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Abstract
Optical signal-to-noise ratio (OSNR) monitoring is one of the core tasks of advanced optical performance monitoring (OPM) technology, which plays an essential role in future intelligent optical communication networks. In contrast to many regression-based methods, we convert the continuous OSNR monitoring into a classification problem by restricting the outputs of the neural network-based classifier to discrete OSNR intervals. We also use a low-bandwidth coherent receiver for obtaining the time domain samples and a long short-term memory (LSTM) neural network as the chromatic dispersion-resistant classifier. The proposed scheme is cost efficient and compatible with our previously proposed multi-purpose OPM platform. Both simulation and experimental verification show that the proposed OSNR monitoring technique achieves high classification accuracy and robustness with low computational complexity.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical signal-to-noise ratio (OSNR) is one of the critical parameters reflecting the quality-of-transmission (QoT) in optical communication networks. Its estimation is one of the core tasks of advanced optical performance monitoring (OPM) technology [1,2]. The standard way to monitor the in-band OSNR is based on estimating the in-band noise power by taking the linear interpolation of the noise power at the two sides of the signal spectrum [3]. However, this standard method becomes obsolete with the advent of modern dense wavelength division multiplexing (DWDM) optical networks. Because it is almost impossible to measure correctly the out-of-band noise power due to the tight spectrum spacing. In addition, the optical channel filtering effect alters the noise power level at the channel edges and therefore undermines the noise estimation based on linear interpolation. Numerous methods have been proposed to improve the accuracy of the in-band OSNR monitoring in such scenarios [4–15], among which those based on machine learning (ML) have attracted lots of attention [8–15]. Most recently, long short-term memory (LSTM), Gaussian process (GP) and support vector regression (SVR) have been shown to be effective in estimating the in-band OSNR from the time-domain signals [10], the optical spectral components [11] and the Stokes parameters [12,13], respectively. In addition, the techniques proposed in [10,13–15] are for high-speed digital coherent receivers which require no additional hardware, whereas those described in [11,12] need standalone hardware and can work at the intermediate nodes of optical networks. In particular, one requires high-resolution optical power spectral data [11] and the other one uses low-bandwidth optical polarimeter [12].
Note that the ML-based OSNR monitoring schemes quoted above consider a continuous-input and continuous-output (CICO) learning problem. Namely, the true OSNR is unknown and assumed to be uniformly distributed within a certain range, whereas the estimated OSNR is a continuous random variable that has a probability density function (PDF) centered at the true value (i.e., unbiased). In this paper, we propose that an alternative to the method of continuous optical parameter monitoring is to discretize the output of the monitoring device and thus convert the CICO estimation into a classification problem. For example, a discrete classifier divides the continuous OSNR into many intervals of size 1 dB and only determines which interval the true OSNR falls in. In such a way, the OSNR monitor gives up the absolute estimations that must be characterized more accurately by their posterior probabilities in the CICO problems. Instead, the classifier (LSTM in our case) forces the OSNR estimations to fall in discrete intervals, which are modeled as discrete random variables with probability mass functions (PMF). The incentive to consider classification instead of continuous monitoring is due to the fact that the true OSNR of the system is always fluctuating while all OSNR monitoring devices are with finite precision. This results in random OSNR estimates along with certain confidential intervals. However, whether the statistical properties of the OSNR estimation are valuable for network controller is still questionable. The hope of OSNR classification is to de-emphasize the statistical fluctuation of the true OSNR values and hence to simplify the interpretation of the OSNR estimation. In addition, the proposed method exploits a low-bandwidth coherent receiver to obtain the time domain signal samples which makes it fully compatible with the multi-parameter OPM platform introduced in [16]. It is a cost-effective solution for OSNR monitoring which can be deployed at the intermediate nodes of the optical network. In this paper, we extend our previous results [17] by performing experimental verifications and giving more discussions.
2. Low-cost OPM with LSTM classifier
2.1. LSTM-NN
LSTM neural network (LSTM-NN) is a type of recurrent neural network (RNN), used mainly to solve the problem of gradient vanishing and gradient explosion during long sequence training [18]. LSTM usually performs better in long time sequences than the ordinary RNNs. LSTM-NN is characterized by its special structure, which contains internal memory blocks and three multiplicative units called control gates. The internal memory blocks are used to record useful information carried by the previous samples in the time sequences. Whereas, the control gates open or close the access to the internal memories according to the learned information. Figure 1(c) depicts an LSTM-NN block and shows its data flow through input, forget and output gates and a memory cell. The output yt, and cell content ct are determined by both current input xt and previous state yt−1 controlled by the three gates. The outputs of the gates, the content of the cell, and the gate states are calculated according to [19]
where W and U matrices contain the weights of connection f, i, o and c for the forget, input, output gate and the cell state, respectively. The * operator denotes the element wise product, σ is the logistic sigmoid function and h is an input and output tanh activation function [20]. These parameters will be adjusted automatically during the training procedure.
Fig. 1. (a) Block diagram of the proposed in-band OSNR monitoring method. Structure of (b) the LSTM-NN and (c) one node of the memory layer used in the proposed in-band OSNR monitoring.
2.2. Proposed low-cost OPM with discrete classifier
We study the application of the LSTM-NN classifier to the OSNR monitoring based on the time-domain signals [10,17], although this idea should be more general and applicable to the cases using spectral information as well. In favor of a low-cost OSNR monitoring device, we propose to use a low-bandwidth single-polarization coherent receiver for data collection. Figure 1(a) illustrates the schematic of the proposed OSNR monitoring technique. The quadratures (I/Q) data obtained by the coherent receiver are fed subsequently into an LSTM-NN classifier, which could be implemented in a digital signal processor and outputs estimation of OSNR intervals. Examples of these OSNR intervals are {[1 1.99], [2 2.99], [3 3.99], etc.} with each of these intervals labelled by {1, 2, 3, etc.}. The OSNR monitoring scheme is fully compatible with our previously proposed universal OPM hardware platform [16] and hence can be considered as one of the subsystems. In contrast, the methods given by [10] and [13] work inside the digital coherent receivers, which requires no additional hardware except for more computational resources or more gates in cases of real-time implementation. The work presented in [11] needs dedicated device for obtaining the high-resolution spectral data, which is of interest at optical nodes that can provide such devices. Reference [12] in principle can use a low bandwidth polarimeter which is more cost effective than our scheme. However, it only offers OSNR monitoring whereas our proposed scheme can share hardware with other OPM tasks as described in [16].
Figure 1(b) shows the structure of the LSTM-NN classifier, which consists of four layers. Namely, the input layer with 8 neurons, the memory layer with 48 neurons, the hidden layer with 64 neurons, and finally the output layer with 10 neurons. The output is then mapped to 10 probabilities with the SoftMax activation function, indicating the probabilities of which OSNR intervals the current input to the classifier belongs to. The one with the maximum probability represents the estimated OSNR interval. The cross-entropy loss function used to evaluate the convergence of the LSTM-NN classifier during the training process is written as
where Ty (My) denotes the soft classification of the input (output) OSNR, represented as a k-tuple vector, and n is the number of samples. We use in our study k=10 OSNR intervals but it should be adjusted accordingly in the real use cases. Depending on the real scenarios, both the maximal OSNR range and the size of each OSNR intervals could be adjusted and the classifier could be retrained to adapt to new optical network configurations. The Ty vector encodes the distances of any input OSNR to its two nearest integer neighbors (e.g., 15.2 dB is encoded as having 80%/20% chances being classified into 15 dB and 16 dB respectively and the input feature vector is therefore Ty = [0.8, 0.2, 0, 0, 0,…] for OSNR range of 15–24 dB). For integer inputs, it simply reduces to the One-Hot encoding [21]. One could also consider other types of encoding of the input vector (e.g., encoding the likelihood of 15.2 dB assuming a certain probability distribution of all the possible OSNR values in a given range). Note that as the classification intervals approaching zero, the input and the output vectors tend to be continuous. However, the cross-entropy function would still have a distinct form compared to the common loss functions (e.g., the mean squared error (MSE) type of loss functions) used in continuous regression problems. Whether the classification described above converges into an existing continuous regression model desires further investigation.3. Simulation results and discussions
We study the performance of the low-cost OSNR monitoring by simulating a PDM-16QAM system with a 30 GHz baudrate. We also simulate a single-mode fiber transmission with varying distance of 80∼120 km to include the chromatic dispersion (CD) effect as shown in Fig. 3. Optical ASE noise is loaded for each distance to adjust the actual OSNR value of the signal, varying from 15 dB to 24 dB with 1 dB interval. At the monitoring point, we use a low-bandwidth coherent receiver with 1 GHz lowpass filters and 5 GHz ADCs to obtain the sequential I/Q data. Segments of the I/Q data consisting of 64 samples per quadrature are first organized into a two-dimensional array of size 2 × 64 and then duplicated into 8 × 64 to match the size of the input layer of the LSTM-NN without additional pre-processing. The 4-fold duplication produces the most stable training process of the classifier. We conjecture that by duplicating the input the number of adjustable parameters of the memory layer increases and this helps the searching of the optimal parameter set. Since each input OSNR is an integer, we simply adopted the one-hot encoding for the input feature of the LSTM explained in the last section. To increase the stability and accuracy of the classifier, one could use more non-integer inputs for training. In total 3000 sets of data are collected and then divided into the training data set (75%) and the testing data set (25%). The activation functions of LSTM are leaky rectified linear units (Leaky ReLU) except for the output layer, which uses SoftMax instead. The optimizer we adopted in the training procedure is Adaptive gradient momentum (Adam), which combines the advantages of adaptive gradient (AdaGrad) and root-mean-square prop (RMSprop) optimization algorithms [22]. The learning rate is set to be 0.01 throughout the training process, Furthermore, gradient clipping and dropout (drop probability of 0.3) are used during the training process in order to keep the training process more stable and improve the generalization ability of the LSTM-NN [23]. The LSTM-NN is implemented with Pytorch deep learning framework. The training and testing process are performed on a personal computer with graphics processing unit (GPU) accelerator.
Fig. 2. Simulation results: (a) Losses versus the iteration, (b)The accuracy rate of OSNR monitoring versus iterations, CD equals to 1700 ps/nm, (c) Overall accuracy rate of OSNR monitoring averaged over 15 to 24 dB versus the CD values, (d) The PMF of the in-band OSNR monitoring of 19 dB OSNR.
Fig. 3. Simulation setup of the proposed low-cost OPM with LSTM-NN classifier. The OSNR is controlled by adjusting the noise source.
Fig. 4. Experimental results: (a) Losses versus the iteration, (b) Accuracy rate of OSNR monitoring versus iterations with CD equal 1700 ps/nm, (c) Accuracy rate of OSNR monitoring versus the CD values, (d) The PMF of the in-band OSNR monitoring results for true OSNR of 19 dB.
Figure 2(a) and Fig. 2(b) shows respectively the evolution of the loss and the accuracy rate of the LSTM-NN with respect to the number of iterations when the link CD is equal to 1700 ps/nm. It is seen that after 1000 iterations, the loss is close to zero. The small rise in the loss curve is due to the random training data, we have observed other curves without such rises. It shows that the predicted OSNR distribution of the current training samples by the neural network is very close to the true distribution. The accuracy rate of the classification using the test samples changes synchronously with that of the training samples. Figure 2(c) shows the accuracy rate of LSTM-based OSNR monitoring with respect to the varying CD values while the bandwidth of LPF is equal to 1 GHz. We also consider the length of the data samples per quadrature as time steps of the memory layer of the LSTM-NN. We observe that as the time steps increase, the LSTM classifier performs better, at the expense of increased computational complexity. The accuracy rate of the OSNR prediction is insensitive to the CD values. Because, for each CD value, the LSTM-NN is trained independently. Note that this is different from the joint monitoring scheme such as the one in [10]. Here we do not require the LSTM-NN to estimate the CD as well, although in principle the joint CD and OSNR monitoring should also be feasible provided a joint cross-entropy loss is considered [10]. The exclusive of CD fluctuating in the test samples provide a more accurate assessment of the OSNR monitoring idea.
The LSTM-NN generates only integer estimates, which in our case cover the OSNR from 15 to 24 dB with 1 dB intervals. The range could be enlarged further due to the memory limit of our GPU accelerator. The OSNR range could be made arbitrarily large and the intervals could be made arbitrarily small by expanding the output layer of LSTM classifier. However, it would be incautious to state that with the infinitesimal OSNR intervals, the proposed method converges into the classical regression-based method [10]. Although by training the classifier with smaller OSNR intervals would improve the monitoring resolution, careful study should be performed to reveal more about the convergence property. After training the neural network, the OSNR value of 19 dB is tested and the PMF of the classifier output is shown in Fig. 2(d). The result with full-speed ADCs (60 GSps) is also plotted for comparison. The low bandwidth LPF (1 GHz) and low sampling rate ADC (5 GSps) flatten the PMF slightly. Table 1 and 2 tabulate the classification results in detail. The standard deviations (STDs) of the results obtained by using time step of 48 are within 0.6 dB, whereas the STDs reduce to 0.4 dB for time step of 64. Note that these results are obtained by using very short data segments (2 × 64 samples) for each point. In practice, one could also average over several estimates to improve the OSNR monitoring accuracy. This increases the OSNR estimation variance and latency but keeps the neural network at low complexity. By reducing the size of data sets, we obtained the results covering the OSNR range 15–30 dB, as shown in Table 3. Due to the lack of enough training data, the MAE of these results are found to be larger than those shown in Table 1 for the same set of simulation parameters. The OSNR monitoring accuracy is found to be insensitive to the CD and the bandwidth of LPF to some extent. When compared to the LSTM with full-speed ADC and CICO estimation, our method not only requires low sampling rate but also uses fewer neurons. We have {8, 48, 64, 10} neurons in the four layers of LSTM whereas [10] uses {4, 160, 128, 2} respectively. Note that the mean absolute errors (MAE) in our simulation are slightly better than that given in [10], which could be attributed to the fact that the OSNR monitoring is performed with classifier trained independently under different CD, instead of joint CD and OSNR monitoring in [10].
Table 1. Performance of the LSTM classifier over the test data set with 1 GHz LPF, 5 GHz sampling rate, 1700ps/nm link CD, and time steps of 48.
Table 2. Performance of the LSTM classifier over the test data set with 1 GHz LPF, 5 GHz sampling rate, 1700ps/nm link CD, and time steps of 64.
Table 3. Performance of the LSTM classifier over the test data set with 1 GHz LPF, 5 GHz sampling rate, 1700ps/nm link CD, and time steps of 48.
4. Experimental verification
4.1 Experimental setup
Experiments are carried out with a 30 Gbaud DP-QPSK signal to validate the proposed low-cost OSNR monitoring with LSTM classifier. The experiments follow the setup depicted in Fig. 5. A distributed feedback (DFB) semiconductor laser at 1550 nm acts as the light source at the transmitter side. The DP-QPSK signal is generated by using an arbitrary waveform generator (AWG) and optical DP-IQ modulator. A standard single mode fiber (SSMF) link with variable length of 50 km, 80 km, and 100 km is used to introduce different CD values, respectively. The optical ASE noise is generated with an erbium-doped fiber amplifier (EDFA) and then loaded to the signal to adjust the OSNR value of the received signal. At the receiver, the signal is mixed with the local oscillator (LO) for the single polarization optical coherent detection. The electrical signals after the balanced photodetectors (BPD) are filtered by 1 GHz low-pass filters (LPF) and then sampled by 5 GSps ADCs. The mismatch between the receiver diagrams in Fig. 5 and Fig. 3 is simply due to the lack of a true low bandwidth coherent receiver, which must be emulated by using high bandwidth receiver with external lowpass filters. For the data processing, a series of consecutive samples of length 36, 48 or 64 are intercepted from the in-phase component (I) and quadrature component (Q) branches of the received signal. Therefore, the time steps of the LSTM are comparable to those used in the simulations. Then, the two branches are duplicated four times to match the input size of the first layer of LSTM-NN. Hence, the input data are always organized in the two-dimensional array of size 8 × 36 (8 × 48, or 8 × 64) and fed into the LSTM-NN without additional pre-processing. For each OSNR value, in total 3000 sets of data samples are collected. Then, all sets are randomly divided into training set (75%) and testing set (25%) in order to train and test the LSTM-NN, respectively.
Fig. 5. Experimental setup of the proposed low-cost OPM with LSTM-NN classifier. A VOA is used to ensure the received optical power is about −20 dBm at the monitoring point. The ASE noise source consists of another EDFA and VOA. DP: dual polarization; AWG: arbitrary waveform generator; VOA: variable optical attenuator; LPF: low-pass filter; ADC: analog-to-digital convertor.
4.2. Results and discussion
The experimental results of the proposed OSNR monitoring based on low-bandwidth coherent receiver and LSTM classifier are shown in Fig. 4. Since the LSTM-NN used in the proposed scheme only generates integer outputs, the performance is evaluated with the classification accuracy. The experimental results are consistent with the simulation results presented earlier. The rises in the curves of Fig. 4(a) and 4(b) are also due to the random training data. We have observed curves with/without such rises when using other set of data. Moreover, Table 4 to 6 (at the end of the paper in prior to the reference section) provide the details of classification results with in total 750 sets of test data and time steps 36, 48 and 64, respectively. The LSTM classifier successfully distinguishes different OSNR intervals with high probabilities. One may argue that the maximum error of the proposed method is large, which might lead to serious problems in real use cases. However, larger time steps reduce the outage probabilities and promises better performance, albeit with more computation. As shown in Table 5, the large estimation errors almost vanish with time steps 64. To keep the LSTM-NN low complexity, a trick to reduce the large error would be averaging few estimates of a small time-step classifier over several runs and using the averaged value as the final estimation. Note that the true OSNR values are measured with a standard optical spectral analyzer (OSA) and hence these values also vary within a small range. On the other hand, the LSTM classifier always outputs integer OSNR estimates as shown in these tables. Also, it is evident that the classifier does make mistakes with small probabilities, due to the fact that there are many uncontrollable factors in real experiments. However, the high classification accuracy, small MAEs and small STDs indicate that the LSTM classifier does have good performance with low computational complexity. Note that in the experimental results, the MAEs are again slightly better than that obtained via the joint CD and OSNR monitoring [10]. When compared to the regression-based OSNR monitoring, the mean-square error (STD squared) of our results are worse than the simulation results in [11]. However, the simulations are performed without any CD effect. The work presented in [12] does not give statistics on monitoring errors, which we cannot compare here. The method given by [13] results in about 0.21 dB estimation STD, which is slightly better than what is achieved here. Moreover, the fiber launch power is kept below 0 dBm in our experiments such that little fiber nonlinearity noise is generated. Note that the current setting of the LSTM classifier cannot tell apart the fiber nonlinearity noise from the ASE noise. By including more optical parameters indicating the fiber link setup may offer a useful solution for nonlinearity resistant OSNR monitoring solution.
Table 4. Performance of the LSTM classifier over the test data set with 1 GHz LPF, 5 GHz sampling rate, 1700ps/nm link CD, and time steps of 36.
Table 5. Performance of the LSTM classifier over the test data set with 1 GHz LPF, 5 GHz sampling rate, 1700ps/nm link CD, and time steps of 48.
Table 6. Performance of the LSTM classifier over the test data set with 1 GHz LPF, 5 GHz sampling rate, 1700ps/nm link CD, and time steps of 64.
5. Conclusion
In conclusion, we propose to consider the conventional continuous OSNR monitoring as a classification problem. A low-cost in-band OSNR classification method is proposed based on a low-bandwidth coherent receiver and an LSTM classifier. The proposed method is fully compatible with our previously proposed multi-parameter OPM platform. By restricting the OSNR estimates to be integer values only, the OSNR monitoring simplifies the used neural network and still achieves reasonable estimation accuracy and robustness. Both simulation and experimental results show that the LSTM classifier based OSNR classification achieves high classification accuracy with small complexity. The OSNR monitoring is insensitive to the link CD if the classifier is properly trained with the CD value. This idea can be easily generalized to other OPM problems as well.
Funding
National Key Research and Development Program of China (2019YFA0706300); National Natural Science Foundation of China (61525502, 61772233); Science and Technology Planning Project of Guangdong Province (2017B010123005, 2018B010114002, 2020B0303040001); Key Project for Science and Technology of Guangzhou City (201904020048).
Disclosures
The authors declare no conflicts of interest.
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