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Abstract
Modulation format identification (MFI) and optical signal-to-noise ratio (OSNR) monitoring are important portions of optical performance monitoring (OPM) for future dynamic optical networks. In this paper, we proposed a fusion module few-shot learning (FMFSL) algorithm as an improvement upon the ordinary few-shot learning algorithms for image recognition with the specialty in adopting a combination of a dilated convolutional group and an asymmetric convolutional group to advance the feature extraction. FMFSL algorithm is applied in MFI and OSNR monitoring in coherent optical communication systems with its performance investigated in both back-to-back and fiber transmission scenarios using small-scale constellation diagrams. The results show that FMFSL algorithm can achieve 100% accuracy in MFI and higher OSNR monitoring accuracy compared to the few-shot learning algorithms Deep Nearest Neighbor Neural Network (DN4) and Prototypical Nets (PN) with 2.14% and 4.28% for 64QAM and 3.38% and 8.06% for 128QAM, respectively, without much increase in time consumption. Furthermore, the trained FMFSL algorithm remains excellent in MFI and OSNR monitoring without retraining while employed in back-to-back transmission scenarios with smaller OSNR intervals and fiber transmission scenarios with different amounts of Kerr nonlinearity, demonstrating its high capabilities in generalization and robustness. FMFSL algorithm provides a potential solution for OPM in future dynamic optical networks as a novel machine learning tool.
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1. Introduction
Dynamic optical networks are advanced networks that can flexibly adjust their resource allocation and signal transmission parameters based on the real-time demands and conditions of the networks [1,2]. Within such networks, it is crucial to monitor various network parameters to ensure high-quality service and allocate adequate system margin. Consequently, optical performance monitoring (OPM) is indispensable to enable flexibility and efficiency for dynamic optical networks [3–7]. Modulation format and optical signal-to-noise ratio (OSNR) are two important monitoring parameters in OPM. Modulation format identification (MFI) can provide information on the modulation format to assist system resource allocation and improve transmission performance [8,9]. OSNR is directly related to the bit error rate (BER) of optical signal transmission and can reflect the transmission quality of the optical networks [10,11].
With the continuous development of artificial intelligence techniques, machine learning has attracted widespread attention for solving complex problems and driving innovation due to its powerful self-learning and computational capabilities [12,13]. Machine learning has been widely applied in MFI and OSNR monitoring which guarantees the accuracy and effectiveness of the MFI and OSNR monitoring. Various schemes based on machine learning have been proposed to identify modulation formats and monitor OSNR [14–18]. However, these schemes typically struggle to extract key features from the limited data and require a large amount of training data to achieve satisfactory model performance. For example, 100 amplitude histograms or 100 constellation diagrams are required for each OSNR value of each modulation format [16,17]. Moreover, a typical drawback of these schemes is their very limited generalizability. Changes in transmission scenarios and parameters necessitate retraining models and even re-collecting extensive new data. This process is complex and time-consuming, inevitably increasing training costs. Generalizability refers to the algorithm's ability to perform effectively on new data, representing its adaptability to new situations. Thus, it is crucial to develop a joint MFI and OSNR monitoring model with high generalizability for dynamic optical networks that can be initially trained on a small-scale dataset in one scenario and generalized to other different scenarios. Few-shot learning with limited data is a promising method that uses prior knowledge to enable rapid self-learning in new tasks [19–22]. However, limited samples may affect more or less the model's ability in extracting key features, and thus the performance and generalizability.
In this paper, we address the challenges in extracting key features in few-shot learning from limited data by proposing a fusion module few-shot learning (FMFSL) algorithm, which adopts a combination of a dilated convolutional group and an asymmetric convolutional group to extract features. The dilated convolutional group enhances the model's feature perception by expanding the receptive field without adding parameters [23]. Meanwhile, the asymmetric convolutional group boosts the model’s expressive capacity and sensitivity to multi-scale features with varying kernel sizes [24]. By capturing broader contexts and extracting multi-scale features, FMFSL algorithm can learn more powerful and representative features. This enhanced feature extraction capability enables the model to adapt more widely to different data distributions and tasks, improving its performance on unseen data and elevating its generalizability. Thereby the proposed FMFSL algorithm improves upon the ordinary few-shot learning algorithms for image recognition by enhancing feature extraction capabilities and model’s generalizability. FMFSL algorithm can have more extensive usage in other image recognition fields as an ordinary few-shot learning algorithm. We employ it for joint MFI and OSNR monitoring for fast adaptation to dynamic optical networks. Remarkably, only 20 constellation diagrams in the dataset are required for each modulation format at each OSNR, largely reducing the number of samples. Constellation diagrams are commonly used as the data feature representations in OPM, providing essential monitoring information for analyzing the quality and performance of signals. The shape of the constellation point distribution can be used to extract information about the modulation format, while the dispersion of constellation points can represent the noise impact on the signal during transmission. The exceptional capability of FMFSL algorithm in extracting key features from samples makes it well-suited for the MFI and OSNR monitoring based on constellation diagrams. Treating MFI and OSNR monitoring as classification problems proves to be effective [15–18]. The randomness of various noise sources in the system leads to fluctuations and discontinuities in the true OSNR values, and the monitoring precision is limited by OSNR monitoring equipment. These factors result in the random OSNR values and the existence of a certain confidence interval, and furthermore to inspire us to consider the OSNR monitoring as a classification task instead of a continuous monitoring task. In this work, both back-to-back and fiber transmission cases are dealt with. The performance of FMFSL algorithm was compared with a few of other few-shot learning algorithms, and its generalizability in back-to-back transmission scenarios with smaller OSNR intervals and fiber transmission scenarios with different amounts of Kerr nonlinearity was verified. The results demonstrate that the proposed FMFSL algorithm can achieve high accuracy, show strong generalizability with limited training data, and is applicable in future dynamic optical networks.
2. Simulation setup
In this study, we set up the simulated dual-polarization coherent optical communication systems based on simulation software (Fig. 1). We employed a pseudo-random binary sequence (PRBS) with a length of 216 to modulate optical signals. The signal rate for every modulation format is 25Gbaud. For the back-to-back case, we generated nine modulation formats including BPSK, QPSK, 8PSK, 8QAM, 16PSK, 16QAM, 32QAM, 64QAM, and 128QAM. We used an OSNR setting block to set different OSNR values with a step of 0.5 dB and 1 dB, respectively. The specific values are shown in Table 1. For the case with fiber transmission, we generated three commonly used modulation formats, QPSK, 16QAM, and 64QAM. The transmission link was composed of N spans of an 80 km standard single-mode fiber (SSMF) with dispersion parameter D, attenuation coefficient α, and nonlinear coefficient γ of 16.75 ps/nm/km, 0.2 dB/km, and 2.6 × 10−20 m2/W, respectively. Three transmission distances were selected for each modulation format, the longest fiber transmission distances are up to 1040 km for QPSK, 800 km for 16QAM, and 640 km for 64QAM. And three launched powers of 0, 3, and 6 dBm were selected for QPSK, 16QAM, and 64QAM to identify the impact of Kerr nonlinearity. Fiber loss of each span was compensated using an EDFA with 4 dB noise figure. A variable optical attenuator (VOA) was used to adjust the OSNR with a step of 1 dB. The specific values are also shown in Table 1. At the receiver, the signal was passed through an optical bandpass filter (OBPF) with bandwidth of 75 GHz in front of the receiver to filter out the out-of-band noise and coherently detected by two 90° optical hybrid receivers. After synchronous sampling by four analog-to-digital converters (ADCs), signals containing the in-phase (I) and quadrature (Q) information were obtained. The I and Q information were then sent into digital signal processing (DSP) module for further processing, which mainly comprised IQ imbalance compensation, chromatic dispersion (CD) compensation, timing recovery, adaptive equalizer, frequency offset compensation and carrier phase estimation. Finally, the generated constellation diagrams were sent to the FMFSL model for combined MFI and OSNR monitoring.
Table 1. OSNR values in back-to-back and fiber transmission scenarios.
3. Model framework and operating mechanism
Our proposed FMFSL algorithm is an advance on the ordinary few-shot learning algorithms for image recognition with the main optimization for the ordinary convolutional group in the feature extraction module. Specifically, it replaces the ordinary convolutions with a combination of dilated and asymmetric convolutions to reduce the feature information loss and improve the performance of the feature extraction module. Meanwhile, it incorporates a feature fusion operation to fuse features from different stages in order to obtain more comprehensive and representative features. As shown in Fig. 2, the FMFSL algorithm is composed of two main modules: feature extraction module δ and image classification module θ. The feature extraction module plays an important role in extracting deep local features from all images. It consists of a dilated convolutional group and an asymmetric convolutional group for extracting features. The dilated convolutional group consists of three 3 × 3 convolutional layers, where each layer has a different dilation rate (d = 1, d = 2, d = 3). This dilation rate is chosen to avoid the loss of sample information due to grid effects [25]. The main function of the dilated convolution is to expand the perceptual area while preserving the dimensionality of the feature map, thereby enabling information extraction without losing critical data [23]. The asymmetric convolutional group includes three asymmetric convolutional layers of 3 × 3, 3 × 1, and 1 × 3, which could enhance the representation capability of the standard square convolutional kernel and improve the robustness of the model to rotation [24]. There are three reasons for placing the dilated convolutional group before the asymmetric convolutional group. The first is that the dilated convolutional group can capture features of different scales with different dilation rates (1, 2, 3), allowing the model to extract multiscale information in the initial stages, and aiding in better understanding of both the global structure and local details in the input data. The second is to further capture directional features. The third is to leverage the multiscale characteristics of dilated convolutions, providing richer input features for the asymmetric convolutions and thus enhancing the model's performance and robustness. Each convolutional layer in the feature extraction module is followed by a rectified linear unit (ReLU) and batch normalization (BN) to enhance model performance and reduce overfitting [26,27]. It is important to note that unlike the deep features obtained from the fully-connected layers in traditional feature extraction networks, the output of the feature extraction module is deep local features that are a fusion of the features extracted from the dilated convolutional group and the asymmetric convolutional group. Summarizing the local features of an image into a compact image-level representation through global average pooling or fully-connected layer mapping could lose considerable discriminative information. It will not be recoverable when the number of training examples is small [28]. Therefore, when calculating class similarity based on features, we do not use image level feature vectors. Instead, we use several deep local features, with each deep local feature corresponding to a partial feature representation of the image. We directly compare the similarity between the input image and the deep local features of each class, using this information for classification. Specifically, given an image $X$, the module $\delta (X )$ outputs a three-dimensional tensor of $h\textrm{ } \times \textrm{ }w\textrm{ } \times \textrm{ }d$. This tensor can be viewed as consisting of $n\textrm{ }({n\textrm{ } = \textrm{ }h \times w} )$ features of feature dimension d, which is represented as follows:
where δ is the feature extraction module, $x_i$ is the $i$-th deep local feature, and $R$ is a set of $d\textrm{ } \times \textrm{ }n$. In our study, given an image with a resolution of 84 × 84, we can get $h = w = 72$ and $d\textrm{ } = \textrm{ }64$.The image classification module θ constructs the deep local features of all training images in a category as a space of deep local features. In this space, the cosine distance from the deep local features of the images to the deep local features of each category is computed, and then the nearest neighboring category is searched using the K-Nearest Neighbors (KNN) algorithm. Specifically, after the feature extraction module δ, a query image $q$ is represented as a collection of multiple deep local features $\delta (q) = [{x_{1}}, \ldots, {x_{n}}] \in {R^{d \times n}}$, and for each deep local feature $x_i$, we find its k-nearest neighbors $ {\hat{x}_i^j} |_{j = 1}^k$ in a class c. Then we calculate the similarity between each deep local feature $x_i$ and each $\hat{x}_i$ using the cosine distance, and sum these similarities as the similarity value between images $q$ and class c, which can be expressed by using the following equation [22]:
The feature extraction module and the image classification module are trained end-to-end within the same network. The trained model is then tested on a test set to evaluate its performance. As illustrated in Fig. 3, the entire training process employs an episodic training mechanism, in which each task is treated as a training instance and the task’s internal algorithm is updated through episode (task by task). Each episode consists of a support set and a query set. For training and test, C classes with K labeled samples per class, are randomly selected from the dataset as the support set S. Then a certain number of samples from the remaining data in these C classes are chosen as the query set Q, and the model is trained by minimizing the error calculated on the query set. In other words, the model is required to learn how to distinguish each unlabeled sample in Q according to the set S, and such a task is called the C-way K-shot problem [22]. Each episode is constructed to solve this problem, and the criterion of the episodic training mechanism is to maintain consistency between the training and test conditions. We construct a large number of tasks similar to the target small-sample task in the training set, and multiple episodic training tasks are randomly sampled to learn the target classification model. After training, the trained model can be used to classify the samples in the query set Q according to the support set S. In traditional supervised learning, during each iteration of the model's training process, a certain number of samples are typically selected for learning and making output predictions. However, in few-shot learning, it is common to construct multiple tasks from the data, each task contains multiple data samples, and the model's training treats each task as a training instance, updating the task algorithm one by one, and ultimately making output predictions. Through the episodic training mechanism, the model can learn transferable knowledge despite the limited number of samples. This strategy allows the model to continuously simulate the test environment during the training process, resulting in an algorithm that can better adapt to the test environment [29,30]. During each iteration of episodic training, the support set S and the query image q are inputted into the FMFSL model. With the feature extraction module δ, we can obtain all depth local representations of these images. Then the module θ calculates the similarity of images to classes between q and each class using Eq. (2), assigning the highest scoring class to q.
Few-shot learning aims to train a model that has good generalization performance. Unlike traditional convolutional neural networks, where the training and test sets share the same classes, few-shot learning requires disjoint training and test sets. The trained model is tested on completely unseen classes, to ensure that the model can correctly handle unknown classes. In this study, we collect 20 constellation diagram images for each OSNR value of each modulation format. The shape of the constellation point distribution can be used to extract information about the modulation format, while the dispersion of constellation points can represent the impact of noise on the signal during transmission. Therefore, constellation diagrams assist the model in extracting crucial information. In addition, constellation diagrams exhibit similar characteristics across different transmission scenarios, which is highly beneficial for the development of OPM models with good generalization performance. The dataset for the back-to-back case contains 9 modulation formats and 16 OSNR values for each modulation format. The two datasets with OSNR intervals of 0.5 dB and 1 dB, each contain 20 × 9 × 16 = 2880 images, respectively, which are divided into a training set and a test set at a 50%:50% ratio. For the fiber transmission case, there are two scenarios: (1) three datasets under 0 dBm launched power for three different transmission distances; and (2) another three datasets under three different launched powers with 640 km transmission distance. Each dataset contains 3 modulation formats and 16 OSNR values for each modulation format with 20 × 3 × 16 = 960 images and is only used to test the generalizability of the trained model. Each image in the dataset is assigned a label, which is composed of binary bits that reflect the modulation format and OSNR information of the image. Considering that our scheme has 9 modulation formats and 16 OSNR values for each modulation format, thus the label consists of 25 bits, first 9 bits denote the modulation formats, with only one bit set to “1” and the rest set to “0”, which indicates the corresponding modulation format class. For example, 000000001 refers to BPSK, while 100000000 refers to 128QAM. Similarly, the last 16 bits represent the OSNR value, with only one bit set to “1” and the rest 15 bits set to “0”, indicating the corresponding OSNR value. For example, 0000000000000001 refers to the minimum value of the OSNR range for the modulation format, while 1000000000000000 refers to the maximum value of the OSNR range for the modulation format.
All training in this study is conducted via the episodic training mechanism, using the C-way K-shot task framework. The operating mechanism of the FMFSL algorithm is illustrated in Algorithm 1. Specifically, 4000 episodes are randomly sampled and constructed during the training process to train the model through the episodic training mechanism. For a 5-way 1-shot task, each episode consists of 5 support images and 75 query images. During the training process, the model is trained by minimizing the error computed on the query set. The PolyLoss is selected as the loss function [31], the loss function is minimized by the Adam optimizer. The initial learning rate is set to 1 × 10−3 and the learning rate is dynamically adjusted during the training process, while the value of k is set to 1. For the test phase, 200 episodes are randomly sampled from the test set and used for evaluation. The top-1 classification accuracy is adopted as the evaluation criterion. The test process is repeated five times, and the average accuracy is calculated as the final result. The training process is conducted end-to-end, with the model being saved upon completion of training. Subsequently, the model is tested on the test set without any fine-tuning.
Algorithm 1. Operating mechanism of the FMFSL
4. Results and discussion
4.1 Modulation format identification and OSNR monitoring in back-to-back transmission scenarios at 1 dB OSNR interval
4.1.1 Modulation format identification
We first evaluated the performance of FMFSL algorithm for MFI in the case of back-to-back transmission. We conducted the 5-way 1-shot tasks to calculate the accuracy of FMFSL algorithm in MFI. As shown in Fig. 4, even with very limited samples (only 20 constellation diagrams required for each modulation format at each OSNR) the MFI accuracy can reach 100% for all nine formats. The differences between different modulation formats are distinct, allowing FMFSL algorithm to easily identify nine formats with limited data.
4.1.2 OSNR monitoring
For OSNR monitoring, it is significantly more challenging than MFI because the features presented by the adjacent OSNR values are very similar, which increases the probability of misclassification. Thus, we focus more on the OSNR monitoring. The performance of the FMFSL model in OSNR monitoring was validated using a dataset with 1 dB interval for the back-to-back case, as depicted in Fig. 5. The FMFSL model demonstrated excellent performance in the OSNR monitoring task, achieving accuracy of 100% for most modulation formats, except for 64QAM and 128QAM, where the accuracy was 98.95% and 88.25%, respectively. This decrease in accuracy can be attributed to the increasing modulation order of the modulation formats, which results in a greater number of symbol points, smaller spacing between symbol points, and more complex features, thus raising the difficulty of OSNR monitoring. The deep local features extracted by the model in this study outperform the features obtained from existing CNN network models, which typically add a fully-connected layer after the convolutional layer to obtain a feature representation of an image for final classification. However, the number of features obtained in this way is limited and information loss occurs when passing through the fully-connected neural network. Therefore, we only use the deep local features provided by the convolutional layer in our model to calculate the distance from the image to each class. This approach benefits from the exchangeability of deep local features, and the class distribution composed of deep local features is more efficient at the image level, especially for few-shot learning, where richer deep local features are similar to the performance improvement brought by the data augmentation. To illustrate this point, we added a fully-connected layer behind the asymmetric convolutional group of the FMFSL model as a commonly used CNN model for comparison (denoted as FMFSL with FC). As shown in Fig. 5, the FMFSL with FC, which uses features processed through a fully-connected layer to compute similarity, exhibits inferior accuracy in OSNR monitoring, particularly for higher-order modulation formats. It is clear that there is a significant drop in monitoring accuracy, which indicates that the commonly used network models are not applicable to few-shot learning. Therefore, algorithms more adapted to few-shot learning are needed to solve such problems.
Fig. 5. The accuracy of OSNR monitoring with four schemes at 1 dB OSNR interval for the back-to-back case.
In addition, the effectiveness of incorporating dilated and asymmetric convolutions was verified. The OSNR monitoring performance of FMFSL algorithm without dilated and asymmetric convolutions (denoted as FMFSL without DC and FMFSL without AC, respectively) was evaluated. Specifically, FMFSL without DC adopts asymmetric convolutions instead of dilated convolutions, while FMFSL without AC uses only dilated convolutions instead of asymmetric convolutions. Both FMFSL without DC and FMFSL without AC use the deep local features to compute the similarity. As seen in Fig. 5, FMFSL without DC and FMFSL without AC, which utilize deep local features, also outperform FMFSL with FC which uses features processed through a fully-connected layer, in terms of OSNR monitoring. Furthermore, the FMFSL model that combines dilated and asymmetric convolutions exhibits superior OSNR monitoring performance compared to both FMFSL without DC and FMFSL without AC. The enhanced performance of the FMFSL model with combined dilated and asymmetric convolutions can be attributed to the ability of dilated and asymmetric convolutions to retain key feature information and augment the model's characterization capabilities. The performance of the model is improved with the addition of dilated and asymmetric convolutions.
As shown in Fig. 6, this paper also compares the performance of two other prevalent and effective few-shot learning algorithms, Deep Nearest Neighbor Neural Network (DN4) and Prototypical Nets (PN), in the OSNR monitoring task of using 1 dB OSNR interval dataset for the back-to-back case. The results show that FMFSL algorithm outperforms DN4 and PN algorithms, especially for higher-order modulation formats such as 64QAM and 128QAM. In particular, compared with DN4 and PN algorithms, FMFSL algorithm gains 2.14% and 4.28% improvements in accuracy for 64QAM OSNR monitoring task, and 3.38% and 8.06% improvements in accuracy for 128QAM OSNR monitoring task, respectively. The results suggest that the FMFSL algorithm with the incorporation of dilated and asymmetric convolutional groups and the utilization of deep local features is more effective for few-shot learning in OSNR monitoring compared to other advanced algorithms.
Fig. 6. The accuracy of OSNR monitoring with three few-shot learning algorithms at 1 dB OSNR interval for the back-to-back case.
To further demonstrate FMFSL's performance in OSNR monitoring, we also calculate the mean square error (MSE) between the predicted values and the actual values as the OSNR monitoring error. Table 2 provides the OSNR monitoring accuracy and error for FMFSL algorithm. From Table 2, it can be seen that when the OSNR monitoring accuracy of FMFSL algorithm reaches 100%, the predicted values match the actual values perfectly. For 64QAM, the OSNR monitoring error is 0.042 dB, while for 128QAM, the OSNR monitoring error is 0.654 dB. This is primarily due to the smaller space between constellation points in the 128QAM constellation diagrams, making OSNR monitoring more challenging. However, it is worth noting that an OSNR monitoring error of 0.654 dB is considered good enough in the field of OSNR monitoring. Generally, OSNR monitoring errors within 1 dB are acceptable. These results demonstrated the exceptional performance of FMFSL algorithm in OSNR monitoring.
Table 2. OSNR monitoring accuracy and error of FMFSL algorithm at 1 dB OSNR interval for the back-to-back case
In addition, the model complexity is also taken into account. As summarized in Table 3, we evaluated the model's performance by calculating its actual time consumption and the total number of parameters, which reflect the model's operational efficiency and size. Compared to DN4 and PN algorithms, FMFSL algorithm exhibits a reasonable increase in network complexity, but it can extract more crucial and detailed feature information. In fact, testing time of the model is the key factor that affects processing performance, as once the model is trained, it can be directly applied to MFI and OSNR monitoring with no need of retraining. the testing time of one episode for the FMFSL model is 0.25s with just a slight increase compared to the 0.15s for PN and 0.17s for DN4. This slight increase is also reasonable, especially while the final OSNR monitoring performance has been improved. For example, compared to DN4 and PN algorithms, FMFSL algorithm can improve the OSNR monitoring accuracy for 64QAM by 2.14% and 4.28%, and for 128QAM by 3.38% and 8.06%, respectively. Thereby, we consider such a minor increase in complexity to be acceptable.
Table 3. Comparison of three few-shot learning algorithms on time consumption and total parameters
4.2 Generalizability of FMFSL algorithm in different transmission scenarios
4.2.1 OSNR monitoring in back-to-back transmission scenarios at 0.5 dB OSNR interval
This section evaluates the generalizability of FMFSL algorithm in back-to-back transmission scenarios under various OSNR intervals. We trained FMFSL algorithm using datasets with OSNR intervals of 1 dB and 0.5 dB, defined as FMFSL_1 and FMFSL_0.5, respectively. The results in Fig. 7 show that as the OSNR interval of the dataset reduces from 1 dB to 0.5 dB, the performance of the model in the OSNR monitoring task declines slightly. This decline in performance is because, as the OSNR interval decreases, the difference between the constellation diagrams that need to be distinguished also diminishes, making it more difficult for the model to identify them. However, the model still maintains good OSNR monitoring efficiency on the 0.5 dB OSNR interval dataset, achieving an accuracy of over 82% for all modulation formats.
Fig. 7. The OSNR monitoring performance of FMFSL algorithm at 0.5 dB and 1 dB OSNR intervals for the back-to-back case.
And then we tested the generalization performance of FMFSL_1 without retraining for OSNR monitoring at 0.5 dB OSNR interval. For comparison, we also presented the performance of FMFSL_0.5 in monitoring OSNR at 0.5 dB OSNR interval, where FMFSL_0.5 is the model that was retrained specifically for the 0.5 dB OSNR interval dataset. This means that in this case, the OSNR intervals of the training and testing datasets for FMFSL_1 are different, while for FMFSL_0.5, they are same. Through this method, we can have a clearer understanding of the model's adaptability and generalizability under different OSNR intervals. As shown in Fig. 8, the OSNR monitoring accuracy of FMFSL_1 decreased compared to FMFSL_0.5 due to the reduced feature differences in a smaller interval, but the decline is acceptable. In fact, the OSNR monitoring performance remains commendable, with the accuracy of 80.3% for 128QAM and over 90% for other modulation formats. These results indicate that FMFSL algorithm has good enough generalization performance for back-to-back transmission scenarios with smaller OSNR intervals.
Fig. 8. Generalization performance of FMFSL_1 on ONSR monitoring at 0.5 dB OSNR interval for the back-to-back case. FMFSL_1 represents the FMFSL algorithm trained using datasets with 1 dB OSNR interval, which is directly applied to monitor OSNR at 0.5 dB OSNR interval with no need of retraining. FMFSL_0.5 represents the FMFSL algorithm retrained using datasets with 0.5 dB OSNR interval, which is then applied to monitor OSNR at 0.5 dB OSNR interval.
4.2.2 Modulation format identification and OSNR monitoring in fiber transmission scenarios
Firstly, we explore the generalizability of FMFSL algorithm for the MFI task in fiber transmission scenarios under the influence of Kerr nonlinearity. We evaluated the impact of transmission distance and launched power on the model's MFI performance. Specifically, two fiber transmission scenarios were considered for QPSK, 16QAM, and 64QAM: (1) with a launched power of 0 dBm and transmission distances of 1040 km, 800 km, and 640 km respectively; and (2) with a launched power of 6 dBm, where each format was transmitted over a distance of 640 km. As shown in Fig. 9, FMFSL algorithm achieved 100% accuracy for both of these scenarios in MFI, demonstrating its superior generalization performance and the robustness to the nonlinearity.
Simultaneously, with the trained FMFSL algorithm for the OSNR monitoring in back-to-back case we investigated its generalization in fiber transmission scenarios that have more impairments. We selected three commonly used modulation formats for fiber transmission data test, namely QPSK, 16QAM, and 64QAM, with the OSNR range introduced earlier in Table 1. Three transmission distances were selected for each modulation format and the launched power is set to be 0 dBm. We employed the trained FMFSL model with 1 dB OSNR interval in the back-to-back scenario to monitor the OSNR in the fiber transmission scenario for the three modulation formats. We calculated both the OSNR monitoring accuracy and error as shown in Table 4. These results indicate that FMFSL algorithm can still perform well in OSNR monitoring when dealing with fiber transmission datasets experiencing greater nonlinear damage without the need for retraining. This demonstrates high generalizability.
Table 4. OSNR monitoring accuracy and error of FMFSL_1 for the fiber transmission case with different transmission distances
Additionally, we further evaluated the performance of FMFSL algorithm on OSNR monitoring under the influence of Kerr nonlinearity at different launched powers. We selected QPSK, 16QAM, and 64QAM with a transmission distance of 640 km, and set the launched powers to be 0 dBm, 3 dBm, and 6 dBm, respectively. We tested the generalization of FMFSL algorithm on OSNR monitoring at different launched powers with no need of retraining. We calculated both the OSNR monitoring accuracy and error as shown in Table 5. It is denoted that FMFSL algorithm can still perform well in OSNR monitoring for the fiber transmission case with different launched powers. These results further demonstrate the generalization of FMFSL algorithm under the presence of different amounts of Kerr nonlinearity and its robustness to the nonlinearity.
Table 5. OSNR monitoring accuracy and error of FMFSL_1 for the fiber transmission case with different launched powers
Through the above discussion, it can be concluded that the FMFSL algorithm trained in back-to-back transmission scenarios still maintains good performance and exhibits high generalizability without the need for retraining in the faces of (1) back-to-back transmission scenarios with smaller OSNR intervals and (2) fiber transmission scenarios. This is attributed to FMFSL’s enhanced feature extraction capabilities and its adoption of an episodic training mechanism, which are beneficial for enhancing the generalizability. Moreover, the similarity of constellation diagrams in different transmission scenarios also contributes to the generalizability of the algorithm.
5. Conclusions
In this paper, we have proposed the FMFSL algorithm with the improvements upon the ordinary few-shot learning algorithms for image recognition, which enhances feature extraction capabilities and model’s generalizability by using a combination of a dilated convolutional group and an asymmetric convolutional group. FMFSL algorithm can serve as a universal few-shot learning algorithm for image recognition in many fields. The performance of FMFSL algorithm in joint MFI and OSNR monitoring was investigated using small-scale data and its generalizability in different transmission scenarios was also explored. The results show that FMFSL algorithm can achieve high accuracy and have excellent performance in MFI and OSNR monitoring tasks. Meanwhile, it demonstrates high generalizability without retraining data in both back-to-back transmission scenarios with smaller OSNR intervals and fiber transmission scenarios with increased Kerr nonlinearity, showing its robustness to nonlinearity as well. These indicate that FMFSL algorithm is well suited to the dynamic, complex and heterogeneous characteristics of next-generation optical networks. It’s expected that FMFSL algorithm has potential application prospects in intelligent signal analysis for monitoring and optimization to ensure stable operation and efficient transmissions.
Funding
National Key Research and Development Program of China (2016YFA0302001); Science and Technology Commission of Shanghai Municipality (2019SHZDZX01, 22DZ2229004); National Natural Science Foundation of China (11654005, 11874152, 11904227, 12204304, 12234014, 12274132, 91536114); Innovation Program for Quantum Science and Technology (2021ZD0303200).
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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