# Post doc NFDM

# Nonlinear Frequency-Division Multiplexing in Realistic Systems

**Axis :**ComEx

**Coordinators :**Mansoor Yousefi, LTCI - Yann Frignac,SAMOVAR

**Candidate :**En attente de candidat (03/09/2018)

**Institutions:**LTCI & SAMOVAR

**Administrator laboatory :**LTCI

**Working group reference :**GT O'COMEX

**Engagements:**1 an - Au plus tard le 01/01/2019

**Context :**

As a result of the diffulties that fiber nonlinearity brings about, half a century since the introduction of the optical fiber, the problem of determining its capacity remains open. Most current approaches assume a linearly-dominated regime of operation 7, consider the nonlinearity as a small perturbation 8, or are geared towards managing and suppressing the (detrimental) effects of the nonlinear and dispersive terms 3. The capacity of the discrete-time model of the NLS channel is upper bounded by logp1+SNRq, where SNR is signal-to-noise ratio 9. The asymptotic capacity of the discrete-time model of the dispersive optical fiber was shown to be 1 2n log logpPq op1q, wheren is the fixed size of the input vector in the discrete model 11. The fact that the capacity does not decrease with the input power is proved in 12. There are a myriad of papers presenting lower bounds on capacity based on numerical simulations that hold good in the low power regime; see e.g., 3 and references therein. Data transmission using the NFT has been studied in several recent closely-related works 2, 5, 6, 13{28. Fast nonlinear Fourier transforms were introduced by Wahls et al. in 18{20. In 13{15, Prilepsky, Le, Turitsyn and co-authors, proposed nonlinear inverse synthesis based on NFT. They demonstrated spectrum modulation and reported low bit error rates 21. Noise in the nonlinear Fourier domain is studied in 25, 29{31. Distribution of the spectral parameters for the special case that channel is noise-free and input is a white Gaussian stochastic process is calculated 5 in 29. A lower bound on spectral efficiency of multi-solitons is obtained in 30. Noise models in the spectral domain, including models for spectral amplitudes, are studied in 25, 31. Transmission based on the nonlinear Fourier transform was recently demonstrated in experiments 22{24,26, 28, 32. Bulow 22{24, and subsequently Aref and others 28, showed that one can recover information via eigenvalues and other parts of the nonlinear spectrum. Dong et al. successfully demonstrated errorfree transmission of three-eigenvalue NFDM signals over 1800 km 26. An important consequence of these works is that, the end-to-end channel appears nearly integrable in practice as indicated by the stability of eigenvalues.

**Objective :**

The main objective of this proposal is to develop NFDM for practical optical fiber transmission systems.

Towards this main objective, the specific sub-objectives of the project are the following:

O1. To quantify the impact of signal-noise interactions on AIRs of NFDM at high powers;

O2. To perform experimental demonstrations and examine the practicality of the NFDM in realistic systems. Upon successful completion of the project, the following results are anticipated.

R1. Impact of the signal-noise interactions on the nonlinear Fourier spectrum is determined. This includes analytic description of the second-order noise statistics in the nonlinear Fourier domain, namely, noise variance and correlations, as a function of the input signal power;

R2. Using the experimental platform at Telecom ParisTech, transmission based on NFT is demonstrated

in the lab. The project aims to reach spectral effciencies of 3 bits/s/Hz and baud rates higher than

32 Gbs.