LO) laser phase noise (LPN). The impact of EEPN scales increases with the increase of the fiber dispersion, laser linewidths, symbol rates, signal bandwidths, and the order of modulation formats. In this work, the phase noise cancellation (PNC) employing a radio frequency (RF) pilot tone in coherent optical transmission systems has been investigated. A 28-Gsym/s QPSK optical transmission system with a significant EEPN has been implemented, where the carrier phase recovery (CPR) was realized using the one-tap normalized least-mean-square (NLMS) estimation and the differential phase detection (DPD), respectively. It is shown that the RF pilot tone can entirely eliminate the LPN and efficiently suppress the EEPN when it is applied prior to the CPR.

Brillouin optomechanics in nanophotonic structures

The interaction between light and mesoscopic mechanical degrees of freedom has been investigated under various perspectives, from spectroscopy in condensed matter, optical tweezer particle trapping, and long-haul optical fiber communication system penalties to gravitational-wave detector noise. In the context of integrated photonics, two topics with dissimilar origins—cavity optomechanics and guided wave Brillouin scattering—are rooted in the manipulation and control of the energy exchange between trapped light and mechanical modes. In this tutorial, we explore the impact of optical and mechanical subwavelength confinement on the interaction among these waves, coined as Brillouin optomechanics. At this spatial scale, optical and mechanical fields are fully vectorial and the common intuition that more intense fields lead to stronger interaction may fail. Here, we provide a thorough discussion on how the two major physical effects responsible for the Brillouin interaction—photoelastic and moving-boundary effects—interplay to foster exciting possibilities in this field. In order to stimulate beginners into this growing research field, this tutorial is accompanied by all the discussed simulation material based on a widespread commercial finite-element solver.

Energy-Efficient High-Throughput VLSI Architectures for Product-Like Codes

Implementing forward error correction (FEC) for modern long-haul fiber-optic communication systems is a challenge, since these high-throughput systems require FEC circuits that can combine high coding gains and energy-efficient operation. We present very large scale integration (VLSI) decoder architectures for product-like codes for systems with strict throughput and power dissipation requirements. To reduce energy dissipation, our architectures are designed to minimize data transfers in and out of memory blocks, and to use parallel noniterative component decoders. Using a mature 28-nm VLSI process technology node, we showcase different product and staircase decoder implementations that have the capacity to exceed 1-Tb/s information throughputs with energy efficiencies of around 2 pJ/b.

Chromatic dispersion mitigation in long-haul fiber-optic communication networks by sub-band partitioning.

We propose and experimentally demonstrate a novel sub-band multiplexed data architecture for chromatic dispersion (CD) mitigation. We have demonstrated 32 GBaud multi-sub-band (MSB) dual-polarization (DP) 16QAM transmission over 2400 km. Using this approach, the transmitted signal bandwidth is divided into multiple narrow-bandwidth sub-bands, each operating at a lower baud rate. Within each sub-band bandwidth, the CD frequency response can be approximated as a linear-phase band-pass filter, which can be considered as an analog delay that does not require compensation. Therefore, the resulting receiver digital signal processing (DSP) is simplified due to the removal of the CD compensation equalizer. In addition, this leads to efficient parallelization of DSP tasks by deploying multiple independent sub-band processors running at a lower clock rate. The proposed system reduces receiver computational complexity and offers 1 dB higher Kerr-nonlinearity tolerance and 2% extended transmission reach in comparison to the conventional single carrier systems.

Modified Nonlinear Decision Feedback Equalizer for Long-Haul Fiber-Optic Communications

In a long-haul optical fiber communication system, fiber attenuation, dispersion, and nonlinearity combined with nondeterministic noise from optical amplifiers used for periodic regeneration cause adverse effects on system performance. Several optical and electrical signal processing techniques have been proposed, and implemented to extract the transmitted data; some provide better performance than others, but at a cost of higher computational complexity. We present a modified nonlinear decision feedback equalizer designed for use in a legacy optical communication system with periodic dispersion compensation. The effects of noise and nonlinearity on the equalizer coefficients are investigated, and a suboptimal convergence algorithm to reduce such effects is proposed and verified. Our equalizer provides performance comparable to that obtained using digital backpropagation, while being computationally simpler, compensating linear and nonlinear physical impairment effects effectively even at high power levels where fiber nonlinearity is significant. Performance prediction of the designed DFE is also discussed, using a numerical method, with and without error propagation.

On achievable rates for long-haul fiber-optic communications.

Lower bounds on mutual information (MI) of long-haul optical fiber systems for hard-decision and soft-decision decoding are studied. Ready-to-use expressions to calculate the MI are presented. Extensive numerical simulations are used to quantify how changes in the optical transmitter, receiver, and channel affect the achievable transmission rates of the system. Special emphasis is put to the use of different quadrature amplitude modulation formats, channel spacings, digital back-propagation schemes and probabilistic shaping. The advantages of using MI over the prevailing Q-factor as a figure of merit of coded optical systems are also highlighted.

Future Prospects for FEC in Fiber-Optic Communications

This paper reviews the application of forward error correction (FEC) techniques to long-haul fiber-optic communication systems. A brief tutorial on error-correcting codes and a discussion of their fundamental limits (on the additive white Gaussian noise channel and on a nonlinear fiber-optic transmission channel) is provided. To illustrate the potential for applying advanced FEC techniques that take channel nonlinearities into account, a novel faster than Nyquist style binary signaling scheme, providing significant rate improvements over a reference benchmark system, is described. To achieve higher spectral efficiencies, the judicious combination of higher order modulation schemes with FEC is discussed. Finally, several potential directions for further research in the application of advanced FEC systems to nonlinear fiber-optic channels are given.

Compensación Electrónica de la Dispersión en Fibras Ópticas Usando el Conjugado de Fase Óptica

El tópico de este artículo, abordará la investigación de una técnica novedosa para la compensación electrónica de la dispersión en comunicaciones por fibra óptica a larga distancia, en la cual una señal es pre-compensada eléctricamente usando un modulador diferencial Mach-Zender, controlado por filtros digitales no lineales. La dispersión cromática fue efectivamente compensada con el uso del conjugado de fase óptica en el transmisor a través de los 4000 Km de fibra mono modo (carente de no-linealidad y atenuación) en donde la dispersión es compensada para una señal de NRZ (no retorno a cero) de intensidad modulada a 10 Gb/s. La compensación de la dispersión fue confirmada midiendo la razón de error de bit y observando los diagramas de ojo detectados.

Mitigation of the effects of self phase modulation and group-velocity dispersion in fiber optic communications: dispersion- and power-map cooptimization using the genetic algorithm

We show that co-optimization of dispersion and power maps in long-haul fiber optic communications can significantly mitigate the effects of group-velocity dispersion (GVD) and self phase modulation (SPM). A genetic algorithm is used for arriving at the optimal (or a near-optimal) link design in reasonable time, since exhaustive search is almost impossible for this intractable problem. Design of a 20-span×80 km/span link that can recover an input Gaussian pulse almost in its original form is presented. This design provides near-optimum values of the required net dispersion, dispersion map, and power map to mitigate the effects of SPM and GVD