REMOTE CHARACTERIZATION OF OPTICAL COMPONENTS IN MULTI-SPAN OPTICAL FIBER LINKS

Abstract

The present disclosure relates to a remote characterization of optical components in multi-span fiber links, the characterization based on a parametric model of optical components, such as a machine learning model. The present disclosure also relates to the use of the presently disclosed model for optimization of a link, based on an arbitrary optimization strategy related to the spectral power profile and the quality of service of the link.

Claims

1. A method for obtaining a parametric model of a first optical component of a set of optical components of a probed link in a WDM optical network comprising a plurality of link sections, the probed link comprising one or more of said link sections, each link section comprising a length of optical fiber and at least one of said set of optical components the probed link probed by a predefined WDM input signal and a measured WDM output signal, the method comprising: providing a link transfer model based on the predefined WDM input signal and the measured WDM output signal; isolating the first optical component from the link transfer model by using an analytical model for the optical fiber and removing the impact of the optical fiber from the link transfer model to obtain an optical component model; and determining a set of parameters of the optical component model, based on the predefined WDM input signal, by iteratively comparing a calculated WDM output signal and the measured WDM output signal.

2. The method according to claim 1, wherein the probed link includes a second optical component of the set of optical components, the second optical component different from the first optical component, and wherein the first optical component is isolated from the link transfer model by also removing the impact of said second optical component.

3. The method according to claim 1, wherein the first optical component is an Erbium-Doped Fiber Amplifier (EDFA).

4. The method according to claim 1, wherein the first optical component is selected from the group consisting of an optical amplifier, a switch, a filter, and combinations thereof.

5. The method according to claim 1, wherein the set of parameters of the optical component model is determined by training the optical component model using machine learning based on the predefined WDM input signal and the measured WDM output signal.

6. The method according to claim 1, wherein the set of parameters of the optical component model is determined by using one or both of statistical modelling and linear regression.

7. The method according to claim 1, wherein the determination of the set of parameters of the optical component model is based on an input power profile of the WDM input signal, an operating point of the first optical component, and an output spectral power profile of the probed link.

8. The method according to claim 1, wherein the WDM input signal, used for determining the set of parameters of the optical component model, is a shaped spectrum load signal with a random profile.

9. The method according to claim 8, wherein the WDM input signal is shaped with an amplified spontaneous emission spectrum with a random profile or sets of discrete optical carriers.

10. The method according to claim 1, wherein the measured WDM output signal, used for determining the set of parameters of the optical component model, includes a wavelength dependent output power profile and amplified spontaneous emission noise.

11. The method according to claim 1, wherein determining the set of parameters of the optical component model is performed by a computer system.

12. The method according to claim 1, further comprising providing a differentiable interpolation model for wavelength dependent implementation penalties of a transmitter-receiver (TRX).

13. The method according to claim 1, wherein the optical component model includes a gain profile of the first optical component.

14. The method according to claim 1, wherein the optical component model includes a gain profile of the first optical component and a calculated profile of amplified spontaneous emission (ASE).

15. A method for optimizing a quality of service of a remote link in a WDM optical network, the remote link comprising a plurality of link sections, each link section comprising a length of optical fiber and at least one optical component, the method comprising: modelling the remote WDM optical network link based on a link configuration to obtain a digital twin model of the WDM optical network link, wherein the digital twin model includes an analytical model for the optical fiber and a parametric model for at least one of the optical components; calculating a predicted output optical signal to noise ratio of each one of a set of input WDM signals based on the digital twin model; and optimizing the quality of service of the remote WDM optical network link by determining an optimal input WDM signal of the set of input WDM signals that optimizes the corresponding predicted output optical signal to noise ratio, wherein one or more parameters of the parametric model for the at least one optical component are determined based on measurements on a probed link of the WDM optical network, and wherein the probed link is different from the remote link.

16. The method according to claim 15, wherein the probed link comprises optical components of one or both of a same type and a same manufacturer as the optical components in the remote link.

17. The method according to claim 15, wherein the parametric model is a machine learning model trained on a probed input WDM signal and measured output WDM signals of the probed link.

18. The method according to claim 15, wherein optimizing the corresponding predicted output optical signal to noise ratio includes a method selected from the group consisting of maximizing the signal to noise ratio in a worst case scenario, equalizing the signal to noise ratio for all users, obtaining a custom distribution of the output signal to noise ratio per user, for example depending on subscriptions of each user, and combinations thereof.

19. The method according to claim 15, wherein optimizing the quality of service is provided in real-time.

20. The method according to claim 15, wherein the parametric model for the at least one optical component is obtained according to the method of claim 1.

Description

DESCRIPTION OF THE DRAWINGS

[0025] The present disclosure will in the following be described in further detail with reference to the accompanying drawings:

[0026] FIG. 1 shows a flow diagram of one embodiment of the presently disclosed method for modelling at least one optical component;

[0027] FIG. 2 shows a flow diagram of one embodiment of the presently disclosed method for optimization;

[0028] FIG. 3 shows a schematic diagram of an embodiment of a training process for the machine learning model used in one embodiment of the presently disclosed method for modelling at least one optical component;

[0029] FIG. 4 shows an embodiment of a transceiver setup for a communication link comprising a transmitter Tx, a Receiver Rx and a fiber network;

[0030] FIG. 5 shows calculated and measured SNR margin to the SNR decoding threshold and measured and predicted OSNR for two exemplary links, with flat input power distribution; and.

[0031] FIG. 6 shows optimized SNR margin profiles for two exemplary links using embodiments of the presently disclosed optimization method.

DETAILED DESCRIPTION

Definitions

[0032] As used in this description and the accompanying claims, the following terms shall have the meanings indicated, unless the context otherwise requires:

[0033] A set includes at least one member.

Method for Modelling an Optical Component

[0034] In one embodiment of the present disclosure the optical component is an Erbium-Doped Fiber Amplifier (EDFA).

[0035] EDFA are optical components that suffer from non-linearity and are difficult to be characterized by analytical models based, for example, on laboratory data. EDFAs suffer, for example, from aging and their behavior may be very difficult to predict once the EDFAs are installed or deployed in a link. Modelling EDFAs remotely while they are installed or deployed in a link is advantageous for being able to obtain a model that reflects aging effects or any other effect due to deployment, which cannot be modeled in the laboratory. The presently disclosed method, applied to a link comprising a fiber channel and an EDFA, permits remote characterization and/or modelling of the EDFA, based on knowledge of input signals at a remote input end of the fiber and based on measurements at the remote output end of the link and based on training or optimization of a parametric model of the optical component, in combined with an analytical model of the fiber channel. The combined model of the fiber channel and the EDFA is a twin model or hybrid model, as it comprises an analytical model for the fiber channel and a parametric or machine learning model for the EDFA. This is shown in FIG. 3 where the parametric model for the optical component 402 is combined with the analytical model 401 for the fiber channel. The analytical model 401 may, for example, be a Gaussian Noise model including attenuation and stimulated Raman scattering (SRS) effects. A detailed description of an exemplary analytical model can be found in M. P. Yankov, P. M. Kaminski, H. E. Hansen, and F. Da Ros, SNR optimization of multi-span fiber optic communication systems employing EDFAs with non-flat gain and noise figure, J. Light. Technol. 39, 6824-6832 (2021), which is incorporated herein by reference in its entirety.

[0036] In one embodiment of the present disclosure, the optical component is a switch or a filter. Other optical components that suffer from deployment dependent effects are switches or filters.

[0037] In the present disclosure, the model of the optical component may be parametric, i.e. it may contain parameters. Parameters of the model are obtained by iterative comparison between experimental results and model predictions. In one embodiment of the present disclosure the model of the optical component may be a machine learning model with parameters, such as weights and biases of a neural network. Parameters of the machine learning model may be obtained by training based on measurements and comparison with predictions of the machine learning model. In particular, the training data set of the machine learning model may comprise transmitted input signal values of a fiber link and measured output signal values of the fiber link.

[0038] In one embodiment of the present disclosure, the parameters of the optical component model are determined by training the optical component model by means of machine learning based on the predefined WDM input signal and the measured WDM output signal. Measurement data of the output signals are recorded for a given time, together with input signals and this data is used for training of the machine learning model.

[0039] FIG. 1 discloses one embodiment 100 of the present disclosed approach of obtaining a parametric model of a first optical component of a set of optical components of a probed link in a WDM optical network comprising a plurality of link sections, the probed link comprising one or more of said link sections, each link section comprising a length of optical fiber and at least one of said set of optical components the probed link probed by a predefined WDM input signal and a measured WDM output signal. In 101 a link transfer model is initially provided based on the predefined WDM input signal and the measured WDM output signal. Then in 102 the first optical component is isolated from the link transfer model by using an analytical model for the optical fiber and removing the impact of the optical fiber from the link transfer model to obtain an optical component model. And finally in 103 parameters of the optical component model are determined, based on the predefined WDM input signal, by means of iterative comparison between calculated WDM output signal and the measured WDM output signal.

[0040] FIG. 2 discloses another embodiment 200 of the present disclosed approach of optimizing a quality of service of a remote link in a WDM optical network, the remote link comprising a plurality of link sections, each link section comprising a length of optical fiber and at least one optical component. Initially in 201 the WDM optical network link is modelled based on the link configuration to obtain a digital twin model of the WDM optical network link, wherein the digital twin model comprises an analytical model for the optical fibers and a parametric model for at least one of the optical components. In 202 an output optical signal to noise ratio of an input WDM signal based on the digital twin model is calculated and/or predicted. And then in 203 the quality of service of the WDM optical network link is optimized by determining an input WDM signal that optimizes the corresponding output optical signal to noise ratio.

[0041] FIG. 3 shows an embodiment of the training process 300 of one embodiment of the presently disclosed method. In this embodiment the link is modelled by an analytical model 401 modelling the fiber channel and by a machine learning model 402 modelling the optical component, such as an EDFA. The prediction of the combined hybrid or twin model 401 and 402 is compared with experimental data from a deployed link with deployed fiber channels 301 and deployed optical component 302 and the optical component model 402 is trained. The analytical part of the hybrid model ensures that the EDFA weights are only responsible for modelling EDFA effects. In a way, the NNs (neural networks) in the EDFA ML (machine learning) model are naturally regularized against overfitting to link-specific effects.

[0042] In one embodiment of the present disclosure, training of the optical component model may be done as follows: the EDFA model weights are initialized, and a cascade digital twin model of the fiber-EDFA-fiber link is created. Probe signals are sent on the link, and the system response is measured. The input probe signals consist of a shaped amplified spontaneous emission (ASE) spectrum with a random power profile. The spectrum is shaped so as to emulate a C-band, 48-channel, 12.5 GBd WDM signal on a 100 GHz grid. The response measurements consist of wavelength dependent power profile and ASE noise added at each channel of interest, measured using an optical spectrum analyzer (OSA). The mean squared error (MSE) between the model prediction and the measurements is estimated and used as cost for gradient descent-based EDFA weight updates. The analytical part of the EDFA hybrid model ensures that the EDFA weights are only responsible for modelling EDFA effects. In a way, the NNs in the EDFA ML model are naturally regularized against overfitting to link specific effects.

[0043] In one embodiment of the present disclosure, the parameters of the optical component model are determined by means of statistical modelling, linear regression, or other similar mathematical tools applied to predicted and experimental data, as known to the skilled person.

[0044] Input to the determination of the parameters of the optical component model, and/or for training of the optical component model, may be input spectral power profile to the probe link of input WDM signals, an operating point of the optical component, such as total input and total output power of the optical component, and an output spectral power profile of the probe link. Output for the determination of the parameters of the optical component model, and/or for training of the optical component model, may be the parameters of the optical component model.

[0045] Input to the determination of the power spectral profile output of the optical component may be the input power spectral profile of the optical component, which may be obtained from analytical models of the preceding optical fiber and/or hybrid analytical/machine learning models of preceding sections of the optical test link, and an operating point of the optical component, such as total input and total output power.

[0046] Output for the determination of the power spectral profile output of the optical component may be total power dependent gain profile and noise figure profile of the optical component.

[0047] In one embodiment of the present disclosure, the WDM input signals, used for determining the parameters of the optical component model and/or for training of the optical component model, may be shaped spectrum load signals with a random profile, such as shaped with amplified spontaneous emission spectrum with a random profile or sets of discrete optical carriers.

[0048] The measured WDM output signal, used for determining the parameters of the optical component model and/or for training of the optical component model, may be wavelength dependent output power profile and amplified spontaneous emission noise profile.

[0049] In the present disclosure, determining the parameters of the optical component model may be conducted on a computer system, for example on an embedded system or in a cloud system.

[0050] One embodiment of the present disclosure may further comprise providing a differentiable interpolation model for wavelength dependent implementation penalties of a transmitter-receiver (TRX).

[0051] In the present disclosure, the optical component model may comprise a gain profile of the optical component.

[0052] In the present disclosure the optical component model may comprise a calculated profile of amplified spontaneous emission (ASE).

[0053] Once the optical component model has been trained, using data from a link including, for example, only one optical component, the model so obtained may be used for modelling a fiber network with several optical components. If the optical components are of same make and manufacturer, the modelling of the fiber network with several optical components may be accurate.

[0054] FIG. 5 shows a comparison 500 between experimental data in solid lines and modelling data in dashed lines, of two networks, of different lengths (439.4 km and 592.4 km respectively), comprising several EDFAs (4 and 6, respectively). The figure shows how the prediction is very close to measured data for both networks. Measured and predicted OSNR 501 are very close and measured and predicted SNR margin to SNR decoding threshold 502 are also very close.

[0055] Method for optimizing quality of service Once a model for the optical component, such as an EDFAs, has been obtained using the first presently disclosed characterization and/or modelling method, a remote link comprising one or more than one optical components may be modelled and optimized. In particular, a model of a remote link may comprise models of the optical components and models of the fiber channels and may predict output WDM signals from input WDM signals.

[0056] In one embodiment of the present disclosure, The EDFA ML (machine learning) model obtained using the presently disclosed characterization and modelling method is used in cascade with analytical fiber models and a TRX penalty model for performance prediction and gradient descent optimization of the input power profile to a chosen link of the network. The chosen cost function is Cost=min_(SNR()), targeting a flat SNR

[0057] In one embodiment of the present disclosure, the optical components of the remote link may be of same type and/or same manufacturer as the optical component of the probed link. If that is the case, the same model, obtained using the probed link, may be used for all optical components of the remote link. If EDFAs of different type or different manufacturer are used in the remote link, a probed link with one optical component for each of the different types or each of the different manufactures may be used to obtain tailored models for each of the optical components of the remote link.

[0058] The optical component model may be a parametric model.

[0059] The optical component model may be a machine learning model trained on probed input WDM signal and measured output WDM signals of the probed link.

[0060] In one embodiment of the presently disclosed method, optimizing the corresponding output optical signal to noise ratio is provided by maximizing the signal to noise ratio in a worst case scenario, or equalizing the signal to noise ratio for all users, or obtaining a custom distribution of the output signal to noise ratio per user, for example depending on subscriptions of each user.

[0061] In the presently disclosed method, optimization may be done based on different criteria. Optimization is achieved by obtaining, for example, an optimum distribution of input power for all users and/or all wavelengths. In one embodiment, optimization may target a flat output SNR for all users. In the presently disclosed optimization method, equalizing the SNR for all users to a maximum SNR for all users for a given input power may be obtained by adjustment of the input spectral power per user, that is the input power profile, without requiring feedback on the quality of transmission and without requiring gain flattening filters for the EDFA. That is possible thanks to a link model comprising analytical models for the fiber channels and parametric and/or trained models for the EDFAs. The link model may also comprise differentiable interpolation model for wavelength dependent implementation penalties of the transmitter-receiver (TRX) chain. One embodiment of the TRX chain 400 is shown in FIG. 4. A result of one embodiment of the optimization 600 is shown, for example, in FIG. 6, where an almost flat distribution of the SNR is obtained for all wavelengths, for two different fiber links of length respectively 439.4 km 601 and 592.4 km 602. The flat SNR may be the highest possible achievable flat SNR over all wavelengths, given a total input power. FIG. 6 shows optimization in three different levels of complexity of the digital twin hybrid models: 1) model including all impairments with triangles; 2) model excluding stimulated Raman scattering and Kerr fiber nonlinearities (NL) with rhombus; 3) excluding NL and penalties of the transmitter TRX with circles.

[0062] In one embodiment of the present disclosure, distribution of input power may be optimized in order to achieve a higher output SNR for the wavelengths or the user that pay a higher subscription.

[0063] In one embodiment of the present disclosure, a worst case scenario is defined by at least a majority of users being active at the same time or by at least a majority of users requesting a high data rate at the same time, or by the remote link being overloaded or fully loaded or almost fully loaded.

[0064] In one embodiment of the present disclosure, the probed link is a laboratory WDM link or a pre-existing and and/or pre-deployed WDM link.

[0065] In one embodiment of the present disclosure, optimizing an obtained output signal to noise ratio for different wavelengths or for different users, is done by optimizing the input power profile of the link over the wavelengths, for a given total input power of the link.

[0066] In one embodiment of the present disclosure, the probed link may be a portion of the remote link. In particular, the probed link may be a portion of the remote link, comprising one optical component.

[0067] In one embodiment of the present disclosure, optimizing the quality of service is provided in real-time. As the remote link may be fully modelled by using trained optical component models and fiber channel analytical models, optimization of the input power profile over all the wavelengths may be obtained in real time, for example by using a cost function for the optimization.

[0068] The presently disclosed optimization method, may be based on a link model comprising parametric model(s) for the optical components obtained according to the presently disclose characterization and/or modelling method.

[0069] In one embodiment of the present disclosure, full modelling of field-deployed links without requiring access to all nodes nor feedback from the network on the current performance is achieved. modelling and optimization of operational systems, only requiring characterization of an isolated link is also achieved.

Further Details

[0070] 1. A method for obtaining a parametric model of a first optical component of a probed link in a WDM optical network comprising a plurality of link sections, the probed link comprising one or more of said link sections, each link section comprising a length of optical fiber and at least one of said first optical components, such as an optical amplifier, the probed link probed by a predefined WDM input signal and a measured WDM output signal, the method comprising the steps of: [0071] providing a link transfer model based on the predefined WDM input signal and the measured WDM output signal; [0072] isolating the first optical components from the link transfer model by using analytical models for the optical fiber and removing the impact of the optical fiber from the link transfer model to obtain an optical component model; and [0073] determining parameters of the optical component model, based on the predefined WDM input signal, by means of iterative comparison between calculated WDM output signal and the measured WDM output signal. [0074] 2. The method according to item 1, wherein the probed link comprises at least one second optical component different from the first optical component and wherein the first optical components is isolated from the link transfer model by also removing the impact of said at least one second optical component. [0075] 3. The method according to any one of the preceding items, wherein the optical component is an Erbium-Doped Fiber Amplifier (EDFA). [0076] 4. The method according to any one of the preceding items, wherein the optical component is a switch or a filter. [0077] 5. The method according to any one of the preceding items, wherein the parameters of the optical component model are determined by training the optical component model by means of machine learning based on the predefined WDM input signal and the measured WDM output signal. [0078] 6. The method according to any one of the preceding items, wherein the parameters of the optical component model are determined by means of statistical modelling and/or linear regression. [0079] 7. The method according to any one of the preceding items, wherein determination of the parameters of the optical component model is based on input power profile of input WDM signals, an operating point of the optical component, such as total input and total output power of the optical component, and an output spectral power profile of the probed link. [0080] 8. The method according to any one of the preceding items, wherein the WDM input signals, used for determining the parameters of the optical component model, are shaped spectrum load signals with a random profile, such as shaped with amplified spontaneous emission spectrum with a random profile or sets of discrete optical carriers. [0081] 9. The method according to any one of the preceding items, wherein the measured WDM output signal, used for determining the parameters of the optical component model, are wavelength dependent output power profile and amplified spontaneous emission noise. [0082] 10. The method according to any one of the preceding items, wherein the step of determining the parameters of the optical component model is conducted on a computer system, for example on an embedded system or in a cloud system. [0083] 11. The method according to any one of the preceding items, further comprising providing a differentiable interpolation model for wavelength dependent implementation penalties of a transmitter-receiver (TRX). [0084] 12. The method according to any one of the preceding items, wherein the optical component model comprises a gain profile of the optical component. [0085] 13. The method according to any one of the preceding items, wherein the optical component model comprises a calculated profile of amplified spontaneous emission (ASE). [0086] 14. A method for optimizing the quality of service of a remote link in a WDM optical network, the remote link comprising a plurality of link sections, each link section defined by a length of optical fiber and at least one optical component, such as an optical amplifier, the method comprising the steps of: [0087] modelling the WDM optical network link based on the link configuration to obtain a digital twin model of the WDM optical network link, wherein the digital twin model comprises an analytical model for the optical fibers and a parametric model for at least one of the optical components; [0088] calculating or predicting an output optical signal to noise ratio of an input WDM signal based on the digital twin model; and [0089] optimizing the quality of service of the WDM optical network link by determining an input WDM signal that optimizes the corresponding output optical signal to noise ratio, [0090] wherein parameters of the parametric model(s) for the at least one optical component are determined based on measurements on a probed link of the WDM optical network, and wherein the probed link is different from the remote link. [0091] 15. The method according to item 14, wherein the probed link comprises optical components of same type and/or the same manufacturer as the optical components in the remote link. [0092] 16. The method according to any one of items 14-15, wherein the parametric model is a machine learning model trained on probed input WDM signal and measured output WDM signals of the probed link. [0093] 17. The method according to any one of items 14-16, wherein optimizing the corresponding output optical signal to noise ratio is provided by maximizing the signal to noise ratio in a worst case scenario, or equalizing the signal to noise ratio for all users, or obtaining a custom distribution of the output signal to noise ratio per user, for example depending on subscriptions of each user. [0094] 18. The method according to item 17, wherein the worst case scenario is defined by at least a majority of users being active at the same time or by at least a majority of users requesting a high data rate at the same time, or by the remote link being overloaded or fully loaded or almost fully loaded. [0095] 19. The method according to any one items 14-18, wherein the probed link is a laboratory WDM link or a pre-existing and and/or pre-deployed WDM link. [0096] 20. The method according to any one items 14-19, further comprising optimizing an obtained output signal to noise ratio for different wavelengths or for different users, by optimizing the input power profile of the link over the wavelengths, for a given total input power of the link. [0097] 21. The method according to any one of items 14-20, wherein the probed link is a portion of the remote link. [0098] 22. The method according to any one of items 14-21, wherein optimizing the quality of service is provided in real-time. [0099] 23. The method according to any one of items 14-22, wherein the parametric model(s) for the at least one optical component is/are obtained according to the method of any of items 1-13.