Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImproved Simulation Accuracy of the Split-Step Fourier Method
110
0
0.0
(
0
)
Added by
Shen Li
Publication date
2020
fields
Electronic Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We investigate a modified split-step Fourier method (SSFM) by including low-pass filters in the linear steps. This method can simultaneously achieve a higher simulation accuracy and a slightly reduced complexity.
rate research
Read More
Optimizing modulation and detection strategies for a given channel is critical to maximize the throughput of a communication system. Such an optimization can be easily carried out analytically for channels that admit closed-form analytical models. However, this task becomes extremely challenging for nonlinear dispersive channels such as the optical fiber. End-to-end optimization through autoencoders (AEs) can be applied to define symbol-to-waveform (modulation) and waveform-to-symbol (detection) mappings, but so far it has been mainly shown for systems relying on approximate channel models. Here, for the first time, we propose an AE scheme applied to the full optical channel described by the nonlinear Schr{o}dinger equation (NLSE). Transmitter and receiver are jointly optimized through the split-step Fourier method (SSFM) which accurately models an optical fiber. In this first numerical analysis, the detection is performed by a neural network (NN), whereas the symbol-to-waveform mapping is aided by the nonlinear Fourier transform (NFT) theory in order to simplify and guide the optimization on the modulation side. This proof-of-concept AE scheme is thus benchmarked against a standard NFT-based system and a threefold increase in achievable distance (from 2000 to 6640 km) is demonstrated.
The iterated Crank-Nicolson (ICN) method is a successful numerical algorithm in numerical relativity for solving partial differential equations. The $theta$-ICN method is the extension of the original ICN method where $theta$ is the weight when averaging the predicted and corrected values. It has better stability when $theta$ is chosen to be larger than 0.5, but the accuracy is reduced since the $theta$-ICN method is second order accurate only when $theta$ = 0.5. In this paper, we propose two modified $theta$-ICN algorithms that have second order of convergence rate when $theta$ is not 0.5, based on two different ways to choose the weight $theta$. The first approach employs two geometrically averaged $theta$s in two iterations within one time step, and the second one uses arithmetically averaged $theta$s for two consecutive time steps while $theta$ remains the same in each time step. The stability and second order accuracy of our methods are verified using stability and truncation error analysis and are demonstrated by numerical examples on linear and semi-linear hyperbolic partial differential equations and Burgers equation.
We provide a systematic comparison of two numerical methods to solve the widely used nonlinear Schrodinger equation. The first one is the standard second order split-step (SS2) method based on operator splitting approach. The second one is the Hamiltonian integration method (HIM). It allows the exact conservation of the Hamiltonian at the cost of requiring the implicit time stepping. We found that numerical error for HIM method is systematically smaller than the SS2 solution for the same time step. At the same time, one can take orders of magnitude larger time steps in HIM compared with SS2 still ensuring numerical stability. In contrast, SS2 time step is limited by the numerical stability threshold.
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a non-convex optimization problem. Such schemes are ill-suited to find the optimum solution for sparse data, since the recorded image does not correspond exactly to the original wave function. We construct a convex optimization problem using a relaxed support constraint and a maximum-likelihood treatment of the recorded data as a sample from the underlying wave function. We also stress the need to use relevant windowing techniques to account for the sampled pattern being finite. On simulated data, we demonstrate the benefits of our approach in terms of visual quality and an improvement in the crystallographic R-factor from .4 to .1 for highly noisy data.
In this paper, we discuss the nonlinear stability and convergence of a fully discrete Fourier pseudospectral method coupled with a specially designed second order time-stepping for the numerical solution of the good Boussinesq equation. Our analysis improves the existing results presented in earlier literature in two ways. First, an $l_infty(0, T^*; H2)$ convergence for the solution and $l_infty(0, T^*; l_2)$ convergence for the time-derivative of the solution are obtained in this paper, instead of the $l_infty(0, T^*; l_2)$ convergence for the solution and the $l_infty(0, T^*; H^{-2})$ convergence for the time-derivative, given in [17]. In addition, the stability and convergence of this method is shown to be unconditional for the time step in terms of the spatial grid size, compared with a severe restriction time step restriction $Delta t leq Ch^2$ reported in [17].
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
