Nonlinear inverse synthesis technique for optical links with lumped amplification

Abstract

The nonlinear inverse synthesis (NIS) method, in which information is encoded directly onto the continuous part of the nonlinear signal spectrum, has been proposed recently as a promising digital signal processing technique for combating fiber nonlinearity impairments. However, because the NIS method is based on the integrability property of the lossless nonlinear Schrödinger equation, the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we propose and assess a modified scheme of the NIS method, which can be used effectively in standard optical links with lumped amplifiers, such as, erbium-doped fiber amplifiers (EDFAs). The proposed scheme takes into account the average effect of the fiber loss to obtain an integrable model (lossless path-averaged model) to which the NIS technique is applicable. We found that the error between lossless path-averaged and lossy models increases linearly with transmission distance and input power (measured in dB). We numerically demonstrate the feasibility of the proposed NIS scheme in a burst mode with orthogonal frequency division multiplexing (OFDM) transmission scheme with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 3.5 dB; these results are comparable to those achievable with multi-step per span digital back-propagation.

Nonlinear Inverse Synthesis for Optical Links With Distributed Raman Amplification

“…The resulted transmission methods can be termed as NFDM, NIS and eigenvalue communication, respectively. Herein, we focus on the NIS scheme as it can be combined effectively with high modulation format and traditional coherent transmission technologies, offering highest flexibility in the system design [25,26]. In the second design, the NFTs are used to cancel the nonlinearity distortion in fiber optical communication systems.…”

“…This high level of non-flatness may deprive all the nonlinearity cancellation benefit of NIS and of other NFTbased transmission schemes. As a result, the LPA model for Raman-based optical links should be developed in a similar manner to EDFA-based optical links [26] in order to apply NIS and, potentially, other NFT-based transmission schemes. The general model of the NLSE for optical links with Raman amplifiers can be written as …”

“…Of course, as shown in [26] the LPA NLSE is an approximated model so its accuracy depends strongly on the signal and system parameters such as bandwidth, pulse shape, power and transmission distance. A detailed investigation on the accuracy of LPA NLSE model for optical links with lumped amplifications can be found in [26]. Based on the obtained LPA NLSE model, we can design the appropriate modified NIS scheme accounting for the non-ideal Raman gain profile as shown in Fig.…”

“…However, the usage of mapping given by Eq. (14), utilized in the series of previous works on the NIS method [17,[25][26], ensures the exact convergence of the nonlinear quantities to the respective linear analogs in the low power limit, which simplifies the system design and checks.…”

“…However, the NFDM method requires considerable optimization of the pulse shapes for the purpose of maximizing the resulting spectral efficiency (SE) [24]. The second approach based on the modulation of the continuous part of the nonlinear spectrum, has been proposed in [17] and assessed in detail in [25,26] (for ideal Raman amplification and EDFA-based optical links) -and was termed there as the nonlinear inverse synthesis (NIS) method. Finally we note that there already exists a very recent study where both the continuous and discrete parts of the nonlinear spectrum have been used simultaneously [27].…”