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.

Analysis of Nonlinear Fiber Kerr Effects for Arbitrary Modulation Formats

Journal of Lightwave Technology

Coherent optical transmission systems can be modeled as a four-dimensional (4D) signal space resulting from the two polarization states, each with two quadratures. Recently, nonlinear analytical models have been proposed capable of capturing the impact of Kerr nonlinearity on 4D constellations. None of these addresses the inter-channel nonlinear interference (NLI) imposed by arbitrary modulation formats in multi-channel wavelength division multiplexed (WDM) systems. In this paper, we introduce a general nonlinear model for multi-channel WDM systems that is valid for arbitrary modulation formats, even asymmetric ones. The proposed model converges to the previous models, including the EGN model, in the special case of polarization multiplexed systems. The model focuses on the cross-phase modulation (XPM) nonlinear term that lies at the heart of the NLI in multi-channel WDM systems operating on standard high dispersion single-mode fiber. We show that strategic mappings of the modulation format's coordinates to the polarization states can reduce the NLI undergone by these formats.

Digital Back-Propagation Performance in Wideband Optical Fibre Transmission Systems

2017 European Conference on Optical Communication (ECOC), 2017

Single channel digital back-propagation (SC-DBP) performance with different transmission bandwidths is experimentally and theoretically investigated. The SC-DBP gain reduces with transmission bandwidth; from 1.2 b/sym for single channel to 0.2 b/sym for C-band transmission at 2000 km.

Reduced Complexity Digital Back-Propagation Methods for Optical Communication Systems

JOURNAL OF LIGHTWAVE TECHNOLOGY, 2014

Next-generation optical communication systems will continue to push the (bandwidth · distance) product towards its physical limit. To address this enormous demand, the usage of digital signal processing together with advanced modulation formats and coherent detection has been proposed to enable data-rates as high as 400 Gb/s per channel over distances in the order of 1000 km. These technological breakthroughs have been made possible by full compensation of linear fiber impairments using digital equalization algorithms. While linear equalization techniques have already matured over the last decade, the next logical focus is to explore solutions enabling the mitigation of the Kerr effect induced nonlinear channel impairments. One of the most promising methods to compensate for fiber nonlinearities is digital back-propagation (DBP), which has recently been acknowledged as a universal compensator for fiber propagation impairments, albeit with high computational requirements. In this paper, we discuss two proposals to reduce the hardware complexity required by DBP. The first confirms and extends published results for non-dispersion managed link, while the second introduces a novel method applicable to dispersion managed links, showing complexity reductions in the order of 50% and up to 85%, respectively. The proposed techniques are validated by comparing results obtained through post-processing of simulated and experimental data, employing single channel and WDM configurations, with advanced modulation formats, such as quadrature phase shift keying (QPSK) and 16-ary quadrature amplitude modulation (16-QAM). The considered net symbol rate for all cases is 25 GSymbol/s. Our post-processing results show that we can significantly reduce the hardware complexity without affecting the system performance. Finally, a detailed analysis of the obtained reduction is presented for the case of dispersion managed link in terms of number of required complex multiplications per transmitted bit.