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Abstract
Fiber nonlinearity is one of the major impairments for long-haul transmission systems. Therefore, estimating the nonlinear signal-to-noise ratio (SNRNL) is indispensable to guarantee the quality of transmission and manage the operation of optical networks. The deep neural network (DNN) has been successfully applied for the SNRNL estimation. However, the performance substantially degrades, when the mega dataset is inaccessible. Here, we demonstrate an accurate SNRNL estimation based on the data augmentation (DA)-assisted DNN with a small-scale dataset in the frequency domain. When the 95-GBaud dual-polarization 16 quadrature amplitude modulation (DP-16QAM) signal with variable optical launch powers from -2 to 4-dBm is numerically transmitted from 80-km to 1520-km standard single-mode fiber (SSMF), we identify that, in comparison with traditional DNN scheme, the DA allows the reduction of the training dataset size by about 60% while keeping the same mean absolute error (MAE) as 0.2-dB of SNRNL estimation. Meanwhile, the DA-assisted DNN scheme can reduce the MAE by about 0.14-dB compared with the traditional DNN scheme, when both SNRNL estimation schemes use 100 raw datasets which contain 700 symbols. Due to these observations, the DA-assisted DNN scheme is promising for field-trial nonlinear SNR estimation, especially when the collection of mega datasets is inconvenient.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The demand for network capacity is rapidly increasing, due to emerging Internet applications such as high-definition video streaming, cloud, virtual reality, and so forth. Serving as the infrastructure of the global Internet, optical networks are becoming more flexible, dynamic, and heterogeneous, in order to enhance the networking capacity. Thus, the need to continuously estimate the transmission impairment, for the ease of network controlling and management, has become even more urgent [1]. To achieve such a goal, physical layer impairments should be accurately and timely estimated [2]. Among all parameters, SNR is the most important metric to be estimated, as it is helpful to evaluate the bit-error-ratio (BER) performance, select the optimal routine path, and realize flexible transmission. The traditional scheme of SNR estimation, which is realized by comparing the electrical signal power to the electrical noise power within the signal bandwidth due to the amplified spontaneous emission (ASE) noise, is defined as the SNRASE. The ASE from the use of Erbium-doped fiber amplifiers (EDFA) has the characteristic of zero-mean random white Gaussian noise [3]. When the baud-rate and the transmission reach are further enhanced, the transmission performance is constrained by the ultimate impairment from the fiber nonlinearity. Thus, when optical networks evolve towards high baud-rate long-haul dense wavelength division multiplexing (DWDM) transmission, fiber nonlinear interference noise (NLIN) originating from interactions among all electromagnetic waves within the standard single mode fiber (SSMF), needs to be taken into account the same as the ASE noise [4]. The associated SNR estimation by comparing the signal power to the NLIN power is defined as SNRNL. However, it is challenging to distinguish between the ASE and NLIN contributions in the time domain, because both nonlinear noise and ASE noise are included in the electrical sampling waveform. Therefore, there exists an increasing demand for optical performance monitoring (OPM) techniques that reliably estimate the SNRNL. Some SNRNL estimation schemes have been proposed, such as the differential pilot aided technique [5,6], a correlation function with calibration factor method [7,8,9], and time domain pilot aided with fractional Fourier transformation (FFT) technique [10]. However, all those schemes need additional optoelectrical devices and manual operation, which is not only inefficient but also difficult to obtain accurate results.
To overcome those drawbacks, artificial intelligence (AI) techniques with the ability to model the target relationship from the mega dataset have been proposed for the SNRNL estimation. Some schemes firstly extract statistical features from nonlinear noise variance [11,12], nonlinear noise auto-correlation functions [13], constellation diagram [14,15,16], and fast BER histogram (FBH) [17] in the time domain after the data-preprocessing, and then realize the SNRNL estimation with the help of various deep neural networks (DNNs). These schemes can realize a standard deviation from 0.2-dB to 0.3-dB for 35-Gbaund dual-polarization 16 quadrature amplitude modulation (DP-16QAM) signal over the transmission over 1200-km SSMF, under the launch power of 4-dBm. However, the data preprocessing needs to collect mega data to generate statistical features as the DNN input, such as a simulation dataset of 432 nonlinear noise variances from ${2^{18}}$ data samples [11]. To overcome the mega data in the DNN training, physics-guided neural network (PGNN) is able to achieve the same accuracy with less dataset with root mean squared error (RMSE) of 0.7-dB for the 35-Gbaud DP-16QAM signal transmission over 2000-km SSMF, under the launch power of 4-dBm [18]. However, in comparison with the black-box NN, this scheme has a complex data-preprocessing because PGNN works with the help of the Gaussian noise (GN) model for the knowledge extraction. Consequently, both complex data preprocessing and mega datasets are required for the SNRNL estimation in the time domain. Alternatively, other schemes extract features directly from four-tributary signals in the frequency domain after the coherent detection. These schemes use long short-term memory NN (LSTM-NN) to estimate the SNRNL[19,20] with the MAE of less than 0.3-dB for the 28-Gbaud DP-16QAM signal transmission over 1000-km SSMF, under the launch power of 3-dBm. Although the complicated dataset preprocessing is avoided, 1146880 symbols are still necessary for the LSTM-NN training [20]. Since the large-scale dataset is inconvenient to be acquired in practice, a small-scale dataset becomes a bottleneck for existing DNN-based SNRNL estimation schemes. Furthermore, most traditional DNN-based SNRNL estimation schemes are only evaluated under a baud rate of less than 35G-baud [11–20], so the impact of a high baud-rate is not taken into account. In order to realize the SNRNL estimation for the high baud-rate signal, under the condition of a small-scale dataset, data augmentation (DA) becomes a promising solution that allows for insufficient data to generate value equivalent to the mega dataset, by integrating the enhanced data with the original dataset into a more comprehensive dataset and extracting more information [21]. As for optical communication, DA can improve the accuracy of failure predictions by 3.5%-5.5% in the way of value-shift, Gaussian noise, class balance [22], and generative adversarial network (GAN) [23]. As for the nonlinear equalization [21], the DA consisting of phase shift, time-inversion, and polarization swapping can reduce the dataset size by 4 to 6 times, in comparison with the traditional DNN scheme. As for the SNRASE estimation, the DA consisting of phase shift and time-inversion can reduce the dataset size by 50%, in relevant to the traditional DNN scheme [24].
In current submission, we propose the DA-assisted DNN for the SNRNL estimation of high baud-rate signal with a small-scale dataset. In order to avoid the complicated data preprocessing and NN structure, the SNRNL is estimated in the frequency domain with DNN. Then, the performance of the DA-assisted DNN scheme which extracts features directly from the raw datasets is evaluated. It is numerically identified that, the DA can increase the diversity of datasets and enhance the characteristic of the small-scale dataset to be more representative, when the 95-GBaud DP-16QAM signal with variable launch powers from -2 to 4-dBm is transmitted over a variable SSMF reach from 80-km to 1520-km. The DA-assisted DNN scheme allows the reduction of the training dataset size by about 60%, while keeping the same mean absolute error (MAE) of SNRNL estimation as 0.2-dB, in comparison with the traditional DNN scheme. The proposed scheme can reduce the MAE of the SNRNL estimation by about 0.14-dB, when the training datasets size is 100 for both the proposed scheme and the traditional DNN scheme. And these 100 training datasets contain 700 symbols.
2. Operation principle
In order to validate the SNRNL estimation through the DA-assisted DNN scheme, we should first obtain the target SNRNL which is defined as:
where ${W_{sig}}$ and ${W_{NL}}$ are the signal power and the nonlinear noise power. The target SNRNL is obtained by comparing the electrical signal power to the electrical NLIN power. However, the ${W_{NL}}$ cannot be directly acquired, leading to the difficulty in calculating the target SNRNL. Alternatively, we define SNRASE and generalized signal-to-noise ratio (GSNR), respectively, where ${W_{ASE}}$ is the ASE noise power. After compensating chromatic dispersion (CD) and NLIN, SNRASE is acquired by comparing the electrical signal power to the electrical noise power within the signal bandwidth. The GSNR is calculated by comparing electrical signal power to the NLIN and ASE noise power, when only CD is compensated. Thus, considering the relationship among SNRNL, SNRASE and GSNR, the target SNRNL can be calculated as [25],Therefore, the target SNRNL used as the benchmark to evaluate the accuracy of SNRNL estimation by the DA-assisted DNN scheme can be calculated indirectly through GSNR and SNRASE. The operation principle of the DA-assisted DNN scheme is based on the Manakov equation, which describes the dual-polarization (DP) optical signal propagation over a fiber link as [26,27],
As shown in Fig. 1, the input dataset is tailored to a two-dimensional matrix in the time domain. Each column has a window of symbols with a length of $\frac{{{l_{tap}}}}{2}$ for each polarization, and the number of windows represents the dataset size. Then both datasets at two orthogonal polarizations are combined vertically, meaning each column of the input dataset has symbols with a length of ${l_{tap}}$. Next, in order to transform the input dataset into the frequency domain, FFT that has a length of $\frac{{{l_{tap}}}}{2}$ is applied to each column of two orthogonal polarizations, respectively. As for the DNN, the whole amount of dataset to be used as the DNN input becomes $({S_1} + {S_2})\ast L$, where ${S_1}$ and ${S_2}$ are the numbers of windows for the raw data and the DA data. L is the number of discrete SNRNL. Our research motivation is to realize the SNRNL estimation, under the use of a small-scale dataset by reducing ${S_1}$ and ${l_{tap}}$. The fully connected DNN consists of an input layer with the number of neurons equal to ${l_{tap}}$ of the input dataset, three hidden layers with ReLU as the active function, and an output layer with only one linear neuron. All weights and biases of DNN are updated through the gradient descent method optimized by the Adam and minibatch algorithm. The loss function is the MAE, which is a straightforward metric of SNRNL estimation than both the RMSE and the mean squared error (MSE) [28]. MAE is widely used as the loss function to train the DNN [14,19,20]. Then the estimated SNRNL by the DA-assisted DNN scheme is compared with the target SNRNL, by calculating the MAE as,
3. Simulation setup
The simulation setup to evaluate the proposed SNRNL estimation scheme is shown in Fig. 2 (a). Initially, we need to obtain the correct value of the target SNRNL. At the transmitter (Tx) side, two bit-streams are mapped into a 95-GBaud DP-16QAM signal by a root-raised-cosine pulse shaping with a roll-off factor of 0.02. The launch power of the transmitted signal varies from -2 to 4-dBm with a resolution of 0.5dB. When it comes to the SSMF transmission, each SSMF span has a length of 80-km, an attenuation coefficient of 0.22-dB/km, a nonlinear coefficient of 1.3-(W*km)-1, and the CD coefficient of 16.89-ps/(nm*km). The number of spans can be varied from 1 to 19, in order to emulate the multi-span fiber optical transmission. Meanwhile, EDFAs are used to compensate for the transmission loss of each span. The noise figure of EDFA is 4.5-dB. At the receiver (Rx) side, the sampling rate of the received signal is 190-GSa/s. Then the received signal is filtered out for the subsequent DSP. Digital back propagation (DBP), matched filtering, down-sampling, and phase de-rotation are implemented. DBP which uses the split-step Fourier method (SSFM) to solve Eq. (5) can compensate both CD and NLIN effectively [29]. When both CD and NLIN are compensated, the SNRASE and GSNR can be calculated through Eq. (2) and Eq. (3), respectively. Finally, the target SNRNL can be obtained by Eq. (4). Since the target SNRNL calculated by the SSFM has a high accuracy, when a small step size is set during the numerical simulation, it can be treated as the bench-mark during the accuracy evaluation of SNRNL estimation. Then DNN is used to estimate the SNRNL, as shown in Fig. 2 (b). The Tx side and SSMF transmission are the same as that of Fig. 2 (a), whereas the Rx side is different. After the transmitted signal is coherently detected, the I and Q electrical signals of each polarization are subsequently digitalized and combined as the complex-value input for our DA-assisted DNN scheme. As for the proposed scheme, the input data is transformed into a two-dimensional matrix named the raw data. Then, phase shift, time-inversion, and polarization swapping are separately implemented, in order to generate the DA data. Those three DA methods can enlarge the size of the raw dataset and extract more information. After the DA, both raw data and DA data are combined and transformed into the frequency domain. Next, the augmented dataset is introduced into the DNN to be used for the SNRNL estimation. 80% of the whole dataset is chosen for the purpose of training, while the other 20% is reserved for the testing of individual transmission scenarios. During the training stage, both weights and biases are updated through the gradient descent method, and the MAE is referred to as the loss function to characterize the training error. Once the training stage is completed, the performances of trained DNN is evaluated by the independent testing dataset. During the testing stage, the dataset is used to estimate the corresponding SNRNL. When the MAE between the real value and the estimated value is within 0.20-dB, we can conclude that the DNN can accurately and effectively obtain the SNRNL for individual transmission scenarios.
4. Simulation result
In this part, three DA methods are separately applied to the raw data, for ease of reducing the dataset size. First, the impact of optical launch power which varies from -2-dBm to 4-dBm with a resolution of 0.5-dBm on the DA-assisted DNN scheme is investigated. Next, the proposed SNRNL estimation scheme is investigated with variable SSMF reach. The SSMF transmission distance is within the range of 80-km∼1520-km with an SSMF span of 80-km. Finally, we examine the accuracy and the used dataset of the proposed SNRNL estimation scheme over more complex scenarios, when the optical launch power and the transmission distance of SSMF are jointly varied.
4.1 Optical launch power
We first evaluate the capability of the DA assisted-DNN scheme, when the 95-GBaud DP-16QAM signal is transmitted over 1040-km of SSMF, under the condition of variable optical launch power. Before the use of DA, various constellations of DP-16QAM with the NLIN are compared, in order to ensure the occurrence of nonlinear noise to be estimated, as shown in Fig. 3. The original signal is shown in Fig, 3(a) without any compensation. However, when the CD is compensated, the constellations of Fig. 3(b) become clearer than the original signal in Fig, 3(a). With the help of DBP to compensate for the NLIN, the constellations of DP-16QAM in Fig. 3(c) become clearer than that impaired by the NLIN in Fig. 3(b). Moreover, since the NLIN becomes severe with the growing optical launch powers, the occurred NLIN between Fig. 3(b) and (c) can be estimated by the proposed DA-assisted DNN. We first calculate the target SNRNL, SNRASE, and GSNR by the DBP, as shown in Fig. 4(a). Both the SNRASE and GSNR increase along with the increment of optical launch power. The target SNRNL values range from 22.70-dB to 34.48-dB. Next, the length ${l_{tap}}$ is optimized, under the scenario of various optical launch powers with a window length of 300, as shown in Fig. 4(b). Since larger ${l_{tap}}$ may increase the calculation complexity, ${l_{tap}}$ is optimized to be 222, which is the smallest length to achieve a minimum MAE of SNRNL estimation. The numbers of hidden neurons in the DNN are optimized as 450, 350, 200, and 150, respectively. Meanwhile, both the training epochs and the batch size of the minibatch are 300 and 60, respectively. Then the relationship between the number of windows of the raw data and the MAE of SNRNL estimation is investigated. For the fair comparison, we define a metric P as
Fig. 3. Constellation of 95-Gbaud DP-16QAM signal (a) original one, (b) with NLIN and ASE, (c) only with ASE noise, after transmission over 1040-km, under variable optical launch powers.
Fig. 4. (a) Target SNR for 95-GBaud DP-16QAM signal transmission over the 1040-km SSMF under variable launch power. MAE results with (b) different ${l_{tap}}$, and (c) different dataset size at the ${l_{tap}}$ of 222.
In order to evaluate the capability of the DA assisted-DNN scheme, we investigate the 95-GBand DP-16QAM signal transmission over 1040-km SSMF under various optical launch power, as shown in Fig. 4(c). When the number of raw data increases, the MAE of raw data as well as the augmented data decreases. The MAE of the DA-assisted DNN scheme is always less than that of the traditional DNN scheme. Thus, it is clear that, the phase, time and polarization augmentation methods can reduce the MAE value, leading to a P value of 50%, when 200 and 100 windows are used for the traditional DNN scheme and the DA-assisted DNN scheme to reach the same minimum MAE of 0.15-dB, respectively. Keeping the same windows as 100 for the DA methods to reach the minimum MAE of 0.15-dB, the DMAE value is 0.10-dB.
4.2 Transmission distance
In this section, the relationship between the transmission reach and the performance of the DA-assisted DNN scheme is discussed. Figure 5 presents the results of 95-GBaud DP-16QAM signals transmission over 80-km to 1520-km SSMF with a span length of 80-km under the optical launch power of 4-dBm. Figure 5(a) presents the range of target SNRNLs from 21.66-dB to 37.68-dB. As we can see, both Both the SNRASE and GSNR decrease along with the increment of transmission due to the accumulation of ASE noise. Next, the length ${l_{tap}}$ is optimized to 282 with a window length of 300, under the scenario of variable SSMF reach, as shown in Fig. 5(b). From Fig. 5(c), the DA-assisted DNN scheme is effective for variable SSMF to reach from 80 to 1520-km, and can reduce about 50% used raw dataset when both schemes reach the minimum MAE of 0.15-dB. The number of windows is 100 and 200 for the DA-assisted DNN scheme and traditional DNN scheme, when the proposed scheme can achieve a 50% reduction of raw dataset. As for the accuracy improvement, when the DA-assisted DNN methods to reach the minimum MAE of 0.15-dB, the DMAE is 0.11-dB under the same number of windows.
Fig. 5. (a) Target SNR for 95-GBaud DP-16QAM signal transmitted over the SSMF range from 80 to 1520-km with a span of 80-km under 4-dBm optical launch power. MAE results with (b) different ${l_{tap}}$, and (c) different size of the dataset at the ${l_{tap}}$ of 282.
Fig. 6. MAE results of the 95-GBaud DP-16QAM optical signal transmission over variable SSMF reach under different launch powers (b) different ${l_{tap}}$ and (c) different size of the dataset at the ${l_{tap}}$ of 502.
4.3 Launch power & transmission distance
Finally, we investigate the efficiencies of our DA-assisted DNN scheme under more complex scenarios as shown in Table 1. The input signals have 70 different kinds of discrete SNRNLs. Similar to the previous simulations, we first optimize the ${l_{tap}}$ as 502, taking into account of both the estimation accuracy and the implementation complexity, as shown in Fig. 6(a). Then, the SNRNL estimation results are shown in Fig. 6(b). By the use of the DA-assisted scheme, the MAE can lead to the P value of 60% when the minimum MAE of both schemes is 0.20. The traditional DNN scheme and the DA-assisted DNN scheme need 250 and 100 windows of raw datasets, respectively. When the MAE of the DA-assisted DNN scheme is 0.20-dB, the MAE of the traditional DNN scheme is 0.34-dB, indicating the DMAE is 0.14-dB at the same 100 windows. Thus, the DA-assisted DNN scheme can realize accurate SNRNL estimation of high baud-rate signals with a small-scale dataset, as well as the feasibility to be implemented in complex transmission scenarios.
Table 1. 95 G DP-16QAM system configuration for DA-assisted DNN scheme
5. Conclusion
We have demonstrated an SNRNL estimation technique enabled by the DA-assisted DNN with a small-scale dataset for high baud-rate long-haul transmission. After the linear noise is compensated, the proposed scheme works in the frequency domain to avoid complicated data pre-processing. The launch power and the SSMF reach are investigated for the 95-Gbaund 16-QAM coherent transmission system, which indicates the DA-assisted DNN scheme can estimate SNRNL with the save of 50% raw data, in comparison with the traditional DNN scheme. The DMAE is 0.10-dB, when the launch power and the SSMF reach are varied. Then it is numerically verified that, under the minimum MAE of 0.2-dB, 60% of raw data can be saved for 95-GBaud 16QAM coherent transmission over the SSMF range from 80-km to 1520-km with a span of 160-km under the optical launch power from -2-dBm to 4-dBm, significantly relieving the stress of on-field data acquirement. When the number of windows is 100 which contain 700 symbols, the DA-assisted DNN scheme can reduce 0.14-dB MAE, in comparison with the traditional DNN scheme. Thus, the DA-assisted DNN scheme is verified with the capability of achieving accurate SNRNL estimation with a small-scale dataset.
Funding
National Key Research and Development Program of China (2021YFB2900702); National Natural Science Foundation of China (62025502, 62075046, U21A20506).
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.
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