Digital back propagation performance in spatial multiplexing systems (original) (raw)
On the Performance of Digital Back Propagation in Spatial Multiplexing Systems
Journal of Lightwave Technology, 2020
Nonlinear performance in spatial multiplexing systems is strongly determined by the interplay between differential mode delay, linear mode coupling and Kerr nonlinearity. In this work we review and extend the analysis of different solution methods for the linear coupling operator in the coupled nonlinear Schrödinger equation for spatial multiplexed propagation. Numerical solution methods are compared for different operational regimes as determined by differential mode delay and linear mode coupling. Finally, we review and extend the study of digital methods to mitigate the Kerr nonlinearity for arbitrary levels of random linear mode coupling. For the first time, it is shown that in spatial multiplexing systems transmission performance can be improved by reducing the number of back propagated channels for non-negligible levels of differential mode delay.
Overcoming degradation in spatial multiplexing systems with stochastic nonlinear impairments
Scientific Reports, 2018
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-perbit 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. The Kerr nonlinear limit has imposed an ever-growing capacity gap between the technologies generating/processing data and the technologies transporting it-namely, optical fibre communication systems. The first has consistently grown at 40% compound annual growth rate (CAGR) 1 , but the latter has slowed to 20% CAGR since late 1990s 2. Such large scaling disparity is expected to lead to a full exhaustion of system capacity within the next 5 to 15 years. By 2024, optical networks are projected to require 1 Pb/s transmission capacity which with current technological limits can be expected to be met using 10 parallel line systems each carrying 100 Tb/s per fibre. A trend that would potentially increase the cost-and energy-per-bit by 10 times except for efficiency gains as ancillary functions overhead 3 is reduced via subsystem integration. However, with the number of required spatial paths projected to double every 2-years and the current communications infrastructure accounting for 1-2% of global energy 4 the current paradigm is exhausted. Thus, research effort must be directed towards the development of transformative means for achieving spatial parallelism that can ensure sublinear scaling of the total system cost and energy consumption. Otherwise, the dooming capacity exhaustion will lead to a dramatic increase of the bandwidth price and ultimately bring the information revolution to a halt. Mode-division multiplexing (MDM) over few-mode fibres (FMFs) holds one the greatest potential to deliver future cost-and energy-effective high-capacity systems with spatial parallelism 5,6. Figure 1 shows the basic system concept of a multi-span MDM-FMF system, composed by integrated arrays of M transmitter and M receiver units, mode multiplexers/de-multiplexers (e.g. photonic lanterns 7), and multimode amplifiers 8. The information is carried over a set of orthogonal spatial modes overlapping on a single fibre core. Compared to alternative technologies, such as uncoupled multi-core fibres or single-mode fibre (SMF) bundles 5 , MDM-FMF systems offer a number of advantages, such as lower nonlinear coefficients; higher pump efficiency for their optical amplifiers (similar to core pumped SMF) 9 ; and higher spatial-density level of optical integration for transponders 10 , amplifiers, and add-drop multiplexers (multiple spatial modes can be routed together 11). Nevertheless, coupled-core multi-core fibres (CC-MCFs) offer similar potential to that of FMFs when designed to have similar spatial mode densities 12-14. Finally, the techniques presented in this paper apply to all SDM fibre types, including CC-MCFs.
Nonlinear Digital Compensation for Spatial Multiplexing Systems
2021 17th International Symposium on Wireless Communication Systems (ISWCS), 2021
We review the latest advances on digital backward-propagation for the compensation of inter-channel nonlinear interference in spatial-and wavelength-multiplexed systems. Different solution methods of the multimode Schrödinger equation are compared for challenging linear mode coupling and differential mode delay conditions, highlighting the significant relaxation of the step size requirements provided by the separate-channels approach.
Space-division multiplexing in optical fibres
Nature Photonics, 2013
Optical communications technology has made enormous and steady progress for several decades, providing the key resource in our increasingly information-driven society and economy. Much of this progress has been in finding innovative ways to increase the data carrying capacity of a single optical fibre. In this search, researchers have explored (and close to maximally exploited) every available degree of freedom, and even commercial systems now utilize multiplexing in time, wavelength, polarization, and phase to speed more information through the fibre infrastructure. Conspicuously, one potentially enormous source of improvement has however been left untapped in these systems: fibres can easily support hundreds of spatial modes, but today's commercial systems (single-mode or multi-mode) make no attempt to use these as parallel channels for independent signals.
Expressions for the nonlinear transmission performance of multi-mode optical fiber
Optics Express, 2013
We develop an analytical theory which allows us to identify the information spectral density limits of multimode optical fiber transmission systems. Our approach takes into account the Kerr-effect induced interactions of the propagating spatial modes and derives closed-form expressions for the spectral density of the corresponding nonlinear distortion. Experimental characterization results have confirmed the accuracy of the proposed models. Application of our theory in different FMF transmission scenarios has predicted a ~10% variation in total system throughput due to changes associated with inter-mode nonlinear interactions, in agreement with an observed 3dB increase in nonlinear noise power spectral density for a graded index four LP mode fiber.
Journal of Russian Laser Research, 2020
In spatial division multiplexing (SDM)-based communication systems, each spatial mode can act as an independent information-bearing carrier capable of scaling the total transmission capacity by several orders of magnitude. It has been reported that in SDM networks the signal amplitude depends upon the optical-path-length (OPL) difference between the various optical modes. In this work, we realize SDM technique using a multimode fiber (MMF), because MMFs have a potential to increase transmission capacity drastically by transmitting signals over large number of modes separately. The system performance is analyzed on the basis of following parameters: visualizer spatial profile, mode index profiles, fiber transfer function, refractive index profile, bit error rate, and quality factor. Also we measure changes in the optical path length due to a phase-shifting laser beam. We conclude that MMFs have huge scope for future ultrahigh-capacity transmission systems employing SDM.
Digital Back Propagation via Sub-Band Processing in Spatial Multiplexing Systems
Journal of Lightwave Technology, 2021
An advanced digital backward-propagation (DBP) method using a separate-channels approach (SCA) is investigated for the compensation of inter-channel nonlinearities in spatialand wavelength-multiplexed systems. Compared to the conventional DBP, intra-and inter-mode cross-phase modulation can be efficiently compensated by including the effect of the interchannel walk-off in the nonlinear step of the split-step Fourier method. We found that the SCA-DBP relaxes the step size requirements by a factor of 10, while improving performance by 0.8 dB for large walk-off and strong linear coupling. For the first time, it is shown that in spatial multiplexed systems transmission performance can be improved by sub-band processing of back propagated channels.
Scientific Reports, 2017
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.
In the paper results of analysis of nonlinear phenomena in optical fibres: Self-Phase Modulation, Cross-Phase Modulation, Four-Wave Mixing and Stimulated Raman Scattering and their influence on Dense-Wavelength Division Multiplexed system performance are reported. Different nonuniform optical channel allocation schemes based on ITU Recommendation G.692 100 GHz frequency grid are compared with uniform channel distribution. The level of nonlinear cross-talk is determined for different levels of the total optical power. As an example a 10 Gbit/s D-WDM dispersion-shifted single mode fibre link with dispersion-compensating fibres is envisaged. The directions for optimization of the system design in view of actual international standardization trends are pointed out.