Maximization or leveling: characterization of the trade-offs for the transmission throughput in ultrawideband optical transmission.

In ultrawideband transmission, the overall noise comes from the amplification, fiber properties at different wavelengths, and stimulated Raman scattering, and its impact on channels across transmission bands is different. This requires a range of methods to mitigate the noise impact. Performing channel-wise power pre-emphasis and constellation shaping, one can compensate for the noise tilt and attain maximum throughput. In this work, we study the trade-off between the goals of maximizing the total throughput and leveling the transmission quality for different channels. We use an analytical model for multi-variable optimization and identify the penalty from constraining the mutual information variation.

2048-QAM transmission at 15 GBd over 100 km using geometric constellation shaping.

We experimentally investigated a pilot-aided digital signal processing (DSP) chain in combination with high-order geometric constellation shaping to increase the achievable information rates (AIRs) in standard intradyne coherent transmission systems. We show that the AIR of our system at 15 GBd was maximised using geometrically-shaped (GS) 2048 quadrature amplitude modulation (QAM), reaching 18.0 b/4D-symbol in back-to-back transmission and 16.9 b/4D-symbol after transmission through 100 km of a single-mode fibre after subtracting the pilot overhead (OH). This represents the highest-order GS format demonstrated to date, supporting the highest AIR of any standard intradyne system using conventional optics and 8-bit electronics. Detailed characterisation of the DSP, transceiver performance, and transmission modelling has also been carried out to provide insight into sources of impairments and directions for further improvement.

Performance of momentum-based frequency-domain MIMO equalizer in the presence of feedback delay.

A frequency-domain multiple-input multiple-output (FD-MIMO) equalizer employing a momentum-based gradient descent update algorithm is proposed for polarization multiplexing coherent receivers. Its performance in operation with dynamically varying optical channels is investigated and the impact of filter update delays, arising from the latency of the fast Fourier transforms (FFTs) and other digital signal processing (DSP) operations in the feedback loop, is assessed. We show that the proposed momentum-based gradient descent algorithm used to control the equalizer response has significantly greater tolerance to feedback delay than the conventional gradient descent algorithm. We considered a 92 Gbaud dual-polarization 64 QAM receiver, with DSP operating at two samples per symbol, and with the equalizer operating on blocks of 512 and 1024 samples (i.e., 512/1024-point FFT). We found that at an optical signal-to-noise power ratio (OSNR) of 35 dB, the momentum-based gradient descent algorithm can successfully track state-of-polarization (SOP) rotation at frequencies of up to 50 kHz and with filter update delays of up to 14 blocks (39 ns). In comparison, using the conventional gradient descent algorithm in an otherwise identical receiver, the equalizer performance starts to deteriorate at SOP rotation frequencies above 20 kHz.

Experimental characterization of nonlinear interference noise as a process of intersymbol interference.

We demonstrate a method for experimentally characterizing the second order statistics of nonlinear interference noise (NLIN) as an intersymbol interference (ISI) process. The method enables measurement of the properties of high-order ISI coefficients, which have been largely overlooked in the past. The ability of measuring these statistics is imperative for designing effective NLIN mitigation schemes. The variance, temporal correlation times, and cross correlations of the various ISI coefficients are evaluated in several system implementations.

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.

Investigation of bandwidth loading in optical fibre transmission using amplified spontaneous emission noise.

The use of spectrally shaped amplified spontaneous emission noise (SS-ASE) as a method for emulating interfering channels in optical fibre transmission systems has been studied. It is shown that the use of SS-ASE leads to a slightly pessimistic performance relative to the use of conventionally modulated interfering channels in the nonlinear regime. The additional nonlinear interference noise (on the channel under test), due to the Gaussian nature of SS-ASE, has been calculated using a combination of the Gaussian noise (GN) and enhanced GN (EGN) models for the entire C-band (4.5 THz) and experimentally shown to provide a lower bound for transmission performance.

Span length and information rate optimisation in optical transmission systems using single-channel digital backpropagation.

The optimisation of span length when designing optical communication systems is important from both performance and cost perspectives. In this paper, the optimisation of inter-amplifier spacing and the potential increase of span length at fixed information rates in optical communication systems with practically feasible nonlinearity compensation schemes have been investigated. It is found that in DP-16QAM, DP-64QAM and DP-256QAM systems with practical transceiver noise limitations, single-channel digital backpropagation can allow a 50% reduction in the number of amplifiers without sacrificing information rates compared to systems with optimal span lengths and linear compensation.

Modeling of nonlinearity-compensated optical communication systems considering second-order signal-noise interactions.

An analytical model considering modulation-dependent nonlinear effects and second-order interactions between signal and optical amplifier noise is presented for Nyquist-spaced wavelength-division-multiplexing optical communication systems. System performance of dual-polarization modulation formats, such as DP-QPSK, DP-16QAM, and DP-64QAM, is investigated using both the analytical model and numerical simulations. A good agreement between analytical and numerical results shows that, in the case of full-field nonlinearity compensation, accounting for second-order interactions becomes essential to predict system performance of both single- and multi-channel systems at optimum launched powers and beyond. This effect is validated via numerical simulations for signal bandwidths up to ∼1 THz.

Achievable rate degradation of ultra-wideband coherent fiber communication systems due to stimulated Raman scattering.

As the bandwidths of optical communication systems are increased to maximize channel capacity, the impact of stimulated Raman scattering (SRS) on the achievable information rates (AIR) in ultra-wideband coherent WDM systems becomes significant, and is investigated in this work, for the first time. By modifying the GN-model to account for SRS, it is possible to derive a closed-form expression that predicts the optical signal-to-noise ratio of all channels at the receiver for bandwidths of up to 15 THz, which is in excellent agreement with numerical calculations. It is shown that, with fixed modulation and coding rate, SRS leads to a drop of approximately 40% in achievable information rates for bandwidths higher than 15 THz. However, if adaptive modulation and coding rates are applied across the entire spectrum, this AIR reduction can be limited to only 10%.

Digital back-propagation for nonlinearity mitigation in distributed Raman amplified links.

The performance of digital back-propagation (DBP) for distributed Raman amplified optical communication systems is evaluated through analytical models and numerical simulations, and is compared with conventional lumped amplifier solutions, such as EDFA. The complexity of the DBP algorithm including the characteristic signal power profile of distributed Raman amplifiers is assessed. The use of full-field DBP in distributed Raman amplified systems leads to 1.3 dB additional gain with respect to systems employing lumped amplification, at the cost of only a 25% increase in complexity.

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.

On the limits of digital back-propagation in the presence of transceiver noise.

This paper investigates the impact of transceiver noise on the performance of digital back-propagation (DBP). A generalized expression to estimate the signal-to-noise ratio (SNR) obtained using DBP in the presence of transceiver noise is described. This new expression correctly accounts for the nonlinear beating between the transceiver noise and the signal in the optical fiber transmission link. The transceiver noise-signal nonlinear beating has been identified as the main reason for the discrepancy between predicted and practical performance of DBP; which has not been previously suggested. This nonlinear beating has been included in the GN model, allowing DBP gains in practical systems to be predicted analytically. Experiments and split-step simulations with and without polarization-mode dispersion (PMD) in the transmission link have been performed. The results show that the impact of transceiver noise greatly outweighs that of PMD, and the analytical expressions are confirmed by the numerical simulations.

Achievable information rates estimates in optically amplified transmission systems using nonlinearity compensation and probabilistic shaping.

Achievable information rates (AIRs) of wideband optical communication systems using a ∼40 nm (∼5 THz) erbium-doped fiber amplifier and ∼100 nm (∼12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each individual channel have been evaluated for DP-64QAM, DP-256QAM, and DP-1024QAM modulation formats. The impact of full-field nonlinear compensation (FF-NLC) and probabilistically shaped constellations using a Maxwell-Boltzmann distribution were studied and compared to electronic dispersion compensation. It has been found that a probabilistically shaped DP-1024QAM constellation, combined with FF-NLC, yields achievable information rates of ∼75 Tbit/s for the EDFA scheme and ∼223 Tbit/s for the Raman amplification scheme over a 2000 km standard single-mode fiber transmission.

Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems.

Single-polarization direct-detection transceivers may offer advantages compared to digital coherent technology for some metro, back-haul, access and inter-data center applications since they offer low-cost and complexity solutions. However, a direct-detection receiver introduces nonlinearity upon photo detection, since it is a square-law device, which results in signal distortion due to signal-signal beat interference (SSBI). Consequently, it is desirable to develop effective and low-cost SSBI compensation techniques to improve the performance of such transceivers. In this paper, we compare the performance of a number of recently proposed digital signal processing-based SSBI compensation schemes, including the use of single- and two-stage linearization filters, an iterative linearization filter and a SSBI estimation and cancellation technique. Their performance is assessed experimentally using a 7 × 25 Gb/s wavelength division multiplexed (WDM) single-sideband 16-QAM Nyquist-subcarrier modulation system operating at a net information spectral density of 2.3 (b/s)/Hz.

Maximizing the optical network capacity.

Most of the digital data transmitted are carried by optical fibres, forming the great part of the national and international communication infrastructure. The information-carrying capacity of these networks has increased vastly over the past decades through the introduction of wavelength division multiplexing, advanced modulation formats, digital signal processing and improved optical fibre and amplifier technology. These developments sparked the communication revolution and the growth of the Internet, and have created an illusion of infinite capacity being available. But as the volume of data continues to increase, is there a limit to the capacity of an optical fibre communication channel? The optical fibre channel is nonlinear, and the intensity-dependent Kerr nonlinearity limit has been suggested as a fundamental limit to optical fibre capacity. Current research is focused on whether this is the case, and on linear and nonlinear techniques, both optical and electronic, to understand, unlock and maximize the capacity of optical communications in the nonlinear regime. This paper describes some of them and discusses future prospects for success in the quest for capacity.

High spectral density transmission emulation using amplified spontaneous emission noise.

We demonstrate the use of spectrally shaped amplified spontaneous emission (SS-ASE) noise for wideband channel loading in the investigation of nonlinear transmission limits in wavelength-division multiplexing transmission experiments using Nyquist-spaced channels. The validity of this approach is explored through statistical analysis and experimental transmission of Nyquist-spaced 10 GBaud polarization-division multiplexing (PDM) quadrature phase-shift keying and PDM-16-ary quadrature amplitude modulation (QAM) channels, co-propagated with SS-ASE over single mode fiber. It is shown that this technique, which is simpler to implement than a fully modulated comb of channels, is valid for distances exceeding 240 km for PDM-16QAM with dispersion of 16 ps/nm/km, yields a good agreement with theory, and provides a conservative measure of system performance.

Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multi-channel digital back-propagation.

Superchannel transmission spaced at the symbol rate, known as Nyquist spacing, has been demonstrated for effectively maximizing the optical communication channel capacity and spectral efficiency. However, the achievable capacity and reach of transmission systems using advanced modulation formats are affected by fibre nonlinearities and equalization enhanced phase noise (EEPN). Fibre nonlinearities can be effectively compensated using digital back-propagation (DBP). However EEPN which arises from the interaction between laser phase noise and dispersion cannot be efficiently mitigated, and can significantly degrade the performance of transmission systems. Here we report the first investigation of the origin and the impact of EEPN in Nyquist-spaced superchannel system, employing electronic dispersion compensation (EDC) and multi-channel DBP (MC-DBP). Analysis was carried out in a Nyquist-spaced 9-channel 32-Gbaud DP-64QAM transmission system. Results confirm that EEPN significantly degrades the performance of all sub-channels of the superchannel system and that the distortions are more severe for the outer sub-channels, both using EDC and MC-DBP. It is also found that the origin of EEPN depends on the relative position between the carrier phase recovery module and the EDC (or MC-DBP) module. Considering EEPN, diverse coding techniques and modulation formats have to be applied for optimizing different sub-channels in superchannel systems.

Signal-signal beat interference cancellation in spectrally-efficient WDM direct-detection Nyquist-pulse-shaped 16-QAM subcarrier modulation.

An experimental demonstration of direct-detection single-sideband Nyquist-pulse-shaped 16-QAM subcarrier modulated (Nyquist-SCM) transmission implementing a receiver-based signal-signal beat interference (SSBI) cancellation technique is described. The performance improvement with SSBI mitigation, which compensates for the nonlinear distortion caused by square-law detection, was quantified by simulations and experiments for a 7 × 25 Gb/s WDM Nyquist-SCM signal with a net optical information spectral density (ISD) of 2.0 (b/s)/Hz. A reduction of 3.6 dB in the back-to-back required OSNR at the HD-FEC threshold was achieved. The resulting reductions in BER in single channel and WDM transmission over distances of up to 800 km of uncompensated standard single-mode fiber (SSMF) achieved are presented.

Unrepeatered Nyquist PDM-16QAM transmission over 364 km using Raman amplification and multi-channel digital back-propagation.

Transmission of a net 467-Gb/s PDM-16QAM Nyquist-spaced superchannel is reported with an intra-superchannel net spectral efficiency (SE) of 6.6 (b/s)/Hz, over 364-km SMF-28 ULL ultra-low loss optical fiber, enabled by bi-directional second-order Raman amplification and digital nonlinearity compensation. Multi-channel digital back-propagation (MC-DBP) was applied to compensate for nonlinear interference; an improvement of 2 dB in Q(2) factor was achieved when 70-GHz DBP bandwidth was applied, allowing an increase in span length of 37 km.

Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation.

The achievable transmission capacity of conventional optical fibre communication systems is limited by nonlinear distortions due to the Kerr effect and the difficulty in modulating the optical field to effectively use the available fibre bandwidth. In order to achieve a high information spectral density (ISD), while simultaneously maintaining transmission reach, multi-channel fibre nonlinearity compensation and spectrally efficient data encoding must be utilised. In this work, we use a single coherent super-receiver to simultaneously receive a DP-16QAM super-channel, consisting of seven spectrally shaped 10GBd sub-carriers spaced at the Nyquist frequency. Effective nonlinearity mitigation is achieved using multi-channel digital back-propagation (MC-DBP) and this technique is combined with an optimised forward error correction implementation to demonstrate a record gain in transmission reach of 85%; increasing the maximum transmission distance from 3190 km to 5890 km, with an ISD of 6.60 b/s/Hz. In addition, this report outlines for the first time, the sensitivity of MC-DBP gain to linear transmission line impairments and defines a trade-off between performance and complexity.