Digital Nonlinearity Compensation Research Articles

OPC-aided transmission with low-complexity digital nonlinearity compensation.

Based on the dispersion-folded digital back-propagation (DBP) method, we propose a low-complexity digital nonlinearity-compensation scheme to enhance the system performance of optical phase conjugation (OPC)-aided transmission whilst preserving the low computational requirement of dispersion-folded DBP. When the transmission reach is increased, the computational efficiency of the proposed scheme becomes more apparent compared with conventional DBP while the performance penalty is negligible.

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.

Ku-band analog photonic down-conversion link with coherent I/Q image rejection and digital linearization.

Analog photonic down-conversion links have been widely used in radar, electronic warfare, and satellite communication systems. Aiming at the optimization demands of the link performance, we demonstrate and experimentally verify a Ku-band photonic down-conversion link based on coherent in-phase/quadrature (I/Q) image rejection and digital nonlinear compensation. The image-rejection ratio at 17.5 GHz is measured to be 47 dB. After digital processing, the image intermodulation distortions (MMD) and the intermodulation distortions (IMD3) are suppressed by 18.1 dB and 10.9 dB, respectively. The corresponding spurious-free dynamic range (SFDR) reaches 108.83 dB·Hz2/3.

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.

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.

Digital nonlinearity compensation in the presence of polarization mode dispersion

The impact of polarization mode dispersion (PMD) on the performance of coherent transmission systems employing different digital nonlinearity compensation (NLC) schemes is numerically investigated for a seven-channel PM-16QAM Nyquist-wavelength division multiplexing system at 256 Gbit / s. In these nonlinearity compensation schemes, the digital signal processing is divided between the transmitter (Tx) and receiver (Rx) with different splitting ratios. We demonstrate that by splitting the NLC equally between the Tx and Rx, one can always obtain the best performance improvement regardless of whether PMD is present or not. Results of 1000-km dispersion-unmanaged transmission show that when fiber PMD is equal to 0.05 ps / km, splitting the NLC can give a signal-to-noise ratio improvement of 1.1-dB over receiver-side NLC, while it is 0.9 dB for 0.1 ps / km of the fiber PMD coefficient.

A Blind Nonlinearity Compensator Using DBSCAN Clustering for Coherent Optical Transmission Systems

Coherent fiber-optic communication systems are limited by the Kerr-induced nonlinearity. Benchmark optical and digital nonlinearity compensation techniques are typically complex and tackle deterministic-induced nonlinearities. However, these techniques ignore the impact of stochastic nonlinear distortions in the network, such as the interaction of fiber nonlinearity with amplified spontaneous emission from optical amplification. Unsupervised machine learning clustering (e.g., K-means) has recently been proposed as a practical approach to the blind compensation of stochastic and deterministic nonlinear distortions. In this work, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is employed, for the first time, for blind nonlinearity compensation. DBSCAN is tested experimentally in a 40 Gb/s 16 quadrature amplitude-modulated system at 50 km of standard single-mode fiber transmission. It is shown that at high launched optical powers, DBSCAN can offer up to 0.83 and 8.84 dB enhancement in Q-factor when compared to conventional K-means clustering and linear equalisation, respectively.

Volterra-Assisted Optical Phase Conjugation: A Hybrid Optical-Digital Scheme for Fiber Nonlinearity Compensation

Mitigation of optical fiber nonlinearity is an active research field in the area of optical communications, due to the resulting marked improvement in transmission performance. Following the resurgence of optical coherent detection, digital nonlinearity compensation (NLC) schemes such as digital backpropagation (DBP) and Volterra equalization have received much attention. Alternatively, optical NLC, and specifically optical phase conjugation (OPC), has been proposed to relax the digital signal processing complexity. In this work, a novel hybrid optical-digital NLC scheme combining OPC and a Volterra equalizer is proposed, termed Volterra-Assisted OPC (VAO). It has a twofold advantage: it overcomes the OPC limitation in asymmetric links and substantially enhances the performance of Volterra equalizers. The proposed scheme is shown to outperform both OPC and Volterra equalization alone by up to 4.2 dB in a 1000 km EDFA-amplified fiber link. Moreover, VAO is also demonstrated to be very robust when applied to long-transmission distances, with a 2.5 dB gain over OPC-only systems at 3000 km. VAO combines the advantages of both optical and digital NLC offering a promising trade-off between performance and complexity for future high-speed optical communication systems.

On the Impact of Fixed Point Hardware for Optical Fiber Nonlinearity Compensation Algorithms

Nonlinearity mitigation using digital signal processing has been shown to increase the achievable data rates of optical fiber transmission links. One especially effective technique is digital back propagation (DBP), an algorithm capable of simultaneously compensating for linear and nonlinear channel distortions. The most significant barrier to implementing this technique, however, is its high computational complexity. In recent years, there have been several proposed alternatives to DBP with reduced computational complexity, although such techniques have not demonstrated performance benefits commensurate with the complexity of implementation. In order to fully characterize the computational requirements of DBP, there is a need to model the algorithm behavior when constrained to the logic used in a digital coherent receiver. Such a model allows for the analysis of any signal recovery algorithm in terms of true hardware complexity which, crucially, includes the bit-depth of the multiplication operation. With a limited bit depth, there is quantization noise, introduced with each arithmetic operation, and it can no longer be assumed that the conventional DBP algorithm will outperform its low complexity alternatives. In this work, DBP and a single nonlinear step DBP implementation, the \textit{Enhanced Split Step Fourier} method (ESSFM), were compared with linear equalization using a generic software model of fixed point hardware. The requirements of bit depth and fast Fourier transform (FFT) size are discussed to examine the optimal operating regimes for these two schemes of digital nonlinearity compensation. For a 1000 km transmission system, it was found that (assuming an optimized FFT size), in terms of SNR, the ESSFM algorithm outperformed the conventional DBP for all hardware resolutions up to 13 bits.

Coherent 16 Quadrature Amplitude Modulation (16QAM) Optical Communication Systems

Coherent optical fiber communications for data rates of 100Gbit/s and beyond have recently been studied extensively primarily because high sensitivity of coherent receivers could extend the transmission distance. Spectrally efficient modulation techniques such as M-ary quadrature amplitude modulation (M-QAM) can be employed for coherent optical links. The integration of multi-level modulation formats based on coherent technologies with wavelength-division multiplexed (WDM) systems is key to meet the aggregate bandwidth demand. This paper reviews coherent 16 quadrature amplitude modulation (16QAM) systems to scale the network capacity and maximum reach of current optical communication systems to accommodate traffic growth. Full Text: PDF ReferencesK. Kikuchi, "Fundamentals of Coherent Optical Fiber Communications", J. Lightwave Technol., vol. 34, no. 1, pp. 157-179, 2016. CrossRef S. Tsukamoto, D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, "Coherent Demodulation of 40-Gbit/s Polarization-Multiplexed QPSK Signals with16-GHz Spacing after 200-km Transmission", Proc. OFc, Paper PDP29, (2005). DirectLink K. Kikuchi, "Coherent Optical Communication Technology", Proc. OFC, Paper Th4F.4, (2015). CrossRef J. M. Kahn and K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems", IEEE J. Sel. Topics Quantum Electron., vol. 10, no. 2, pp. 259–272, (2004). CrossRef S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing", IEEE Photon. Technol. Lett., vol. 18, no. 10, pp. 1131–1133, (2006). CrossRef Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, "Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver", Opt. Exp., vol. 17, no. 32, pp. 1435–1441, (2009). CrossRef H. Nakashima, Et al., "Digital Nonlinear Compensation Technologies in Coherent Optical Communication Systems", Proc. OFC, Paper W1G.5, (2017). CrossRef S. J. Savory, "Digital filters for coherent optical receivers", Opt. Exp., vol. 16, no. 2, pp. 804–817, (2008). CrossRef D. S. Millar, T. Koike-Akino, S. Ö. Arık, K. Kojima, K. Parsons, T. Yoshida, and T. Sugihara, "High-dimensional modulation for coherent optical communications systems", Opt. Express, vol. 22, no. 7, pp 8798-8812, (2014). CrossRef R. Griffin and A. Carter, "Optical differential quadrature phase-shift key (oDQPSK) for high capacity optical transmission", Proc. OFC, Paper WX6, (2002). DirectLink K. Kikuchi, "Digital coherent optical communication systems: fundamentals and future prospects", IEICE Electron. Exp., vol. 8, no. 20, pp. 1642–1662, (2011). CrossRef F. Derr, "Optical QPSK transmission system with novel digital receiver concept", Electron Lett., vol. 27, no. 23, pp. 2177–2179, (1991). CrossRef R. No’e, "Phase noise tolerant synchronous QPSK receiver concept with digital I&Q baseband processing", Proc. OECC, Paper 16C2-5, (2004). DirectLink D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation", J. Lightw. Technol., vol. 24, no. 1, pp. 12–21, (2006). CrossRef M. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments", IEEE Photon. Technol. Lett., vol. 16, no. 2, pp. 674–676, (2004). CrossRef S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for Group-velocity dispersion compensation", IEEE Photon. Technol. Lett., vol. 18, no. 9, pp. 1016–1018, (2006). CrossRef S. Tsukamoto, Y. Ishikawa, and K. Kikuchi, "Optical Homodyne Receiver Comprising Phase and Polarization Diversities with Digital Signal Processing", Proc. ECOC, Paper Mo4.2.1, (2006). CrossRef K. Kikuchi and S. Tsukamoto, "Evaluation of Sensitivity of the Digital Coherent Receiver", J. Lightw. Technol., vol. 20, no. 13, pp. 1817–1822, (2008). CrossRef S. Ishimura and K. Kikuchi, "Multi-dimensional Permutation Modulation Aiming at Both High Spectral Efficiency and High Power Efficiency", Proc. OFC/NFOEC, Paper M3A.2, (2014). CrossRef F. I. El-Nahal and A. H. M. Husein, "Radio over fiber access network architecture employing RSOA with downstream OQPSK and upstream re-modulated OOK data", (Optik) Int. J. Light Electron Opt., vol. 123, no. 14, pp: 1301-1303, (2012). CrossRef T. Koike-Akino, D. S. Millar, K. Kojima, and K. Parsons, "Eight-Dimensional Modulation for Coherent Optical Communications", Proc. ECOC, Paper Tu.3.C.3, (2013). DirectLink B. Sklar, Digital communications: Fundamentals and Applications, Prentice-Hall, (2001).

Optimization of Split Transmitter-Receiver Digital Nonlinearity Compensation in Bi-Directional Raman Unrepeatered System

A theoretical model of the nonlinear signal-to-noise interaction (NSNI) in a bi-directional Raman amplified system with receiver-side digital back-propagation (DBP) or split-DBP is given, which is helpful for the design of such a system. In the proposed model, the distributed Raman gain and the spontaneous Raman scattering are taken into account. The results of the theoretical calculation are compared with the results of transmission simulations, which indicates that the theoretical model matches well with the results of simulations when the pre-compensation length is less than 100 km. For the cases of pre-compensation lengths more than 100 km, the theoretical model has an error of less than 0.1 dB compared with the simulations. By using the theoretical model, the efficiency of the split-DBP is analyzed, and the results are compared with transmission simulations. Both the results of theoretical calculation and simulations show that the split-DBP can effectively mitigate the NSNI in such a system. By adopting split-DBP, with an appropriate pre-compensation length, the signal-to-noise ratio (SNR) of the signal increases by about 1 dB. In addition, the impact of the double Rayleigh scattering (DRB) is also analyzed using the proposed model, and the results show that DRB has little impact on the system.

Cost-Optimized Submarine Cables Using Massive Spatial Parallelism

We study the techno-economics of submarine systems constrained by a fixed electrical power supply. We show significant cost savings for high-capacity submarine systems using massive space-division multiplexing (SDM), even without assuming any savings from SDM-specific subsystem integration. Systems with about 100 parallel optical paths, e.g., $\sim$ 50 fiber pairs are shown to provide minimum cost/bit, operating at reduced spectral efficiencies and deep within the linear regime. While advanced nonlinearity-optimized fibers and digital nonlinearity compensation schemes provide little to no gain in such systems, SDM integration of amplifiers and transponders is shown to be a source for significant additional cost savings. We further examine the permissible cost premium for multicore fibers in such massively parallel systems and revisit various design tradeoffs for optical amplifiers, showing that a reduced noise figure can be traded for better power conversion efficiency. We also evaluate potential gains from increasing the available electrical supply power and discuss reliability aspects of massively parallel submarine systems.

25.4-Tb/s Transmission Over Transpacific Distances Using Truncated Probabilistically Shaped PDM-64QAM

Probabilistic constellation shaping (PCS), digital nonlinear compensation, and multirate spatially coupled low-density parity check codes are used to achieve 25.4-Tb/s transmission over 10 285 km EDFA-only straight-line testbed at 6.1 bits/symbol/Hz. The gain provided by PCS over standard 64QAM is investigated over transatlantic and transpacific distances. Moreover, the potential benefits of nonlinear compensation based on digital-backpropagation versus algorithm complexity are addressed.

The Impact of Transceiver Noise on Digital Nonlinearity Compensation

The efficiency of digital nonlinearity compensation (NLC) is analyzed in the presence of noise arising from amplified spontaneous emission noise (ASE) as well as from a non-ideal transceiver subsystem. Its impact on signal-to-noise ratio (SNR) and reach increase is studied with particular emphasis on split NLC, where the digital back-propagation algorithm is divided between transmitter and receiver. An analytical model is presented to compute the SNR's for non-ideal transmission systems with arbitrary split NLC configurations. When signal-signal nonlinearities are compensated, the performance limitation arises from residual signal-noise interactions. These interactions consist of nonlinear beating between the signal and co-propagating ASE and transceiver noise. While transceiver noise-signal beating is usually dominant for short transmission distances, ASE noise-signal beating is dominant for larger transmission distances. It is shown that both regimes behave differently with respect to the optimal NLC split ratio and their respective reach gains. Additionally, simple formulas for the prediction of the optimal NLC split ratio and the reach increase in those two regimes are reported. It is found that split NLC offers negligible gain with respect to conventional digital back-propagation (DBP) for distances less than 1000 km using standard single-mode fibers and a transceiver (back-to-back) SNR of 26 dB, when transmitter and receiver inject the same amount of noise. However, when transmitter and receiver inject an unequal amount of noise, reach gains of 56% on top of DBP are achievable by properly tailoring the split NLC algorithm. The theoretical findings are confirmed by numerical simulations.

Digital nonlinearity compensation in high-capacity optical communication systems considering signal spectral broadening effect

Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions.

On the bandwidth dependent performance of split transmitter-receiver optical fiber nonlinearity compensation.

The Gaussian noise model is used to estimate the performance of three digital nonlinearity compensation (NLC) algorithms in C-band, long-haul, optical fiber transmission, when the span length and NLC bandwidth are independently varied. The algorithms are receiver-side digital backpropagation (DBP), transmitter-side DBP (digital precompensation), and Split NLC (an equal division of DBP between transmitter and receiver). For transmission over 100×100 km spans, the model predicts a 0.2 dB increase in SNR when applying Split NLC (versus DBP) to a single 32 GBd channel (from 0.4 dB to 0.6 dB), monotonically increasing with NLC bandwidth up to 1.6 dB for full-field NLC. The underlying assumptions of this model and the practical considerations for implementation of Split NLC are discussed. This work demonstrates, theoretically, that, regardless of the transmission scenario, it is always beneficial to divide NLC between transmitter and receiver, and identifies the transmission regimes where Split NLC is particularly advantageous.

Modulation format dependence of digital nonlinearity compensation performance in optical fibre communication systems.

The relationship between modulation format and the performance of multi-channel digital back-propagation (MC-DBP) in ideal Nyquist-spaced optical communication systems is investigated. It is found that the nonlinear distortions behave independent of modulation format in the case of full-field DBP, in contrast to the cases of electronic dispersion compensation and partial-bandwidth DBP. It is shown that the minimum number of steps per span required for MC-DBP depends on the chosen modulation format. For any given target information rate, there exists a possible trade-off between modulation format and back-propagated bandwidth, which could be used to reduce the computational complexity requirement of MC-DBP.

Advanced C+L-Band Transoceanic Transmission Systems Based on Probabilistically Shaped PDM-64QAM

We review the most recent advanced concepts and methods employed in the cutting-edge spectrally efficient coherent fiber-optic transoceanic transmission systems, such as probabilistic shaping, adaptive digital nonlinear compensation, rate-adaptive spatially coupled low-density parity check codes, and dual-band C+L-band transmission. Building upon all these concepts and methods, we demonstrate transmission of 179 channels carrying a record net data rate of 65 Tb/s over 6600 km, achieving a spectral efficiency of 7.3 b/s/Hz, and a record average per-channel net bit rate of 363.1 Gb/s. We provide numerical and experimental results, which serve us to comment on the pertinence of the physicist's intuitive measure of performance, the signal-to-noise ratio, versus the information theorist's more accurate measure, the generalized mutual information, for the systems under study.

Nonlinear Interference Mitigation: Methods and Potential Gain

We explore the potential benefits of digital nonlinearity compensation (NLC) techniques in fully loaded coherent wavelength-division multiplexed (WDM) transmission systems. After providing an overview of the various classes of nonlinear interference noise (NLIN) and digital signal processing approaches for their mitigation, we consider the two practically most relevant digital NLC methods known today: back-propagation (BP) and equalization of nonlinear phase and polarization rotation noise (PPRN). We consider a wide range of system configurations including a variety of modulation formats from quadrature phase-shift keying (QPSK) to 256-ary quadrature amplitude modulation (QAM), single-carrier and digital subcarrier multiplexed (SCM) optical superchannels, as well as both point-to-point line systems and optically routed networks (ORNs). Using theoretical predictions from the time-domain model for NLIN, we show that the gain in peak signal-to-noise ratio in fully loaded WDM systems using single-channel and three-channel joint BP is typically limited to 0.5 and 1 dB. The additional gain provided by increasing the number of jointly back-propagated channels beyond three is limited to 0.1 dB per additional back-propagated channel. The remarkably slow growth of the BP gain with the bandwidth of the back-propagated signal is shown to apply also for systems in which the receiver employs PPRN removal. We additionally explore the potential benefits of SCM across a wide range of system configurations, including the impact of BP and PPRN removal on SCM systems. We show that while the BP gain is similar to single-carrier systems, PPRN removal can have a much stronger effect, particularly for higher order QAM systems, implying that SCM can be advantageous not only for constant modulus formats such as QPSK, but also for high spectral efficiency systems. In the context of ORNs, we find that SCM not only improves system tolerance to nonlinearities, but also induces significantly smaller performance variations in various ORN scenarios.

Digital Nonlinear Compensation for Spectrally Sliced Optical Receivers With MIMO Reconstruction

We experimentally investigate, in a 20×56-GBd 400 G WDM transmission system, different approaches for nonlinear compensation in spectrally sliced optical receivers with MIMO-based signal reconstruction. Slice-by-slice nonlinear compensation shows comparable performance to inter-slice nonlinear compensation in a WDM system. In addition, an eight-stages compensation yields a 0.4-dB Q 2 gain equivalent to 250-km distance increase, resulting in 2000-km transparent reach.