Fast and Reliable Detection of Significant Solitons in Signals with Large Time-Bandwidth Products

Fast and Reliable Detection of Significant Solitons in Signals with Large Time-Bandwidth Products

de Koster, P.B.J. (TU Delft Team Sander Wahls)
Wahls, S. (TU Delft Team Michel Verhaegen; TU Delft Team Sander Wahls)

2023

We present a fast method to calculate the significantly large solitonic components of signals with large time-bandwidth products governed by the nonlinear Schrödinger equation, for which the computation typically becomes prohibitively expensive and/or numerically unstable. We partition the full signal in both frequency and time to obtain short signals with a constant number of samples, independent of the size of the full signal. The solitons within each short signal are computed using a conventional nonlinear Fourier transform (NFT) algorithm. The partitioning in general leads to spurious solitons not present in the full signal. We therefore design an acceptance scheme that removes spurious solitons. The remaining solitons are attributed to the full signal. Solitons that are too wide to fit into the short signals cannot be detected by this approach, but since wide solitons must be of low amplitude, the significant solitons will be found. This approach only requires O(N) floating point operations, with N the number of signal samples. It can furthermore be applied to signals with large time-bandwidth products for which conventional NFT algorithms become unreliable or even fail. When applying our proposed method to a signal of 15,000 samples, the significant solitonic components were computed 14 times faster than when considering the whole signal, for which the conventional algorithm furthermore provided wrong results. We found that time-partitioning yields accurate results, while frequency-partitioning causes a small loss in accuracy. Combined frequency-time partitioning leads to the fastest computation, but also suffers from the same loss in accuracy as with frequency-partitioning. As time-partitioning yields a significant speed-up at nearly no loss in accuracy, we regard this as the method of choice in most practical scenarios.

Eigenvalues and eigenfunctions
forward scattering transform
Fourier transforms
nonlinear Fourier transform
Nonlinear Schrödinger equation
Optical fiber communication
Optical fibers
Optical solitons
Solitons
solitons
Time-frequency analysis

http://resolver.tudelft.nl/uuid:56d20aa0-edda-4a35-bd42-eb524534f27b

https://doi.org/10.1109/JLT.2023.3285434

2023-12-13

0733-8724

Journal of Lightwave Technology, 41 (20), 6586-6598

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

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© 2023 P.B.J. de Koster, S. Wahls