Online digital compensation of pump dithering induced phase and amplitude distortions in transmission links with cascaded fibre-optical parametric amplifiers.

We present an advanced online digital signal processing (DSP) method for correcting the phase and amplitude distortions caused by the phase modulation of the pump source and its interaction with the dispersive fibre channel in transmission systems using cascaded fibre-optical parametric amplifiers. The proposed algorithm is numerically demonstrated to achieve significant (up to 3.7 dB for a four-tone pump-phase modulation scheme) Q2-factor performance improvement over conventional DSP in 16 quadrature-amplitude modulation signal transmission.

Kernel adaptive filtering-based phase noise compensation for pilot-free optical phase conjugated coherent systems.

We propose a kernel-based adaptive filtering method to suppress the phase noise (PN) arising from small deviations from ideal counter-phasing in the dual-pump fibre-based optical phase conjugation (OPC) of pilot-free quadrature-amplitude modulation (QAM) signals. We demonstrate experimentally and numerically that the proposed scheme achieves signal-to-noise ratio improvement over conventional PN compensation under optimised pump dithering settings in the OPC device and features no performance penalty across a range of pump-phase mismatch values, when it is used with a 16-QAM signal in an optical back-to-back configuration. We also illustrate the applicability of the method to the 64-QAM modulation format, and evaluate its performance in a transmission setup with mid-link OPC by means of numerical simulations.

Digital compensation of imperfect pump counter-phasing induced phase distortion in optical phase conjugation of high-order QAM.

We propose a new two-stage digital signal processing scheme to suppress the phase distortion that arises from imperfect pump counter-phasing in a dual-pump fibre-based optical phase conjugation system. We demonstrate experimentally and numerically a signal-to-noise ratio improvement of more than 4 dB relative to conventional phase noise compensation, when the proposed scheme is used with 16/64/256 quadrature-amplitude modulation signals at pump-phase mismatch values as large as 8°.

Cost-effective digital coherent short-reach transmission system with D8QAM and low-complexity DSP.

We propose a cost-effective digital coherent scheme with low-complexity digital signal processing (DSP) for short-reach optical interconnection. Differential 8-ary quadrature amplitude modulation (D8QAM) with 1-decision-aided adaptive differential decoding bypasses carrier recovery and enables cycle-slip-free operation. We experimentally demonstrate that the receiver sensitivity of 400-Gb/s D8QAM is insensitive to the laser type, and is the same as 400-Gb/s 16QAM in the case of 2-km transmission with a distributed feedback (DFB) laser. The proposed adaptive equalizer (AEQ) using real-valued finite impulse response (FIR) filters and shorter tap lengths for the real-imaginary filters allows hardware-efficient implementation with high robustness to the receiver-side timing skew. In the case of 400-Gb/s D8QAM 10-km transmission, our AEQ achieves comparable performance as conventional 4×4 real-valued multi-input multi-output (MIMO) and the existing simplified AEQs with complexity reduction of 50% and 14% respectively.

Conjugate nonlinear-optical loop mirror (Conj-NOLM)-based phase-preserving multilevel amplitude regenerator.

We propose a novel phase-preserving multilevel amplitude regenerator scheme by cascading two nonlinear-optical loop mirrors (NOLMs) with an intermediate optical phase conjugator (OPC) stage. Joint parameter optimization of the two NOLM units has been carried out to cancel the introduced phase distortion and enable a more power-efficient performance. Moreover, our scheme combines the operation of the NOLM and the OPC in a single subsystem, enabling the compensation of both amplitude and phase distortions when located symmetrically in a transmission link. To this end, extensive numerical simulations have been performed to evaluate the regeneration performance in a transmission link dominated by amplified spontaneous emission (ASE) noise and Kerr-induced nonlinear distortions (self-phase modulation-induced phase distortion), achieving over 100% reach extension compared to the cases of un-regenerative, or a mid-span OPC-based transmission links.

Overcoming degradation in spatial multiplexing systems with stochastic nonlinear impairments.

Single-mode optical fibres now underpin telecommunication systems and have allowed continuous increases in traffic volume and bandwidth demand whilst simultaneously reducing cost- and energy-per-bit over the last 40 years. However, it is now recognised that such systems are rapidly approaching the limits imposed by the nonlinear Kerr effect. To address this, recent research has been carried out into mitigating Kerr nonlinearities to increase the nonlinear threshold and into spatial multiplexing to offer additional spatial pathways. However, given the complexity associated with nonlinear transmission in spatial multiplexed systems subject to random inter-spatial-path nonlinearities it is widely believed that these technologies are mutually exclusive. By investigating the linear and nonlinear crosstalk in few-mode fibres based optical communications, we numerically demonstrate, for the first time, that even in the presence of significant random mixing of signals, substantial performance benefits are possible. To achieve this, the impact of linear mixing on the Kerr nonlinearities should be taken into account using different compensation strategies for different linear mixing regimes. For the optical communication systems studied, we demonstrate that the performance may be more than doubled with the appropriate selection of compensation method for fibre characteristics which match those presented in the literature.

Amplifier-free 200-Gb/s tandem SSB doubly differential QPSK signal transmission over 80-km SSMF with simplified receiver-side DSP.

We numerically demonstrate 80-km standard single-mode fiber transmission without optical amplification, dispersion compensation or carrier recovery using 200-Gb/s tandem single sideband modulated doubly differential QPSK. Simulation results show that doubly differential encoding enables practically constant system performance for frequency offsets within ± 2.3 GHz and allows a linewidth tolerance of 2.5 × 10-3 at 1-dB receiver sensitivity penalty. Employing 2.9-MHz linewidth lasers, the receiver sensitivity penalty at 7% HD-FEC threshold for 80-km transmission is less than 0.2 dB. By adding a 12-symbol decision feedback in the 2nd differential operation of doubly differential decoding, the receiver sensitivity is improved by 3.7 dB.

Equalization performance and complexity analysis of dynamic deep neural networks in long haul transmission systems.

We investigate the application of dynamic deep neural networks for nonlinear equalization in long haul transmission systems. Through extensive numerical analysis we identify their optimum dimensions and calculate their computational complexity as a function of system length. Performing comparison with traditional back-propagation based nonlinear compensation of 2 steps-per-span and 2 samples-per-symbol, we demonstrate equivalent mitigation performance at significantly lower computational cost.

Ripple distribution for nonlinear fiber-optic channels.

We demonstrate data rates above the threshold imposed by nonlinearity on conventional optical signals by applying novel probability distribution, which we call ripple distribution, adapted to the properties of the fiber channel. Our results offer a new direction for signal coding, modulation and practical nonlinear distortions compensation algorithms.

Sparse identification for nonlinear optical communication systems: SINO method.

We introduce low complexity machine learning method method (based on lasso regression, which promotes sparsity, to identify the interaction between symbols in different time slots and to select the minimum number relevant perturbation terms that are employed) for nonlinearity mitigation. The immense intricacy of the problem calls for the development of "smart" methodology, simplifying the analysis without losing the key features that are important for recovery of transmitted data. The proposed sparse identification method for optical systems (SINO) allows to determine the minimal (optimal) number of degrees of freedom required for adaptive mitigation of detrimental nonlinear effects. We demonstrate successful application of the SINO method both for standard fiber communication links (over 3 dB gain) and for few-mode spatial-division-multiplexing systems.

Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM.

We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats).

Injection locking-based pump recovery for phase-sensitive amplified links.

An injection locking-based pump recovery system for phase-sensitive amplified links, capable of handling 40 dB effective span loss, is demonstrated. Measurements with 10 GBd DQPSK signals show penalty-free recovery of a pump wave, phase modulated with two sinusoidal RF-tones at 0.1 GHz and 0.3 GHz, with 64 dB amplification. The operating power limit for the pump recovery system is experimentally investigated and is governed by the noise transfer and phase modulation transfer characteristics of the injection-locked laser. The corresponding link penalties are explained and quantified. This system enables, for the first time, WDM compatible phase-sensitive amplified links over significant lengths.

Impact of power allocation strategies in long-haul few-mode fiber transmission systems.

We report for the first time on the limitations in the operational power range of few-mode fiber based transmission systems, employing 28 Gbaud quadrature phase shift keying transponders, over 1,600 km. It is demonstrated that if an additional mode is used on a preexisting few-mode transmission link, and allowed to optimize its performance, it will have a significant impact on the pre-existing mode. In particular, we show that for low mode coupling strengths (weak coupling regime), the newly added variable power mode does not considerably impact the fixed power existing mode, with performance penalties less than 2dB (in Q-factor). On the other hand, as mode coupling strength is increased (strong coupling regime), the individual launch power optimization significantly degrades the system performance, with penalties up to ~6 dB. Our results further suggest that mutual power optimization, of both fixed power and variable power modes, reduces power allocation related penalties to less than 3 dB, for any given coupling strength, for both high and low differential mode delays.

Intra-channel nonlinearity compensation for PM-16 QAM traffic co-propagating with 28 Gbaud m-ary QAM neighbours.

We quantify the benefits of intra-channel nonlinear compensation in meshed optical networks, in view of network configuration, fibre design aspect, and dispersion management. We report that for a WDM optical transport network employing flexible 28Gbaud PM-mQAM transponders with no in-line dispersion compensation, intra-channel nonlinear compensation, for PM-16QAM through traffic, offers significant improvements of up to 4dB in nonlinear tolerance (Q-factor) irrespective of the co-propagating modulation format, and that this benefit is further enhanced (1.5dB) by increasing local link dispersion. For dispersion managed links, we further report that advantages of intra-channel nonlinear compensation increase with in-line dispersion compensation ratio, with 1.5dB improvements after 95% in-line dispersion compensation, compared to uncompensated transmission.

Optimal packing for cascaded regenerative transmission based on phase sensitive amplifiers.

We investigate the transmission performance of advanced modulation formats in nonlinear regenerative channels based on cascaded phase sensitive amplifiers. We identify the impact of amplitude and phase noise dynamics along the transmission line and show that after a cascade of regenerators, densely packed single ring PSK constellations outperform multi-ring constellations. The results of this study will greatly simplify the design of future nonlinear regenerative channels for ultra-high capacity transmission.

Phase synchronization scheme for a practical phase sensitive amplifier of ASK-NRZ signals.

We present a phase locking scheme that enables the demonstration of a practical dual pump degenerate phase sensitive amplifier for 10 Gbit/s non-return to zero amplitude shift keying signals. The scheme makes use of cascaded Mach Zehnder modulators for creating the pump frequencies as well as of injection locking for extracting the signal carrier and synchronizing the local lasers. An in depth optimization study has been performed, based on measured error rate performance, and the main degradation factors have been identified.

Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals.

We report a novel real-time homodyne coherent receiver based on a DPSK optical-electrical-optical (OEO) regenerator used to extract a carrier from carrier-less phase modulated signals based on feed-forward based modulation stripping. The performance of this non-DSP based coherent receiver was evaluated for 10.66 Gbit/s BPSK signals. Self-homodyne coherent detection and homodyne detection with an injection-locked local oscillator laser was demonstrated. The performance was evaluated by measuring the electrical signal-to-noise (SNR) and recording the eye diagrams. Using injection-locking for the LO improves the performance and enables homodyne detection with optical injection-locking to operate with carrier-less BPSK signals without the need for polarization multiplexed pilot-tones.

Novel synchronous DPSK optical regenerator based on a feed-forward based carrier extraction scheme.

We experimentally demonstrate a novel synchronous 10.66 Gbit/s DPSK OEO regenerator which uses a feed-forward carrier extraction scheme with an injection-locked laser to synchronize the regenerated signal wavelength to the incoming signal wavelength. After injection-locking, a low-cost DFB laser used at the regenerator exhibited the same linewidth characteristics as the narrow line-width transmitter laser. The phase regeneration properties of the regenerator were evaluated by emulating random Gaussian phase noise applied to the DPSK signal before the regenerator using a phase modulator driven by an arbitrary waveform generator. The overall performance was evaluated in terms of electrical eye-diagrams, BER measurements, and constellation diagrams.

A practical phase sensitive amplification scheme for two channel phase regeneration.

A "black-box" phase sensitive amplifier is presented achieving simultaneous suppression of deterministic phase distortion on two independent 42.66 Gbit/s DPSK modulated signal wavelengths.