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Abstract
We propose a fast quality of transmission (QoT) estimation method based on cascaded artificial neural networks (ANNs) for intensity modulation-direct detection (IMDD) systems. The proposed method can calculate the bit error rate of three-span 36 km transmission within 0.7 seconds while taking account of the deterministic waveform distortion caused by the chromatic dispersion and self-phase modulation (SPM).
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1. Introduction
All-optical networks composed of reconfigurable optical add/drop multiplexers (ROADMs) can provide large-capacity and low-latency end-to-end optical paths by directly connecting end terminals without optical-electrical-optical (o/e/o) conversion or upper layer processing (e.g. switching processing) at the nodes [1,2]. Core networks that use ROADMs commonly employ digital coherent technology to yield maximum transmission distances of hundreds to thousands of kilometers. On the other hand, the application of all-optical networks to relatively smaller networks (e.g. metro data center interconnect (DCI) [3,4], intra-DC network [5,6], metro/access converged network [7–9]) is being studied, where the application of an economical and low-power-consumption intensity modulation-direct detection (IMDD) scheme is expected, because transmission length is short (several tens of km) compared to core networks. In such all-optical networks, the optical path and wavelength need to be dynamically changed when recovering from equipment failure, expanding the network by adding equipment, and changing resource allocation to meet traffic demands. To dynamically change the optical path and wavelength, the network operators must rapidly determine the path parameters that prevent signal distortion, because the quality of transmission (QoT) such as the bit error rate (BER), signal to noise ratio (SNR), varies in a complicated manner depending on the parameters of the transmission line (e.g. number of spans, chromatic dispersion, nonlinear effect, optical amplifier’s gain) and those of the transceiver (e.g. transmitting power, modulation format, forward error correction (FEC) type). Although it is possible to find the optimal path setting through trial and error on a real network in operation, this approach increases the path construction time and may degrade the BER of other existing optical paths. To avoid this, it is effective to fast estimate the QoT for each path and determine the optimal parameters based on the results [10]. One key issue for dynamic and real-time path construction is establishing a QoT estimation method with low calculation load for high-speed calculation.
One typical method to estimate the QoT is the use of linear and nonlinear fiber propagation simulation based on the split step Fourier method (SSFM) [11]. This method strictly calculates waveform change in optical fiber transmission based on the non-linear Schrodinger equation. Although this method can estimate QoT of both digital coherent and IMDD systems of any format by taking into account linear waveform distortion such as chromatic dispersion and nonlinear waveform distortion (self-phase modulation (SPM)/ cross-phase modulation (XPM)/ four-wave mixing (FWM)), the calculation loads are enormous, resulting in excessive calculation resource demands, calculation time, and power consumption.
So far, two attractive approaches have been investigated for the fast QoT estimation of digital coherent transmission schemes; machine learning based methods [10,12,13] and Gaussian noise model based methods [14–16]. Machine learning-based methods estimate QoT by using a simple model to learn the relationship between each transmission parameter and the QoT value. Fast calculation is expected as it does not calculate the complex interaction in fiber propagation. On the other hand, recent studies using GNPy based on the Gaussian noise model have attracted attention [14–16]. GNPy calculates the QoT value considering the optical SNR (OSNR) degradation due to superposition of amplified spontaneous emission (ASE) and nonlinear waveform degradation (SPM/XPM/FWM). While the ASE power is calculated from an optical amplifier model based on the data sheets of the optical amplifiers, the nonlinear waveform distortion is treated as random Gaussian noise whose power is calculated from the Gaussian noise model [17,18]. This method can calculate QoT faster by using a simple approximation to calculate the effect of complex nonlinear waveform distortion.
While various studies have reported QoT estimation methods for digital coherent systems, there are two problems with extending its application area to IMDD based all-optical networks. First, the waveform distortion caused by chromatic dispersion was not considered in previous studies due to the assumption of digital coherent based systems (i). Second, the waveform distortion caused by the nonlinear effect in IMDD was not considered in previous studies (ii) because the nonlinear effect cannot be approximated by random noise in the short transmission distances of IMDD systems. In particular, SPM causes deterministic waveform distortion determined by self-symbol sequence like chromatic dispersion in short transmission distance. A new QoT estimation method that considers points (i) and (ii) is necessary for IMDD systems.
In this paper, we propose a fast QoT estimation method based on artificial neural networks (ANNs) that considers the effects of chromatic dispersion (i) and SPM (ii) as deterministic waveform distortion, assuming a single channel as a first step. The proposed method consists of two ANN blocks, “waveform propagation block” for calculating the waveform change and “BER estimation block” for calculating the BER from the received waveform. To calculate end-to-end received waveforms fast enough, our proposed method propagates features of smaller dimension extracted from the electric field instead of the actual electric field. It is confirmed that our proposal successfully estimates the received waveform and BER of multi-span transmission while considering the effect of chromatic dispersion and SPM through comparison with a commercial SSFM-based propagation simulator. Compared to the conventional SSFM, the proposed method reduces calculation load to less than 1/91 by using small-scale ANNs. In the environment examined, BER of three span transmission was calculated within 0.7 seconds by using the proposed method. The proposed method is expected to match the calculation speeds of GNPy (several seconds per path [19]).
2. Proposed QoT estimation system using small-scale cascaded neural networks
2.1 Transmission path design system based on conventional QoT estimation
Figure 1 (a) shows an all-optical network whose path setting is based on QoT estimation [10,12–16]. End terminals are directly connected via optical nodes that have optical switches to transfer the client signal in any direction without o/e/o conversion and in-line optical amplifiers to compensate for the transmission loss. When a user or network operator requests the construction of a new path, the network controller calculates the QoT value for each path setting, controls the optical nodes based on the results, and constructs a path that satisfies the QoT value specified. Figure 1(b) shows a network model of an all-optical network. The electrical field E0 output from the transmitter is input into the first span (n = 1) with length of L1 and fiber input power of P1. Then, the electric field after propagating the first span E1 is output, which becomes the input electrical field of the next span (n = 2). By repeating this process for each span, the signal is input to the receiver with certain received optical power PRx, and the BER is calculated. Figure 1(c) shows the QoT estimation method based on conventional fiber propagation simulation using SSFM e.g. VPI transmission maker, a popular commercial propagation simulator [20]. The received waveform distorted by chromatic dispersion and SPM is calculated by cascading fiber propagation blocks using SSFM for each span. BER is calculated in the receiver block by adding noise to the received waveform and making decisions. In each fiber propagation block, the output electrical field En + 1 of single span is calculated based on input electrical field En of the span, transmission length Ln, and fiber input power Pn, considering the chromatic dispersion and SPM as waveform distortion. While the received waveform distorted by the chromatic dispersion (i) and SPM (ii) can be properly calculated by SSFM, an increase of calculation loads and computation time are a concern.
Fig. 1. (a)Transmission path design system based on QoT estimation. (b)Network model of an end-to-end optical path. (c) Calculation blocks of SSFM based QoT estimation method.
2.2 Proposed QoT estimation method
Figure 2(a) shows the calculation blocks of the proposed method. The method consists of two calculation blocks, both with ANNs: “waveform propagation block (ANN#1)”, “BER estimation block (ANN#2)”. ANN#1 is a block for emulating the waveform distortion of each span and based on that calculation result, ANN#2 estimates the BER. Details are described below. Whereas electric field En is propagated in the calculation blocks to obtain the received waveform in the conventional SSFM-based approach (Fig. 1(c)), ANN#1 propagates smaller- dimension feature An of the electric field including the effect of chromatic dispersion and SPM which greatly reduces the calculation load (Fig. 2(a)). An indicates the feature of the n-th span output electric field En (method of extracting feature An is described later in this section). Note that A0 is the feature value immediately after the transmitter output. Configuration of ANN#1 is shown in Fig. 2 (b). ANN#1 of n-th span (ANN#1-n) calculates output feature An + 1 by using a neural network whose input parameters are transmission length Ln, fiber input power Pn, and input feature An. When we assume that the network controller has the feature of transmitted signal A0 corresponding to the transmitter type as a table, feature of the received waveform after end-to-end transmission AN is calculated by simply propagating A0 through cascaded ANN#1. The configuration of ANN#2 is shown in Fig. 2(c). ANN#2 calculates the BER by using received feature AN and received optical power PRx as explanatory variables of the neural network.
Fig. 2. (a)Proposed calculation blocks considering deterministic waveform distortion. (b) Waveform propagation block (ANN#1). (c) BER estimation block (ANN#2).
Figure 3(a) shows the flow of dataset generation for the ANNs and training based on them. The dataset is created based on the received waveforms generated by the linear/nonlinear fiber propagation simulator based on SSFM [20]. Focusing on a certain single span, the output electric field En + 1 is calculated when input electric field En is input. In this case, a dataset for ANN#1 is generated by calculating feature values (An, An + 1) from En, En + 1 and combining with Ln, Pn (explanatory variables: An, Ln, Pn, objective variable An + 1). On the other hand, the dataset of ANN#2 is generated from the BER given received waveform of En + 1 (explanatory variables: An + 1, PRx, objective variable: BER). A dataset is created by repeating this calculation while changing the span of interest and the input electric field En. Finally, after training based on the datasets, end-to-end BER can be estimated by copying the trained ANN#1 as many times as there are transmission spans and cascading them with ANN#2 (Fig. 3(b)).
As mentioned above, An is a feature of the electric field En and has information of waveform distortion caused by chromatic dispersion and nonlinear distortion (SPM). We propose to utilize the transmitted distance L’ and the tap coefficients of Volterra nonlinear filter (VNLF) [21], which is a nonlinear filter generally used for equalization of IMDD systems, as feature An to express chromatic dispersion and nonlinear distortion (SPM). Feature An is composed of two parameters, one for chromatic dispersion and the other for SPM. Here, En is assumed to be the electric field after propagation distance of L’ (=$\mathop \sum \limits_{i = 1}^n {L_i}$). As the chromatic dispersion feature, just L’ is employed, while the nonlinear SPM feature is the tap coefficient of the VNLF. Figure 4 shows a proposed block configuration for extracting a SPM feature from the electric field of each span En. Ideal reference electric field Eideal with clear eye, is generated from the same bit sequence as En and input to the block which yields the waveform change due to linear propagation (chromatic dispersion) for transmission length L’. Eideal is converted into the frequency domain by fast Fourier transform (FFT), and then, the phase rotation for linear propagation is given. Electric field after linear propagation E’ideal is given by the following formula: [11]
where ${\beta _2}$ is group-velocity dispersion (GVD) coefficient. After reconverting into time domain by inverse FFT (IFFT), E’ideal is output to VNLF. VNLF tap coefficients are optimized by the least mean square (LMS) [22] algorithm. The mean square error (MSE) between En and the electric field output from the VNLF, Eout, is used as the evaluation function. By using E’ideal after linear propagation as VNLF’s input, the effect of linear chromatic dispersion is removed and the initial value of the error is reduced, improving the convergence characteristics of the LMS. When the LMS algorithm converges the error between En and Eout to zero, En and Eout coincide, which means that effect of the SPM is expressed as the tap coefficients of the VNLF. While the conventional practice is to use the real VNLF for IMDD system equalization, where the received waveform is a real number (intensity not electric field), the proposed method uses the complex VNLF to express the feature of the electric field including phase. This is necessary to yield multi-span estimation, because the waveform output from any single span is determined by input electrical field, not intensity. After the error is converged, dimension of the VNLF tap coefficients is reduced by principal component analysis (PCA) [23] to reduce the dimension of feature An.Our proposed method can, in calculating the BER, consider nonlinear waveform degradation (e.g. SPM) and receiver characteristics (e.g. receiver bandwidth and DSP), which is not possible if the error function is based on SNR, as it is in SSFM. Note that, while feature extraction takes relatively large calculation time in the dataset generation process, the BER is estimated quickly by propagating the A0 stored in a table through the small-scale ANNs (ANN#1, #2) in the QoT estimation phase for the real network. In addition, following advantages are expected from our proposed method.
Advantages of cascading small-scale ANNs
- - Faster QoT estimation is expected while considering the deterministic waveform distortion of chromatic dispersion and SPM by using ANN, compared to the conventional propagation simulation approach using SSFM.
- - Size of each ANN model can be reduced by splitting the transmission line into the individual spans. Small-scale ANNs are less prone to overfitting and are easy to design.
- - Proposed method can support span number increases by simply copying the ANN model according to the number of spans, which yields enhanced scalability.
Advantages of representing transmitter features as transmitting waveforms
- - Proposed method is expected to handle various IMDD transmitter types with different characteristics (e.g. bandwidth, nonlinearity, frequency chirp) because the transmitter characteristics are emulated as electrical field feature A0.
Advantages of separating transmission line and receiver
- - Proposed method can easily support wider receiver types (bandwidth, photo detector type, digital signal processing (DSP), FEC) because the receiver block (ANN#2) is separated from the propagation calculation block (ANN#1) and additional training is closed to the receiver.
3. Accuracy evaluation of the proposed QoT estimation method
3.1 Calculation setup
To validate the proposed method, we conducted end-to-end BER estimation for a three-span configuration, see Fig. 5(a). While the proposed method can be applied regardless of the modulation format, we employed 25-Gbps optical duobinary signals with excellent chromatic dispersion tolerance enabling long distance transmission. We set the wavelength of the main signal to 1553 nm, and GVD coefficient β2 to -20.473 ps2/km assuming chromatic dispersion in the C-band of D = 16 ps/nm/km. For simplicity, we consider the case where the transmission loss in the previous span is completely compensated by an in-line optical amplifier i.e. P1= P2= P3. The ANNs were implemented by using Keras, a Python library for ANNs, where the MSE and Relu functions were used for the loss and activation functions, respectively. The batch size was set to 1 and Adam was used as the optimization algorithm. Third order complex VNLF was used for feature extraction. We employed 31 samples of the electric field waveform as the input waveform for VNLF, where the total number of taps in third order VNLF is 30773 (=311 + 312 + 313). In the PCA process, input variables with large variance are regarded as the main component, and remain after dimensionality reduction. Generally speaking, when the input variable does not have any physical meaning, PCA is applied after performing standardizing the input variables to treat each input variable fairly [23]. On the other hand, in our proposed method, as the VNLF tap coefficients of the input variable have physical meaning (the larger the tap, the larger the impact on the filter output), larger taps with more information must remain after dimensionality reduction. Thus, in this paper, the VNLF tap coefficients are input to the PCA block without standardization. After PCA, the dimension of the feature was reduced from 30773 to 51. ANN#1 and ANN#2 were 5-layer ANNs (number of neurons: 53/200/100/100/51, 52/200/100/100/1), see Fig. 5(b).
Fig. 5. Calculation setup. (a)Network configuration. (b) ANN blocks for BER estimation. (c) Combination of fiber length for each span.
The datasets for ANN#1 and ANN#2 are created based on the received waveforms generated by the VPI transmission maker [20], which is a commercial high-precision linear/nonlinear propagation simulator based on SSFM that uses the procedure detailed in Section 2.2 (see Fig. 3(a)). Sample rate is set to 8 times oversampling. Here, four types of fiber length (3, 6, 9, 12 km) were used for each span. To create a comprehensive, unbiased dataset, training employed a total of 84 patterns of single spans with all combinations of input En and output En + 1 electric field (see Fig. 3(a)). Figure 5(c) shows an image of combinations considering four fiber lengths in a 3-span configuration. For the 1st span, electric field at the transmitter (E0) is input to four types of fiber span. Thus, there are 41 combinations of input and output electric field (En, En + 1). For the 2nd and 3rd span, 42 and 43 combinations of input and output electric field are also obtained considering that 41 and 42 types of electric field are input to four types of fiber span, respectively. From the above, 84 (=41 + 42 + 43) patterns of spans with different combinations of input and output electric field were obtained and used for training as unbiased datasets. We also created a dataset for ANN#2, using PRx values of -24, -23, -22, -21, and -20 dBm and feature value of An + 1 extracted from the 84 patterns mentioned above. The decision threshold was set to the average power of the received signal and BER was calculated from the direct error count. Figures 6(a) and (b) show the convergence characteristic of the loss function for ANN#1 and 2 training schemes. As shown, the convergence characteristics are different since the ANN models are different. We employed the model trained with epoch numbers of 200 and 600 for ANN#1 and 2, respectively, since these numbers allow the loss to converge.
3.2 Feature extraction accuracy
To validate our basic concept of propagation of the feature of the electric field, first we investigated the accuracy of feature extraction. When the feature is properly extracted, electric field En and feature An have a one-to-one relationship, and original electric field En can be regenerated from feature An. Figure 7 shows the calculation block that converted the feature into the electrical field. Based on this, we compared the signal waveform calculated by the proposed method with that of the SSFM based method. Eye patterns calculated by SSFM-based commercial fiber propagation simulator for 40-km single-span transmission with fiber input powers of -1 dBm and 12 dBm are shown in Figs. 8(a) and (b), respectively. When the fiber input power is increased to 12 dBm, waveform distortion due to SPM occurs. We calculated the waveform of 40 km transmission from the feature determined for the 12-dBm case including the effect of SPM and evaluated its validity. Figure 8 (c) shows the eye pattern calculated from the feature extracted by the proposed block (Fig. 4). Figure 8 (d)-(f) show the real part, imaginary part and phase calculated by the proposed method (blue dashed line) and the SSFM (red line). It was confirmed that the waveform calculated from the commercial propagation simulator and electric field feature An agree exceptionally well, even the phase. It is found that the feature can be properly extracted by the proposed method. Figure 9 shows the MSE when applying the LMS algorithm with and without linear propagation blocks. The calculation results show that the MSE increases as the transmission distance increases without the linear propagation block. However, the characteristics improve with use of the linear propagation block. This indicates that the convergence characteristics of the LMS can be improved by using a linear propagation block to reduce the initial value of the error.
Fig. 8. (a) Eye pattern with transmitting power of -1 dBm calculated by SSFM. (b) Eye pattern with transmitting power of 12 dBm calculated by SSFM. (c) Eye pattern with transmitting power of 12 dBm calculated by proposed method. (d)Real part. (e)Imaginary part. (f)Phase.
3.3 BER estimation of multi-span transmission
The proposed method estimates the BER by calculating the received feature after multi-span transmission and converting it into BER. We evaluate the accuracy of the received feature calculation. Figure 10(a) shows the eye pattern calculated by the SSFM based commercial propagation simulator and the proposed method for the three-span configuration composed of 12/12/12 km spans (Configuration A). For comparison, the eye pattern after end-to-end transmission (36 km) with the input optical power of -1 dBm is also shown. From the comparison of the end-to-end (36 km) case at input optical powers of -1 dBm and 12 dBm, it can be seen that the waveform distortion due to SPM occurs at the input optical power of 12 dBm. It is also confirmed that the proposed method successfully estimated the waveform including SPM at all points (12, 24, 36 km) as it agrees with SSFM-based commercial propagation simulator results. Subsequently, the same calculation was performed for 3/3/3 km spans (Configuration B) and 11/9/11 km spans (Configuration C). Note that Configuration C is composed of a span no represented by a dataset (3/6/9/12 km). Figure 10(b) and (c) show the calculation results. The calculation results of SSFM and the proposed method agree in Configuration C (the one with no dataset) as well as Configurations A and B. The above confirms that the trained ANN#1 successfully outputs the feature that well represents multi-span transmission.
Fig. 10. Eye pattern of multi-span transmission. (a)Configuration A (12 km/ 12 km/ 12 km). (b) Configuration B (3 km/ 3 km/ 3 km). (c) Configuration C (11 km/ 9 km/ 11 km).
Finally, we performed end-to-end BER estimation based on the received feature. Figure 11(a) and (b) show the estimated BER for fiber input powers Pn of 12 dBm and 9 dBm, respectively. Calculation results of the proposed method and SSFM are shown for comparison. With the fiber input power Pn of 12 dBm, BER was properly estimated for all patterns, including configuration C and PRx = -22.5, -23.5, -24.5, -25.5, which are not covered by any dataset. When the input optical power Pn is decreased to 9 dBm (Fig. 11(b)), a characteristic improvement due to SPM reduction was observed. The proposed method can estimate BER with high accuracy by using a VNLF with a sufficient number of taps to express SPM’s waveform distortion and effectively reduce dimensionality without losing information. The above demonstrates that our proposed method can properly estimate end-to-end BER including deterministic waveform distortion of chromatic dispersion and the SPM.
4. Comparison of calculation load with the proposed method and SSFM
In this chapter, we evaluate computational complexity of the proposed method through comparison with a linear/nonlinear propagation simulator based on SSFM and show the calculation time in our environment. SSFM is an algorithm that divides a transmission line into small intervals and repeats linear and nonlinear operations in the time and frequency domains for each interval [11], where the FFT and IFFT with enormous computational complexity are used to handle time and frequency domains. The total number of multiplications, Ncalc, is given by:
${N_{FFT}}$ is the multiplications per FFT [24]. ${N_r}$ is the number of repetitions of FFT. Ns is the number of samples for waveform (= number of symbols ${\times} $ oversampling number). Considering that at least 2 FFTs are required per span (time to frequency/frequency to time), 6 FFTs calculations are required for the three-span configuration. Figure 12 shows the total number of multiplications Ncalc for Ns in this case. For example, when the number of symbols is set to 104 for the estimation of BER = 10−3 with 8 times oversampling, Ns is 80000. In this case, the total multiplication number of SSFM is 7818102. On the other hand, the multiplication number of ANN#1 composed of a 5-layer ANN (53/200/100/100/51) is =53 × 200 + 200 × 100 + 100 × 100 + 100 × 50 = 45600. Similarly, the multiplication number of ANN#2 with nodes numbers (52/200/100/100/1) is 52 × 200 + 200 × 100 + 100 × 100 + 100 × 1 = 40500. The total number of multiplications in our proposed method is 86100(=45600 + 40500). Thus, the proposed method can reduce the computational complexity 91 times. As the proposed method does not require various additional calculations such as noise addition, receiver band limitation, receiver digital signal processing, clock recovery, symbol extraction, decision, error counting etc. which is needed for BER calculation in the SSFM-based method, even greater computational complexity reduction and resulting calculation time reduction is expected. In our environment (CPU: Intel Xeon L5640 2.27 GHz, RAM: 32 G), the proposed method completes all processing from propagation waveform calculation to BER estimation in the short time of 0.7 seconds.
5. Conclusion
We proposed a ANN-based fast QoT estimation method for IMDD systems; the proposal considers the effect of chromatic dispersion and SPM as deterministic waveform distortion. The proposed method consists of two ANN blocks, “waveform propagation block” for calculating the waveform change and “BER estimation block” for calculating the BER from the received waveform. To rapidly calculate the effect of waveform distortion after multi-span transmission, the proposed method propagates a single feature of small dimensionality extracted from the electric field instead of the actual electric field itself. We study a feature extraction method that uses a third order nonlinear filter. In the proposed feature extraction method, that complex waveform changes created by chromatic dispersion and SPM characterized by a 51-dimension feature. We conducted end-to-end BER estimations with several configurations of three spans (A:12/12/12 km, B:3/3/3 km, C:11/9/11 km). It was confirmed that the proposed method can properly estimate the received waveforms for all configurations including the one not included in the datasets. Compared with the conventional SSFM-based method, the proposed method can reduce the number of multiplications required for the propagation waveform calculation by a factor of 91. Further computational complexity reduction is expected, as the proposed method eliminates various calculations needed in the conventional SSFM-based method for converting the waveform distortion to BER such as noise addition, receiver band limitation, receiver digital signal processing, clock recovery, symbol extraction, decision, and error counting. In our environment, the proposed method completes all processing from propagation waveform calculation to BER estimation in the short time of 0.7 seconds. It is expected that calculation speeds equivalent to those of GNPy (several seconds per path [19]) can be realized.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. Birk, O. Renais, G. Lambert, et al., “The OpenROADM initiative [Invited],” J. Opt. Commun. Netw. 12(6), C58–67 (2020). [CrossRef]
2. P. Roorda and B. Collings, “Evolution to Colorless and Directionless ROADM Architectures,” in Optical Fiber Communication (OFC) (2008), paper NWE2.
3. G. Khanna, S. Zhu, M. Filer, et al., “Towards all optical DCI networks New York,” in Optical Fiber Communication (OFC) (2020), paper W2A.33.
4. M. Filer, S. Searcy, Y. Fu, et al., “Demonstration and Performance Analysis of 4 Tb/s DWDM Metro-DCI System with 100 G PAM4 QSFP28 Modules,” in Optical Fiber Communication (OFC) (2017), paper W4D.4.
5. N. Parsons and N. Calabretta, “Optical Switching for Data Center Networks,” Springer Handbook of Optical Networks, pp. 795–825 (2020).
6. X. Xue, F. Wang, F. Agraz, et al., “Experimental Assessment of SDN-enabled Reconfigurable OPSquare Data Center Networks with QoS Guarantees,” in Optical Fiber Communication (OFC) (2019), paper M3F.4.
7. M. Yoshino, S. Kaneko, N. Shibata, et al., “New Photonic Gateway to Handle Digital-Coherent and IM-DD User Terminals and Enable Turn-back Connections in Metro/Access-Integrated All-Photonics Network,” in Optical Fiber Communication (OFC) (2023), paper W3F.5.
8. S. Kaneko, K. Honda, T. Kanai, et al., “Photonic Gateway and Protocol-Independent End-to-End Optical-Connection Provisioning in All-Photonic Metro-Access Converged Network,” IEEE Photonics J. 15(3), 7201009 (2023). [CrossRef]
9. H. Nishizawa, T. Sasai, T. Inoue, et al., “Dynamic Optical Path Provisioning for Alien Access Links: Architecture, Demonstration, and Challenges,” IEEE Commun. Mag. 61(4), 136–142 (2023). [CrossRef]
10. S. Allogba, S. Aladin, and C. Tremblay, “Machine-Learning-Based Lightpath QoT Estimation and Forecasting,” J. Lightwave Technol. 40(10), 3115–3127 (2022). [CrossRef]
11. A. Bononi, R. Dar, M. Secondini, et al., “Fiber Nonlinearity and Optical System Performance,” Springer Handbook of Optical Networks, 287–351 (2020).
12. R. Proietti, X. Chen, K. Zhang, et al., “Experimental Demonstration of Machine-Learning-Aided QoT Estimation in Multi-Domain Elastic Optical Networks with Alien Wavelengths,” J. Opt. Commun. Netw. 11(1), A1–A10 (2019). [CrossRef]
13. R. Ayassi, A. Triki, M. Laye, et al., “An Overview on Machine Learning-Based Solutions to Improve Lightpath QoT Estimation,” in 22nd International Conference on Transparent Optical Networks (ICTON) (2020), paper We.A3.1.
14. A. Ferrari, K. Balasubramanian, M. Filer, et al., “Assessment on the in-field lightpath QoT computation including connector loss uncertainties,” J. Opt. Commun. Netw. 13(2), A156–A164 (2021). [CrossRef]
15. A. Ferrari, M. Filer, K. Balasubramanian, et al., “GNPy: an open source application for physical layer aware open optical networks,” J. Opt. Commun. Netw. 12(6), C31–C40 (2020). [CrossRef]
16. G. Borraccini, S. Straullu, A. Giorgetti, et al., “QoT-Driven Optical Control and Data Plane in Multi-Vendor Disaggregated Networks,” in Optical Fiber Communication (OFC) (2022), paper M4F.5.
17. P. Poggiolini, G. Bosco, A. Carena, et al., “The GN-Model of Fiber Non-Linear Propagation and its Applications,” J. Lightwave Technol. 32(4), 694–721 (2014). [CrossRef]
18. P. Poggiolini, G. Bosco, A. Carena, et al., “A detailed analytical derivation of the GN model of non-linear interference in coherent optical transmission systems,” arXiv, arXiv;1209.0394. (2012). [CrossRef]
19. A. Ferrari, J. Kundràt, E. L. Rouzic, et al., “The GNPy Open Source Library of Applications for Software Abstraction of WDM Data Transport in Open Optical Networks,” in 6th IEEE Conference on Network Softwarization (NetSoft) (2020).
20. https://www.vpiphotonics.com/index.php.
21. N-P Diamantopoulos, H. Nishi, W. Kobayashi, et al., “On the Complexity Reduction of the Second-Order Volterra Nonlinear Equalizer for IM/DD Systems,” J. Lightwave Technol. 37(4), 1214–1224 (2019). [CrossRef]
22. C. Lederer and M. Huemer, “Simplified complex LMS algorithm for the cancellation of second-order TX intermodulation distortions in homodyne receivers,” in 45th Asilomar Conference on Signals, Systems and Computers (ASILOMAR) (2011), paper 533–537.
23. F. L. Gewers, G. R. Ferreira, H. F. D. Arruda, et al., “Principal Component Analysis: A Natural Approach to Data Exploration,” ACM Comput. Surv. 54(4), 70 (2021). [CrossRef]
24. P. Duhamel and M. Vetterli, “FAST FOURIER TRANSFORMS: A TUTORIAL REVIEW AND A STATE OF THE ART,” Signal Process. 19(4), 259–299 (1990). [CrossRef]
