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In the presence of additive Gaussian noise, the statistics of the nonlinear Fourier transform (NFT) of a pulse are not yet completely known in closed form. In this paper, we propose a novel approach to study this problem. Our contributions…
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…
In this report, we study communication over an additive white Gaussian noise channel with a fixed signal constellation. We measure how much information we can send through this channel and how to improve the rate of communication by…
This paper investigates the robustness of affine frequency division multiplexing (AFDM) and orthogonal time frequency space (OTFS) modulation schemes against non-white Gaussian noise, which can model various sources of additive disturbances…
We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
In this paper, we investigate an algorithm to attain additive white Gaussian noise (AWGN) performance in spectrally non-white channels, using multicarrier communications, i.e., orthogonal frequency division multiplexing (OFDM) and…
Different aspects of probabilistic shaping for a multi-span optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input…
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…
A continuous-time model for the additive white Gaussian noise (AWGN) channel in the presence of white (memoryless) phase noise is proposed and discussed. It is shown that for linear modulation the output of the baud-sampled filter matched…
The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive…
By exploiting a causality property of the nonlinear Fourier transform, a novel decision-feedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is…
The paper provides a characterization of the complex monopulse ratio in terms of autocorrelation and power spectral density of its fluctuations during satellite tracking, taking into account the presence of additive noise on sum and…
We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a…
Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct…
Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is…
We investigate the transmission of densely multiplexed solitons using a photonic integrated chip and the nonlinear Fourier-transform and analyze required launch conditions, the effect of (de-)multiplexing and noise on the nonlinear…
The statistical properties of nonlinear phase noise, often called the Gordon-Mollenauer effect, is studied analytically when the number of fiber spans is very large. The joint characteristic functions of the nonlinear phase noise with…