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.

AI-optimised tuneable sources for bandwidth-scalable, sub-nanosecond wavelength switching.

Wavelength routed optical switching promises low power and latency networking for data centres, but requires a wideband wavelength tuneable source (WTS) capable of sub-nanosecond switching at every node. We propose a hybrid WTS that uses time-interleaved tuneable lasers, each gated by a semiconductor optical amplifier, where the performance of each device is optimised using artificial intelligence. Through simulation and experiment we demonstrate record wavelength switch times below 900 ps across 6.05 THz (122×50 GHz) of continuously tuneable optical bandwidth. A method for further bandwidth scaling is evaluated and compared to alternative designs.

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.

End-to-end optimized transmission over dispersive intensity-modulated channels using bidirectional recurrent neural networks.

We propose an autoencoding sequence-based transceiver for communication over dispersive channels with intensity modulation and direct detection (IM/DD), designed as a bidirectional deep recurrent neural network (BRNN). The receiver uses a sliding window technique to allow for efficient data stream estimation. We find that this sliding window BRNN (SBRNN), based on end-to-end deep learning of the communication system, achieves a significant bit-error-rate reduction at all examined distances in comparison to previous block-based autoencoders implemented as feed-forward neural networks (FFNNs), leading to an increase of the transmission distance. We also compare the end-to-end SBRNN with a state-of-the-art IM/DD solution based on two level pulse amplitude modulation with an FFNN receiver, simultaneously processing multiple received symbols and approximating nonlinear Volterra equalization. Our results show that the SBRNN outperforms such systems at both 42 and 84 Gb/s, while training fewer parameters. Our novel SBRNN design aims at tailoring the end-to-end deep learning-based systems for communication over nonlinear channels with memory, such as the optical IM/DD fiber channel.

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.

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.

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 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.

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.

Digital backpropagation accounting for polarization-mode dispersion.

Digital backpropagation (DBP) is a promising digital-domain technique to mitigate Kerr-induced nonlinear interference. While it successfully removes deterministic signal-signal interactions, the performance of ideal DBP is limited by stochastic effects, such as polarization-mode dispersion (PMD). In this paper, we consider an ideal full-field DBP implementation and modify it to additionally account for PMD; reversing the PMD effects in the backward propagation by passing the reverse propagated signal also through PMD sections, which concatenated equal the inverse of the PMD in the forward propagation. These PMD sections are calculated analytically at the receiver based on the total accumulated PMD of the link estimated from channel equalizers. Numerical simulations show that, accounting for nonlinear polarization-related interactions in the modified DBP algorithm, additional signal-to-noise ratio gains of 1.1 dB are obtained for transmission over 1000 km.

Increasing the information rates of optical communications via coded modulation: a study of transceiver performance.

Optical fibre underpins the global communications infrastructure and has experienced an astonishing evolution over the past four decades, with current commercial systems transmitting data rates in excess of 10 Tb/s over a single fibre core. The continuation of this dramatic growth in throughput has become constrained due to a power dependent nonlinear distortion arising from a phenomenon known as the Kerr effect. The mitigation of fibre nonlinearities is an area of intense research. However, even in the absence of nonlinear distortion, the practical limit on the transmission throughput of a single fibre core is dominated by the finite signal-to-noise ratio (SNR) afforded by current state-of-the-art coherent optical transceivers. Therefore, the key to maximising the number of information bits that can be reliably transmitted over a fibre channel hinges on the simultaneous optimisation of the modulation format and code rate, based on the SNR achieved at the receiver. In this work, we use an information theoretic approach based on the mutual information and the generalised mutual information to characterise a state-of-the-art dual polarisation m-ary quadrature amplitude modulation transceiver and subsequently apply this methodology to a 15-carrier super-channel to achieve the highest throughput (1.125 Tb/s) ever recorded using a single coherent receiver.

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.

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.

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.

Gain-switched multicarrier transmitter in a long-reach UDWDM PON with a digital coherent receiver.

The authors report on the downlink performance of a 10 Gb/s long-reach and ultra-dense wavelength-division multiplexed passive optical network, based on a multicarrier transmitter realized by using an externally injected gain-switched distributed-feedback laser diode. Each of the comb channels, spaced by 10 GHz, is modulated with a 3 Gbaud dual polarization quadrature phase shift keying signal that included a 20% overhead for forward error correction. Frequency selectivity and enhanced receiver sensitivity is achieved by employing a digital coherent receiver to receive the signal. Experimental results achieved in a back-to-back and 100 km transmission scenarios show an excellent worst case receiver sensitivity of -44 dBm.

Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s.

We demonstrate, for the first time, the generation and transmission of polarization-switched QPSK (PS-QPSK) signals at 42.9 Gb/s. Long-haul transmission of PS-QPSK is experimentally investigated in a recirculating loop and compared with transmission of dual-polarization QPSK (DP-QPSK) at 42.9 Gb/s per channel. A reduction in the required OSNR of 0.7 dB was found at a BER of 3.8 x 10(-3), resulting in an increase in maximum reach of more than 30% for a WDM system operating on a 50 GHz frequency grid. The maximum reach of 13640 km for WDM PS-QPSK is, to the best of our knowledge, the longest distance reported for 40 Gb/s WDM transmission, over an uncompensated link, with standard fiber and amplification.

Ultra-long-haul transmission of 7×42.9 Gbit/s PS-QPSK and PDM-BPSK.

We investigated ultra-long-haul transmission of polarization-switched QPSK (PS-QPSK) and polarization-division-multiplexed BPSK (PDM-BPSK) at 42.9 Gbit/s experimentally as well as by means of computer simulations. PDM-BPSK allowed transmission distances in excess of 14,040 km to be achieved, compared to 13,640 km for PS-QPSK. However, PS-QPSK offers a significant reduction in receiver complexity due to the lower symbol-rate.

A comparison of modulation formats for passive optical networks.

The sensitivity of the four-dimensional modulation format, polarization-switched quadrature phase shift keying (PS-QPSK), is compared with polarization division multiplexed QPSK (PDM-QPSK), binary phase shift keying (PDM-BPSK) and 8-ary quadrature amplitude modulation (PDM-8QAM) at a constant bitrate (12.5 Gbit/s) using a preamplified signal to improve receiver sensitivity. The sensitivity without preamplification is also obtained. PS-QPSK is found to maintain a sensitivity advantage over the reference formats in line with theory with an absolute sensitivity of -52.7 dBm (4.2 photons/bit), assuming hard decision FEC.