Research (aim, approach, methodology)

FONTE’s latest research output is here: deliverablespublications,  conference talks
The NFDM simulation in phyton can be accessed here
A research update is published here

Optical fiber forms the backbone of the communication systems. The exponential increase in data traffic is putting an escalating pressure on fiber-optic networks. Optical fiber is an onlinear medium because its properties change with the signal intensity. It is well known that the fiber nonlinearity limits the achievable information rates of the conventional transmission methods in optical communication.

‘Fibre Optic Nonlinear Technologies [FONTE]’ is a  European  Industrial Doctorate, a 4 year collaborative project funded by the European Commission under the  Marie Skłodowska-Curie Action.

The consortium consists of four academic partners:

and the industry partner Nokia Bell Labs in Stuttgart, Germany.


The objective of the FONTE is to develop communication and coding methods suitable for the nonlinear optical fiber, in order to increase the data rates of the future communication systems. In particular, the project aims to apply nonlinear Fourier transforms to address the limitation that the fiber nonlinearity sets on transmission rates.

Introduction, objectives and overview of the FONTE research programme

Optical fibre systems, responsible for an overwhelming fraction of the world’s information traffic, are the backbone of the global telecommunication network. More than two billion kilometres of optical fibres have been deployed worldwide enabling Internet and digital economy. Optical fibres connect the majority of cell towers. Radio signals from billions of mobile phone users are converted to optical signals for further transmission in all-fibre metropolitan, regional, long-haul and submarine networks that connect cities, countries and continents. It is hard to overstate the impact that fibre-optic communication has made and continues to make on the economy, public and government services, society, and almost all aspects of our lives.

The exponential surge in global data traffic is driven by the proliferation of different bandwidth-hungry on-line services such as cloud computing, on-demand HD video streams, on-line business analytics and content sharing, sensor networks, machine-to-machine traffic arising from data-centre applications, the development of the Internet of Things, and various other broadband services. It is well recognized nowadays that the rapidly increasing data traffic is quickly pushing the current generation of optical fibre communication systems, many of which were originally developed for communication over linear (e.g. radio) channels, towards the limits of modern technology. One of the key challenges is nonlinear property of optical fibre channel.

It is widely accepted that the nonlinear transmission effects in optical fibre are now a major limiting factor in modern fibre-optic communication systems. Nonlinear propagation effects make optical fibre channels very different from traditional linear communications channels such as wireless channels or copper cables. There is a clear need for radically different methods for the coding, transmission, and processing of information that take the nonlinear properties of the optical fibre into account, and for the training of a new generation of engineers with expertise in both optical communications and nonlinear science. The multi-national FONTE project will provide timely doctoral training through industry-relevant research in a quickly growing area of high practical relevance. It will lead to the development of disruptive nonlinear techniques for fibre-optic communications beyond the limits of current technology by constructively exploiting the inherent nonlinearity of optical fibre using advanced digital signal processing (DSP).


Overview of the FONTE research programme and its objectives

The nonlinear Fourier transform (NFT) offers new opportunities for the development of fundamentally novel engineering techniques for the coding, modulation, transmission, and processing of information in optical fibre channels. The EID FONTE aims at training a team of 4 Early Stage Researchers (ESRs) capable of designing, optimising and implementing communication systems based on this promising new approach that exploits nonlinearity of real optical fibres.

The FONTE consortium unites five world leading groups working in this area, which all have already made important contributions to this booming field. Within this EID project, doctoral training will be provided to ESRs that develop and implement novel approaches to NFT-based optical fibre communication. The EID FONTE aims to bring this exciting new approach into commercial application with the help of its world leading industry partner, NOKIA BELL LABS. The ESRs will acquire unique state-of-the-art knowledge and skills. They will be taught to be commercially minded engineers with a responsibility for industrial knowledge transfer. The EID FONTE programme will demonstrate the feasibility and the great potential of NFT-based systems for high capacity fibre-optic communications and comprehensively train 4 ESRs in this highly promising area of engineering.

The specific Research and Training objectives of the EID FONTE are

Research Objectives Training Objectives
RO1: To design and improve NFT transmission techniques for practical high-speed fiber-optic links, and to help the industry partner to implement them in experiments.

RO2: To design pre- and post-processing algorithms and channel characterization for NFT methods using machine learning.

RO3: To analyze the impact of impairments on the NFT, and to exploit this knowledge in robust algorithms and modulation techniques.

RO4: To study network application of the NFT and the NFT-based nonlinear frequency-division multiplexing without nonlinear intra- and inter-channel interference.

RO5: To develop new system designs based on the NFT and experimentally evaluate their performance characteristics.

RO6: To ensure support of long-term, industry oriented research through direct and close collaboration inside and outside of the FONTE consortium, during and beyond the lifetime of the project.

TO1: The general training objectives of FONTE are: (a) to provide opportunity to 4 ESRs to acquire unique multi-disciplinary knowledge and skills in an area of high interest to industry; (b) to advance the strength of the EU in producing top quality experts capable of creating a new generation of high-speed optical communications and nonlinear DSP.

TO2: The ESR-focused training objectives are: (a) to attain, through multi-national and inter-sector (academia/industry) training, the profile of a globally thinking, diverse, and innovative researcher/engineer with excellent integration, communication and leadership skills; (b) to acquire advanced multi-disciplinary knowledge at frontiers of engineering and nonlinear science; (c) to obtain practical and hands-on skills in conducting experiments; (d) to improve employability chances for leading roles in industry.

Research methodology and approach

To achieve the research and training objectives, FONTE will combine methods from nonlinear science, optical communication technologies, signal processing, machine learning and information theory in an interdisciplinary manner.


WP1: Development of new NFT transmission methods (RO1, RO5, TO1, TO2).

WP1, led by Aston (Prof. S. K. Turitsyn), is focused on the design of novel NFT-based modulation and demodulation schemes and (with the help of the industry partner, NOKIA BELL LABS) the integration of these schemes into practical optical fibre communication systems.

Background and motivation. Although several communication methods based on the NFT have been already proposed in the literature, the practical use of the NFT in optical communication systems requires further research. As of today, no commercially viable product based on the NFT exists due to several engineering challenges. FONTE will pioneer the design of new modulation, demodulation and signal processing techniques that take into account the unique advantages of the NFT and real-world constraints. In addition, WP1 seeks to improve and optimize existing NFT approaches that are already established by the members of the consortium.

Preliminary work by beneficiaries. Beneficiaries at FONTE have pioneered data communication using nonlinear Fourier transform in several papers (1,2,3,4). Four distinct NFT-based concepts have been proposed by the project beneficiaries recently: i) nonlinear inverse synthesis; ii) NFT-based digital back-propagation; iii) Nonlinear Frequency Division Multiplexing (NFDM) method; iv) a hybrid method. Their feasibility has been demonstrated by beneficiaries in preliminary proof-of-principle experiments (4,5,6).

Approaches and methods. A comprehensive analysis of the impact of the noise on the nonlinear spectrum of the signal will be carried out for various NFT-based transmission schemes mentioned above. An important task in the WP1 is to optimize modulation formats at the transmitter, and to devise decision rules at the receiver, so as to minimize the estimation error. The new systems developed within this WP will incorporate the advanced robust algorithms developed within WP2 and optimizations from WP3, and will be analysed for the network applications developed within WP4.

Role of industry partner. Aston will provide the initial system designs for fibre-optic transmission experiments at NOKIA BELL LABS. Combining WDM with NFDM (considering both radiation and solitonic modes), AIPT and NOKIA BELL LABS will maximize the achievable transmission rates and reach. The industry partner will participate in system optimizations and will ensure that all practical constraints are taken into account.

1 M. I. Yousefi et al, Information transmission using the nonlinear Fourier transform, Parts I–III, IEEE Trans. Inf. Theory, 60(7) 4312 (2014)

2 J. E. Prilepsky et al, Nonlinear spectral management: Linearization of the lossless fibre channel, Optics Express, 21(20) 24 344 (2013)

3 S. A. Derevyanko, J. E. Prilepsky, and S. K. Turitsyn, Capacity estimates for optical transmission based on the nonlinear Fourier transform, Nature Comm. 7, 12710 (2016)

4 V. Aref et al , “Experimental Demonstration of Nonlinear Frequency Division Multiplexed Transmission,” ECOC 2015, Spain, 2015

5 D. Zhenhua et al., Nonlinear Frequency Division Multiplexed Transmissions Based on NFT, IEEE PTL, 27, 1621 (2015)

6 H. Bülow, Experimental Demonstration of Optical Signal Detection Using Nonlinear Fourier Transform, JLT 33(7) 1433 (2015)


WP2: Impact of practical impairments on the NFT (RO1, RO2, RO3, TO1, TO2).

WP2 led by TUD (Dr. S. Wahls), deals with the analysis of realistic impairments on the NFT and aims at using this knowledge to aid the development of robust numerical NFT algorithms, modulation formats, and equalization methods.

Background and motivation. Any real fibre-optic transceiver suffers from a multitude of impairments such as, for example, various forms of noise, non-ideal amplification, quantization effects, aliasing, or also cross-talk. The impact of such impairments on the NFT is currently not well-understood. The classical analyses of these effects apply only in the weakly non-linear regime. For the highly-nonlinear regime FONTE aims at, only very little is known. The goal of this work package is to analyse the impact of real-world impairments on the NFT and to exploit this knowledge for the development of robust numerical NFT algorithms, modulation formats and equalization techniques that are as insensitive as possible against such impairments.

Preliminary work by beneficiaries. The Beneficiary at TU Delft has proposed various fast and accurate numerical methods for forward and inverse NFTs (7,8,9,10), quantified the impact of the temporal truncation on the NFT9, and derived the first exact characterization of measurement noise on the NFT in the highly nonlinear regime11.

Approaches and methods. First, the most important impairments will be identified based on simulations and the measurements made by NOKIA BELL LABS in real-world experiments. Second, these impairments will be modelled either deterministically or stochastically, depending what turns out to be more appropriate. Finally, these models will be used to develop robust NFT algorithms, modulation techniques and equalizers and/or compensation methods.

Role of industry partner. NOKIA BELL LABS will help with the identification of the most important impairments and evaluate the methods developed in this WP experimentally.

7 S. Wahls and H. V. Poor, Fast Numerical Nonlinear Fourier Transforms, IEEE Trans. Inf. Theory 61(12) 6957 (2015)

8 S. Wahls and H. V. Poor, Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fibre, Proc. IEEE International Symposium on Information Theory (ISIT’15), pp. 1676–1680, Hong Kong, China, Jun. 2015.

9 S. Wahls and V. Vaibhav, Fast Inverse Nonlinear Fourier Transforms for Continuous Spectra of Zakharov-Shabat Type, Preprint, Nov. 2016.

10 V. Vaibhav and S. Wahls, Introducing the Fast Inverse NFT, Accepted for OFC’17, Los Angeles, CA, Mar. 2017


WP3: Machine learning techniques for fibre-optic channels (RO1, RO3, RO5, TO1, TO2).

WP3 led by DTU (Prof. D. Zibar), focuses on the development of the optical performance monitoring schemes and channel estimation algorithms for system that use NFT. Tools from machine learning and data-driven models will be considered for system optimization.

Background and motivation. Optical performance monitoring is vital to ensure robust and reliable operation of optical communication systems. It provides quality-of-transmission metrics, such as Q-factor, and helps approximate channel parameters. The Q-factor is related to the optical signal-to-noise-ratio (OSNR) and can be computed by looking at the eye-diagrams at the monitoring points along the transmission link. These issues are well-studied in systems that use traditional waveforms. However, if future optical networks are going to employ NFT transmission schemes with unconventional waveforms, it is necessary to develop algorithms for measuring quantities such as Q-factor or OSNR. Currently, there is no known method to estimate the Q-factor from the eye-diagrams in NFT signals. Furthermore, fibre parameters are needed to compute the forward and inverse NFT. This calls for accurate estimation algorithms in the presence of the signal-dependent non-Gaussian noise. Machine learning could help with this task.

Preliminary work by beneficiaries.

The beneficiary at DTU has recently introduced machine learning algorithms for amplitude and phase detection in coherent fibre-optic communication12. This work has been recently generalized from time domain to the NFT spectral domain13, demonstrating that machine learning can help symbol detection at the receiver.

Approaches and methods. We will explore parametric and non-parametric supervised learning methods, such as Deep Neural Networks (DNN) and Gaussian Process Regression (GPR), for the estimation of the optical fibre channel parameters. These parameters include dispersion coefficients, polarization mode dispersion, polarization-dependent loss and OSNR. In addition, we will explore DNN and GPR for data-driven learning of the complex relationships between the optical channel parameters and the Q-factor. We will perform model selection, find the most appropriate kernel for GPR and look into various optimization techniques to train DNN. WP3 will also address the complexity of machine learning algorithms and their potential real-time implementation.

Role of industry partner. The academic partner will examine the efficacy and practicality of the proposed optical performance monitoring methods in simulations. NOKIA BELL LABS will highlight the factors that are potentially neglected, providing data sets for training algorithms, and guide of the academic partner in its developing improved learning algorithms.


WP4: Network applications of the NFT technology. (RO4, RO5, TO1, TO2).

WP4, led by Telecom ParisTech (Prof. M. I. Yousefi), focuses on the development of the NFT based nonlinear frequency-division multiplexed (NFDM) systems for optical fibre networks.

Background and motivation. NFDM can be applied to single- and multi-user channels. Present simulations and experimental demonstrations are mostly limited to point-to-point transmission. However, the great advantage of NFDM occurs in networks, where there are multiple transmitters and receivers. WP4 is dedicated to network application of the NFT. This is the most relevant case for the industry partner NOKIA BELL LABS and commercial systems.

Preliminary work by beneficiaries. Beneficiary at TPT has shown the origin of capacity limitation in optical networks and developed NFDM as a communication approach to address these limitations1. In addition to earlier multi-user NFDM simulations1, TPT has recently carried out the first set of simulations where users’ signals are multiplexed in a nonlinear manner14,15. For the first time, it was shown that the NFDM achieves rates higher than the WDM rates. While this provides a proof-of-concept, there is still much work to be done.

Approaches and methods. In WP4, NFDM is applied to multi-user optical fibre channels, where joint signal processing and coding among users is not possible. In contrast to our recent work14,15, realistic signal and system parameters are considered. The continuous-time waveform model is discretized to a discrete-time statistical model, in order to make the NLS equation amenable to information-theoretic analysis. We will study the capacity of the resulting discrete-time channel in the nonlinear Fourier domain, specifying joint data rates that can be achieved by all users. The impact of the in-band and out-of-band noise on the signal of the user-of-interest will be described in the nonlinear Fourier domain. The operation of the transmitter and optimal receiver for each user will be studied. In order to simulate the per-user spectral efficiencies of the NFDM, numerical methods are generalized and tailored to multi-user transmission. WP4 takes our latest research in14, 15 to the next level.

Role of industry partner. NOKIA BELL LABS, with the help of TPT, will demonstrate the first experiment in which NFDM is applied in a network environment – thereby going beyond single-user experiments that NOKIA BELL LABS conducted earlier. Together, they will also report on DSP and equalization adapted to NFDM networks. NOKIA BELL LABS will examine the efficacy and practicality of the proposed multi-user algorithms, and determine suitable transmission regimes.


WP5: Experimental implementation and testing of NFT systems. (RO4, RO5, TO1, TO2).

WP5, led by the FONTE industrial partner NOKIA BELL LABS (Dr. H. Buelow), focuses on the experimental demonstration of the developed algorithms in WP1-WP4, new system designs and techniques, implementation and commercialisation of results.

Background and motivation. The academic partners at FONTE are world leading experts in the NFT. This extraordinary cluster of experts positions NOKIA BELL LABS very well to identify promising technologies in the very early stage, to develop IP licensing, and to decide on commercialization and product development.

Preliminary work by beneficiaries. NOKIA BELL LABS researchers have experimentally demonstrated examples of NFDM systems using 1) conventional modulation formats6, 2) modulation of discrete nonlinear spectrum4, 3) multiplexing of up to 7 users’ signal and 4) and combined modulation of discrete and continuous spectrum (both results presented at ECOC 2016).

Approaches and methods. The performance evaluation of the schemes proposed in WP1-WP4 via numerical simulation can be time-consuming in the highly nonlinear regime. Transmission experiments in the real-world systems offer an alternative approach to evaluate methods that are indicated by theory. All proposed schemes in WP1-WP4 will be carefully examined in WP5, by making use of the extensive fibre-optic communication test-beds available at the industry partner NOKIA BELL LABS. Taking into account practical constraints, such as limited converter resolution and inadequate performance of the existing channel estimation and signal processing algorithms, will have a direct influence on, and provide feedback to, the tasks carried out in WP1-WP4.