Communication System Based on Periodic Nonlinear Fourier Transform with Exact Inverse Transformation

Kamalian, Morteza; Vasylchenkova, Anastasiia; Prilepsky, Jaroslaw E.; Shepelsky, Dmitry; Turitsyn, Sergei K.

doi:10.1109/ecoc.2018.8535278

Cited by 10 publications

(15 citation statements)

References 13 publications

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“…However, this is left for future works, as at the moment we do not present any efficient receiver DSP design that could retrieve the phases. We also notice that a QAM constellation used in our current work may not be the best constellation or at least it can be improved by using probabilistic shaping, and the respective results will be reported in [60]. It is an interesting idea which we have been working on as a separate paper At the end we note that solving the RHP requires extra caution in the case where the jump contour consists of open arcs, because its solution has, in general, singularities at the arc ends.…”

Section: Discussionmentioning

confidence: 93%

“…For example, if increasing the genus entails a larger bandwidth which in turn enhances the fibre distortion, the system will need more accurate numerical calculations realised by more time samples. Another note is that, there are periodic solutions to the NLSE with analytically known closed form based on the algebrogeometric approach that can provide two real degrees of freedom while avoiding the Riemann theta function [42,51,52]. However, these signals are not generalisable to a more symbol per signal case while our RHP approach is.…”

Section: Constructing a Periodic Finite-gap Solution Via The Solmentioning

confidence: 99%

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Signal Modulation and Processing in Nonlinear Fibre Channels by Employing the Riemann–Hilbert Problem

Kamalian

Vasylchenkova

Shepelsky

et al. 2018

J. Lightwave Technol.

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Most of the nonlinear Fourier transform (NFT) based optical communication systems studied so far deal with the burst mode operation that substantially reduce achievable spectral efficiency. The burst mode requirement emerges due to the very nature of the commonly used version of the NFT processing method: it can process only rapidly decaying signals, requires zero-padding guard intervals for processing of dispersion-induced channel memory, and does not allow one to control the time-domain occupation well. Some of the limitations and drawbacks imposed by this approach can be rectified by the recently-introduced more mathematicallydemanding periodic NFT processing tools. However, the studies incorporating the signals with cyclic prefix extension into the NFT transmission framework have so far lacked the efficient digital signal processing (DSP) method of synthesising an optical signal, the shortcoming that diminishes the approach flexibility. In this work we introduce the Riemann-Hilbert problem (RHP) based DSP method as a flexible and expandable tool that would allow one to utilise the periodic NFT spectrum for transmission purposes without former restrictions. First, we outline the theoretical framework and clarify the implementation underlying the proposed new DSP method. Then we present the results of numerical modelling quantifying the performance of longhaul RHP-based transmission with the account of optical noise, demonstrating the good performance quality and potential of RHP-based optical communication systems.

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Section: Discussionmentioning

confidence: 93%

Section: Constructing a Periodic Finite-gap Solution Via The Solmentioning

confidence: 99%

Signal Modulation and Processing in Nonlinear Fibre Channels by Employing the Riemann–Hilbert Problem

Kamalian

Vasylchenkova

Shepelsky

et al. 2018

J. Lightwave Technol.

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“…Due to the trivial and uncoupled evolution of the nonlinear spectrum (NS) components as the signal propagates through the nonlinear fibre for the nonlinear Fourier modes attributed to decaying profiles, the NFT can be efficiently utilised in overcoming nonlinear signal distortions. However, there are many limitations in practical implementation of the "conventional" NFT, where the signal is assumed to vanish in time at some point [4,[7][8][9][10]. One of them is that for the computations involved in the NFT processing to be sufficiently accurate, the signal support should be long enough and account for the dispersion-induced memory.…”

Section: Introductionmentioning

confidence: 99%

“…Such an opportunity was, perhaps, first mentioned in [14] and studied theoretically for an exemplary setup in [19], and a simple system based on the periodic nonlinear modes modulation has been recently demonstrated experimentally [20]. Aside from a row of other advantages listed in the previous works [7,21], the periodic NFT (PNFT) not only provides an explicit control over the signal duration, but can also reduce noticeably the required processing window at the receiver, as we do not have to process the dispersioninduced memory [7,8,17,21,22]. The latter fact can make a substantial difference for long-haul transmission, insofar as using the PNFT we are to process only one period of the signal [7,22].…”

Section: Introductionmentioning

confidence: 99%

Full-Spectrum Periodic Nonlinear Fourier Transform Optical Communication Through Solving the Riemann-Hilbert Problem

Kamalian-Kopae

Vasylchenkova

Shepelsky

et al. 2020

J. Lightwave Technol.

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In this work, for the first time, a full-spectrum periodic nonlinear Fourier transform (NFT) based communication system with the inverse transformation at the transmitter performed by using the solution of Riemann-Hilbert problem (RHP), is proposed and studied. The entire control over the nonlinear spectrum rendered by our technique, where we operate with two qualitatively different components of this spectrum represented, correspondingly, in terms of the main spectrum and the phases, allows us to design a time-domain signal tailored to the characteristics of the transmission channel. In the heart of our system is the RHP-based signal processing utilised to generate the time-domain signal from the modulated nonlinear spectrum. This type of NFT processing leads to a computational complexity that scales linearly with the number of time-domain samples, and we can process signal samples in parallel. In this paper, we suggest the way of getting an exactly periodic signal through the correctly formulated RHP, and present evidence of the analogy between band-limited (in ordinary Fourier sense) signals and finite-band (in RHP sense) signals. Also, for the first time, we explain how to modulate the phases of individual periodic nonlinear modes. The performance of our transmission system is evaluated through numerical simulations in terms of bit error rate and Q 2-factor dependencies on the transmission distance and power, and the results demonstrate the good potential of the approach.

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“…Stable fast algorithms are available for the forward PNFT [14], [15] and a number of data transmission schemes based on modulating a small number of degrees of freedom have been proposed, such as transmission of perturbed plane-waves [15] or soliton-like pulses [16]. Moreover, transmission of specific nonlinear spectra whose computation is simplified through algebro-geometric reduction has been proposed [17]. The first experimental demonstration of PNFT-based data transmission was presented only recently [18].…”

Section: Introductionmentioning

confidence: 99%

Experimental Demonstration of Data Transmission Based on the Exact Inverse Periodic Nonlinear Fourier Transform

Goossens

Jaouën

Hafermann

2019

Optical Fiber Communication Conference (OFC) 2019

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The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission scheme inherently compatible with the nonlinear fiber is obtained. Despite potential advantages, the periodic NFT (PNFT) has been studied less compared to its counterpart based on vanishing boundary conditions, due to the mathematical complexity of the inverse transform. In this paper we extract the theory of the algebrogeometric integration method underlying the inverse PNFT from the literature, and tailor it to the communication problem. We provide a fully automatized algorithm to compute the inverse PNFT. As an application, we employ the algorithm to design a novel modulation scheme called nonlinear frequency amplitude modulation, where four different nonlinear frequencies are modulated independently. Finally we provide two further modulation schemes that may be considered in future research. The obtained algorithm is applied in Part II of this paper in the design of a PNFT-based communication experiment.

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Communication System Based on Periodic Nonlinear Fourier Transform with Exact Inverse Transformation

Cited by 10 publications

References 13 publications

Signal Modulation and Processing in Nonlinear Fibre Channels by Employing the Riemann–Hilbert Problem

Signal Modulation and Processing in Nonlinear Fibre Channels by Employing the Riemann–Hilbert Problem

Full-Spectrum Periodic Nonlinear Fourier Transform Optical Communication Through Solving the Riemann-Hilbert Problem

Experimental Demonstration of Data Transmission Based on the Exact Inverse Periodic Nonlinear Fourier Transform

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