Long-haul Optical Fiber Transmission Research Articles

Power-aided probabilistic shaping parameter optimization for long-haul optical fiber transmission

A power-aided probabilistic shaping (PS) parameter optimization scheme is proposed to localize the optimal transmitting setup and maximize the transmission capacity in long-haul optical fiber transmission. Using a neural network and genetic algorithm (NNGA), the proposed scheme can select the optimal transmission parameter set, including the launching optical power (LOP) and three PS characteristics. We built a testbed using MATLAB and VPI to validate the proposed scheme. The proposed scheme was demonstrated in a dual-polarization coherent transmission system. The results show that the proposed scheme improves the generalized mutual information (GMI) by 0.3035 bits/symbol/pol and normalized GMI by 0.1022 in a 1000 km G.654E fiber transmission at 420-Gbit/s, compared to a traditional MB-based PS technique. The signal-to-noise ratio (SNR) achieves a gain of 1.003 dB, which validates the outperformance of the proposed scheme.

Fast and Accurate Waveform Modeling of Long-Haul Multi-Channel Optical Fiber Transmission Using a Hybrid Model-Data Driven Scheme

The modeling of optical wave propagation in optical fiber is a task of fast and accurate solving the nonlinear Schr\"odinger equation (NLSE), and can enable the optical system design, digital signal processing verification and fast waveform calculation. Traditional waveform modeling of full-time and full-frequency information is the split-step Fourier method (SSFM), which has long been regarded as challenging in long-haul wavelength division multiplexing (WDM) optical fiber communication systems because it is extremely time-consuming. Here we propose a linear-nonlinear feature decoupling distributed (FDD) waveform modeling scheme to model long-haul WDM fiber channel, where the channel linear effects are modelled by the NLSE-derived model-driven methods and the nonlinear effects are modelled by the data-driven deep learning methods. Meanwhile, the proposed scheme only focuses on one-span fiber distance fitting, and then recursively transmits the model to achieve the required transmission distance. The proposed modeling scheme is demonstrated to have high accuracy, high computing speeds, and robust generalization abilities for different optical launch powers, modulation formats, channel numbers and transmission distances. The total running time of FDD waveform modeling scheme for 41-channel 1040-km fiber transmission is only 3 minutes versus more than 2 hours using SSFM for each input condition, which achieves a 98% reduction in computing time. Considering the multi-round optimization by adjusting system parameters, the complexity reduction is significant. The results represent a remarkable improvement in nonlinear fiber modeling and open up novel perspectives for solution of NLSE-like partial differential equations and optical fiber physics problems.

High-Throughput and Long-Distance Transmission With >120 nm S-, C- and L-Band Signal in a 125μm 4-Core Fiber

We investigate recirculating transmission of a wideband S-, C- and L-band signal in a 4-core fiber. We transmit 552 x 25 GHz spaced, 24.5 GBd channels, covering more than 120 nm bandwidth from 1487.8 nm to 1608.33 nm through each core of the multi-core fiber (MCF), which has the same 125μm cladding dimeter as standard single-mode fiber. We first use PDM-16QAM modulation and measure performance at distances up to 3001 km, corresponding to 43 spans of the 69.8 km MCF. At this distance we measure a decoded throughput of 319 Tb/s or 342 Tb/s when estimating from the generalised mutual information (GMI). Extending the transmission distance to 8027 km, a selection of PDM-QPSK modulated channels across the spectrum were received with an average GMI estimated data-rate of 83.7 Gb/s. These results show that wideband transmission including the S-band has the potential to increase data-rates in long-haul optical fiber transmission. Further, our experiment confirms that 125 μm diameter MCFs can multiply transmission capacity whilst offering benefits of resource sharing and integration, expected in SDM systems.

Modeling and Experimental Measurement of Power Efficiency for Power-Limited SDM Submarine Transmission Systems

Power efficiency of long-haul optical fiber transmission has emerged as a critical challenge to cost-effectively increasing submarine cable capacity. Building on previous experimental work and informed by physical system modeling and optimization, we report on extensive amplified transmission experiments characterizing the metric of fiber capacity per unit pump power over a range of amplifier powers and link distances relevant to power-limited spatial-division-multiplexed submarine systems. We compare experimental results with modeling incorporating optical amplifier physics as well as generalized droop, demonstrating excellent agreement over the range of powers and distances tested. We predict the performance gains achievable by further optimizing the system design and implementation within tolerances ideally achieved in deployed submarine systems, and estimate fiber pair counts and total cable capacities achievable for the link distances investigated. Our results suggest the utility of amplifier pump powers as low as 20 mW and output powers as low as 6.5 dBm in reaching Pb/s cable capacities.

Impact of Equalization-Enhanced Phase Noise on Digital Nonlinearity Compensation in High-Capacity Optical Communication Systems.

Equalization-enhanced phase noise (EEPN) can severely degrade the performance of long-haul optical fiber transmission systems. In this paper, the impact of EEPN in Nyquist-spaced dual-polarization quadrature phase shift keying (DP-QPSK), dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM), and DP-64QAM optical transmission systems is investigated considering the use of electrical dispersion compensation (EDC) and multi-channel digital backpropagation (MC-DBP). Our results demonstrate that full-field DBP (FF-DBP) is more susceptible to EEPN compared to single-channel and partial-bandwidth DBP. EEPN-induced distortions become more significant with the increase of the local oscillator (LO) laser linewidth, and this results in degradations in bit-error-rates (BERs), achievable information rates (AIRs), and AIR-distance products in optical communication systems. Transmission systems using higher-order modulation formats can enhance information rates and spectral efficiencies, but will be more seriously degraded by EEPN. It is found that degradations on AIRs, for the investigated FF-DBP schemes, in the DP-QPSK, the DP-16QAM, and the DP-64QAM systems are 0.07 Tbit/s, 0.11 Tbit/s, and 0.57 Tbit/s, respectively, due to the EEPN with an LO laser linewidth of 1 MHz. It is also seen that the selection of a higher-quality LO laser can significantly reduce the bandwidth requirement and the computational complexity in the MC-DBP.

Advanced DSP for Coherent Optical Fiber Communication

In this paper, we provide an overview of recent progress on advanced digital signal processing (DSP) techniques for high-capacity long-haul coherent optical fiber transmission systems. Not only the linear impairments existing in optical transmission links need to be compensated, but also, the nonlinear impairments require proper algorithms for mitigation because they become major limiting factors for long-haul large-capacity optical transmission systems. Besides the time domain equalization (TDE), the frequency domain equalization (FDE) DSP also provides a similar performance, with a much-reduced computational complexity. Advanced DSP also plays an important role for the realization of space division multiplexing (SDM). SDM techniques have been developed recently to enhance the system capacity by at least one order of magnitude. Some impressive results have been reported and have outperformed the nonlinear Shannon limit of the single-mode fiber (SMF). SDM introduces the space dimension to the optical fiber communication. The few-mode fiber (FMF) and multi-core fiber (MCF) have been manufactured for novel multiplexing techniques such as mode-division multiplexing (MDM) and multi-core multiplexing (MCM). Each mode or core can be considered as an independent degree of freedom, but unfortunately, signals will suffer serious coupling during the propagation. Multi-input–multi-output (MIMO) DSP can equalize the signal coupling and makes SDM transmission feasible. The machine learning (ML) technique has attracted worldwide attention and has been explored for advanced DSP. In this paper, we firstly introduce the principle and scheme of coherent detection to explain why the DSP techniques can compensate for transmission impairments. Then corresponding technologies related to the DSP, such as nonlinearity compensation, FDE, SDM and ML will be discussed. Relevant techniques will be analyzed, and representational results and experimental verifications will be demonstrated. In the end, a brief conclusion and perspective will be provided.

Eight-Dimensional Polarization-Ring-Switching Modulation Formats

We propose two 8-dimensional (8D) modulation formats (8D-2048PRS-T1 and 8D-2048PRS-T2) with a spectral efficiency of 5.5 bit/4D-sym, where the 8 dimensions are obtained from two time slots and two polarizations. Both formats provide a higher tolerance to nonlinearity by selecting symbols with nonidentical states of polarization (SOPs) in two time slots. The performance of these novel 8D modulation formats is assessed in terms of the effective signal-to-noise ratio (SNR) and normalized generalized mutual information. 8D-2048PRS-T1 is more suitable for high SNRs, while 8D-2048PRS-T2 is shown to be more tolerant to nonlinearities. A sensitivity improvement of at least 0.25 dB is demonstrated by maximizing normalized generalized mutual information (NGMI). For a long-haul nonlinear optical fiber transmission system, the benefit of mitigating the nonlinearity is demonstrated and a reach increase of 6.7% (560 km) over time-domain hybrid four-dimensional two-amplitude eight-phase shift keying (TDH-4D-2A8PSK) is observed.

Analysis of chromatic dispersion compensation and carrier phase recovery in long-haul optical transmission system influenced by equalization enhanced phase noise

The performance of long-haul coherent optical fiber transmission system is significantly affected by the equalization enhanced phase noise (EEPN), due to the interaction between the electronic dispersion compensation (EDC) and the laser phase noise. In this paper, we present a comprehensive study on different chromatic dispersion (CD) compensation and carrier phase recovery (CPR) approaches, in the n-level phase shift keying (n-PSK) and the n-level quadrature amplitude modulation (n-QAM) coherent optical transmission systems, considering the impacts of EEPN. Four CD compensation methods are considered: the time-domain equalization (TDE), the frequency-domain equalization (FDE), the least mean square (LMS) adaptive equalization are applied for EDC, and the dispersion compensating fiber (DCF) is employed for optical dispersion compensation (ODC). Meanwhile, three carrier phase recovery methods are also involved: a one-tap normalized least mean square (NLMS) algorithm, a block-wise average (BWA) algorithm, and a Viterbi-Viterbi (VV) algorithm. Numerical simulations have been carried out in a 28-Gbaud dual-polarization quadrature phase shift keying (DP-QPSK) coherent transmission system, and the results indicate that the origin of EEPN depends on the choice of chromatic dispersion compensation methods, and the effects of EEPN also behave moderately different in accordance to different carrier phase recovery scenarios.

Information Rates of Next-Generation Long-Haul Optical Fiber Systems Using Coded Modulation

A comprehensive study of the coded performance of long-haul spectrally-efficient WDM optical fiber transmission systems with different coded modulation decoding structures is presented. Achievable information rates are derived for three different square QAM formats and the optimal format is identified as a function of distance and specific decoder implementation. The four cases analyzed combine hard-decision (HD) or soft-decision (SD) decoding together with either a bit-wise or a symbol-wise demapper, the last two suitable for binary and nonbinary codes, respectively. The information rates achievable for each scheme are calculated based on the mismatched decoder principle. These quantities represent true indicators of the coded performance of the system for specific decoder implementations and when the modulation format and its input distribution are fixed. In combination with the structure of the decoder, two different receiver-side equalization strategies are also analyzed: electronic dispersion compensation and digital backpropagation. We show that, somewhat unexpectedly, schemes based on nonbinary HD codes can achieve information rates comparable to SD decoders and that, when SD is used, switching from a symbol-wise to a bit-wise decoder results in a negligible penalty. Conversely, from an information-theoretic standpoint, HD binary decoders are shown to be unsuitable for spectrally-efficient, long-haul systems.

Performance evaluation of hybrid DPSK-MPPM techniques in long-haul optical transmission.

In this paper, we evaluate the performance of hybrid differential phase shift keying-multipulse pulse position modulation (DPSK-MPPM) techniques in long-haul nonlinear-dispersive optical fiber transmission. An expression for the nonlinear interference variance is obtained analytically using the Gaussian noise (GN) model. We derive upper-bound expressions that take into account the fiber nonlinearity impact on the DPSK-MPPM system's performance for both bit- and symbol-error rates (BER and SER). The tightness of the BER's upper bound is verified using Monte Carlo simulation. The numerical analysis is carried out based on the proposed setup supplemented by a realistic simulation scenario for the DPSK-MPPM long-haul optical transmission system. Our results reveal that while the hybrid DPSK-MPPM technique outperforms both traditional DPSK and MPPM techniques under amplified spontaneous emission (ASE) noise (linear limit), it is less robust when fiber nonlinearity is considered. However, under the impact of low nonlinearity, the performance of a hybrid technique still surpasses the traditional ones. We also discuss the effect of some wavelength-division multiplexing (WDM) parameters on optimal system performance. The nonlinear interference penalties on the maximum reachable distances by both hybrid and traditional modulation systems are then investigated at a forward-error correction (FEC) requirement (BER=10-3). In particular, at an average launch power of -8 dBm, the hybrid DQPSK-MPPM system with a total frame length of eight time slots including two signal time slots outreaches a traditional DQPSK system by 950 km.

Multi-Dimensional Coded Modulation in Long-Haul Fiber Optic Transmission

Multi-dimensional-coded modulation approaches the nonlinear Shannon limit due to its high SNR sensitivity and large Euclidean distance between multi-dimensional symbols. It also eliminates phase ambiguity to avoid cycle slips. In this paper, we review the design principles of bit-interleaved-coded modulation with multi-dimensional mapping, and its performance in long-haul transmission experiments with different spectral efficiencies in both dispersion managed and dispersion unmanaged fiber optic systems.

Digital Coherent Technology for Optical Fiber and Radio-Over-fiber Transmission Systems

Current status and the future perspective of digital coherent technology for optical fiber and radio-over-fiber (RoF) transmission systems will be reviewed. For the starter, we will review two key digital coherent techniques; the coherent receiver and compensation techniques for the fiber nonlinearity-induced impairments. Next, we will present a commercial deployment of 100 G digital coherent long-haul optical fiber transmission system and the R&D challenge to 400 G and beyond transmission systems. Finally, we will turn our focus on digital coherent RoF transmission systems. We will introduce an ongoing government-funded R&D program in Japan, entitled “Agile deployment capability of highly resilient optical and radio seamless communication systems.” It was initiated after the disaster in Japan in March 2011, aiming at optical fiber and millimeter-wave-band radio seamless transmission system. It would be a good use case of cutting-edge radio-over-fiber technology for an immediate social need.

Intrachannel cross-phase modulation-induced phase shift in high-speed dispersion-managed optical fiber transmission system

We investigate the intrachannel cross-phase modulation (IXPM)-induced phase shift in optical return-to-zero pulse propagating in a periodically dispersion-managed long-haul optical fiber transmission line. Necessary dynamical equations for various pulse parameters have been derived using variational analysis to estimate the phase shift. These equations are solved by the Runge–Kutta method. The analytical result is verified by numerical simulation based on split-step Fourier method. We therefore explore the effects of various parameters, such as transmission distance, input power, duty cycle, dispersion map strength, and residual dispersion, on phase shift for a 40 Gb/s single-channel transmission system. We also check the impact of variation of bit rate on phase shift. We find that IXPM-induced phase shift can be mitigated by proper adjustment of dispersion management and different pulse parameters like duty cycle, dispersion map strength, and peak power.

Experimental demonstration of 108 Tb/s PDM CO-SCFDM transmission over 3170 km SSMF

Coherent optical single-carrier frequency-division-multiplexing (CO-SCFDM) is a promising candidate for future high-speed long-haul optical fiber transmission system. Being a modified form of coherent optical orthogonal frequency division multiplexing (CO-OFDM), the CO-SCFDM can inherit the advantages such as low computation complexity and high flexibility, while suffers less nonlinear impairment due to much lower peak-to-average power ratio (PAPR). In this paper, we experimentally demonstrate 1.08 Tb/s polarization-division multiplexing (PDM) CO-SCFDM transmission over 3170 km standard single-mode fiber (SSMF) with Erbium-doped fiber amplifier (EDFA) only. The back-to-back and nonlinear transmission performances for CO-OFDM and CO-SCFDM are also compared.

Comparison of Transmission Performances for CO-SCFDE and CO-OFDM Systems

Single-carrier (SC) and multicarrier (MC) transmissions have emerged as two competitive technologies for long-haul coherent optical fiber transmission systems. In this letter, we compare chromatic dispersion (CD) and nonlinearity tolerances for coherent optical SC frequency-domain-equalization and SC orthogonal frequency-division-multiplexing systems. We establish the simulation systems employing the same structures of transmitter and receiver, the same structure of frame, and almost the same frequency-domain equalization method except the inverse fast Fourier transform processing. Both CD tolerance and nonlinear transmission performance in single-channel and wavelength-division-multiplexing scenarios are investigated. The comparison can reveal the difference of SC and MC transmissions.

Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission

We present digital signal processing techniques and algorithms for improving the tolerance of polarization-division multiplexed (PDM) coherent optical orthogonal frequency-division multiplexing (CO-OFDM) to fiber nonlinear effects, in both single-channel and wavelength-division multiplexed (WDM) transmission. For single-channel transmission, we discuss a self-phase modulation (SPM) compensation method that jointly processes two polarization components of a PDM CO-OFDM signal. For WDM transmission, we describe a novel OFDM channel estimation scheme that reduces the cross-phase-modulation (XPM) penalty among the WDM channels. The nonlinear tolerance improvements enabled by these signal processing techniques are quantified through numerical simulations for both dispersion-unmanaged and dispersion-managed long-haul optical fiber transmission with 112-Gb/s PDM CO-OFDM wavelength channels.

40-Gb/s Adaptive Electronic Polarization-Mode Dispersion Compensator Using a Hybrid-MIC 3-Tap Linear Equalizer

We report a 40-Gb/s adaptive electronic dispersion compensator (EDC) for mitigation of polarization mode dispersion (PMD). The EDC employs a 3-tap linear equalizer acting as a transversal filter and manufactured on a substrate of duroid 5880 by using hybrid-monolithic-integrated-circuit (MIC) technology. The experimental results showed that for a given 20-ps differential group delay (DGD), the measured eye-opening penalty (EOP) after compensation was improved by 11 dB. This 40-Gb/s adaptive EDC demonstrated the possibility of its use for PMD compensation in a 40-Gb/s long-haul fiber-optic transmission system.

Pulse Energy Probability Density Functions for Long-Haul Optical Fiber Transmission Systems by Using Instantons and Edgeworth Expansion

In this work, we use a new approach to model pulse energy in long-haul optical fiber transmission systems. Existing approaches for obtaining probability density functions (pdfs) rely on numerical simulations or analytical approximations. Numerical simulations make far tails of the pdfs difficult to obtain, while analytical approximations are often inaccurate, as they neglect nonlinear interaction between pulses and noise. Our approach combines the instanton method from statistical mechanics to model far tails of the pdfs, with numerical simulations to refine the middle part of the pdfs. We combine the two methods by using an orthogonal polynomial expansion constructed specifically for this problem. We demonstrate the approach on an example of a specific submarine transmission system.

Polarization-mode dispersion of a circulating loop

We derive an analytic expression for the evolution of the differential group delay (DGD) in a fiber-optic circulating loop. We distill a simple analytic solution for the average DGD and show that it accumulates approximately linearly with transmission distance. The scaling of this linear function is confirmed experimentally using a long-haul fiber-optic transmission test-bed. This result is contrasted with DGD accumulation in a long straight-line transmission system, where the average DGD accumulates as a square root of the system’s length.

Direct-detection optical differential 8-level phase-shift keying (OD8PSK) for spectrally efficient transmission

An implementation of optical differential 8-level phase-shift keying (OD8PSK) is proposed for spectrally efficient high capacity long-haul optical fiber transmission systems. Interferometric demodulation and direct detection at the receiver yield three output binary sequences identical to the three input binary sequences. This is accomplished by proper design of electrical encoding and optical encoding at the transmitter. Three optical encoding schemes are proposed with corresponding differential electrical encoding schemes. Numerical simulations are performed for a single channel transmission to evaluate the transmission performances of OD8PSK systems.