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Abstract
A modulation format recognition (MFR) scheme based on multi-core fiber (MCF) is proposed for the next generation of elastic optical networks (EONs). In this scheme, multiple Stokes sectional planes images are used as signal features which are typed into a transfer learning (TL) assisted convolutional neural network (CNN) to realize MFR. Compared with the traditional Jones matrix, the Stokes space mapping method is insensitive to polarization mixing, carrier frequency skew and phase offset, therefore, it has better feature representation ability. TL is introduced to transfer the model used in standard single-mode fiber (SSMF) to MCF transmission, reducing the required training data and complexity. In addition, multiple Stokes sectional planes images are input simultaneously, which improves the accuracy of the neural network. Experimental verifications were performed for a polarization division multiplexing (PDM)-EONs system at a symbol rate of 12.5GBaud by 5 km MCF. Nine modulation formats, including three standard modulation formats (BPSK, QPSK, 8PSK), three uniformly shaped (US) modulation formats (US-8QAM, US-16QAM, US-32QAM) and three probabilistically shaped (PS) modulation formats (PS-8QAM, PS-16QAM, PS-32QAM), were recognized by our scheme. The experimental results show that the scheme achieves high recognition accuracy even at low optical signal-to-noise ratio (OSNR). Moreover, the required number of training samples is less 40% compared to the traditional CNN. The proposed scheme has a high tolerance to the crosstalk damage of MCF itself and can realize the short training time of large-capacity space division multiplexing (SDM)-EONs. Our findings have the potential to be used in the next generation of a SDM fiber transmission system.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1 Introduction
In recent years, data services such as Internet of Things (IoT), cloud computing, virtual reality (VR) and artificial intelligence (AI) have emerged one after another, driving optical networks to flourish in the direction of super-large capacity. To meet service transmission requirements, optical networks are evolved and upgraded accordingly [1,2]. Elastic optical networks (EONs) is an ideal solution for ultra-high speed optical transmission in the future by combining transponder, flexible grid transmission and switching technologies to meet the capacity and dynamic requirements of future core networks [3–5]. However, the dynamic configuration of optical signals leads to uncertainty of the modulation format arriving at the coherent receiver, which makes the polarization multiplexing, frequency offset and carrier phase estimation algorithms dependent on the modulation format unable to work properly. Therefore, the key to realize EONs is to design a flexible transceiver without interruption to recognize the modulation format at the receiver which ensures correct demodulation and meet the requirements of instantaneous transmission services [6].
The capacity of standard single-mode fiber (SSMF) in its transmission system approaches Shannon's theoretical limit by using multiplexing techniques and high order modulation. However, with the rapid growth of communication services, the capacity of single-mode fiber cannot satisfy the requirements of users. Space division multiplexing (SDM) is a capacity expansion technology for multi-core fiber (MCF) and multi-mode fiber (MMF) structures under physical phenomena. With the development of SDM, super-capacity optical networks have been realized, which effectively reduces the pressure of channel services [7,8]. In addition to the physical technology, probabilistic shaping (PS) technology can also improve the transmission capacity, which aims to increase the transmission probability of internal constellation points through reducing the transmission probability of external constellation points. Due to its high spectral efficiency, PS technology has become a research hotspot in recent years [9,10]. Furthermore, as EONs grow in capacity, their complexity increases rapidly. To allocate network resources reasonably, the receivers in EONs must be more intelligent in identifying network states such as modulation format, transmission rate and spectral efficiency [11,12]. The corresponding demodulation and compensation schemes can be designed according to the modulation format, so that optimal demodulation results can be obtained. Thus, the MFR plays an important role in the demodulation process. Many scholars have done a lot of research in MFR, but most of them concentrate on SSMF, while MFR based on SDM is seldom studied at present [13–19].
With the application of SDM and PS in commercial equipment, the existing optical network is in urgent need of a MFR technology suitable for multiple modulation formats in MCF transmission systems. At present, MFR methods can be roughly divided into three categories. The first is maximum likelihood hypothesis test. Based on decision theory, the identification process conforms to hypothesis testing and is suitable for a limited number of modulation formats [13,14]. Different modulation format types present different profile features, which can be regarded as a classification metric. The second is statistical pattern recognition, which is based on the extraction of feature parameters. Prior to recognition, previously marked feature parameters should be extracted from an unknown signal, and then pattern recognition can be carried out according to the extracted parameters [15,16]. They use the specific features of received signals’ density distributions in Stokes axes combined with deep neural networks (DNNs). They propose a constellation MFI scheme based on the density-based spatial clustering of applications with noise (DBSCAN) machine learning algorithm, and the MFI process is set at the receiving end of the CV-QKD system. The third scheme, based on Stokes space mapping, uses Stokes space mapping to give signal classification features and then uses machine learning for recognition. Due to its insensitivity to polarization mixing, carrier frequency skew, phase shift and other losses, it has better representation ability compared with the traditional Jones matrix. Therefore, the scheme has attracted great attention [17–19]. In Ref. [18], although transfer learning (TL) is used to further improve the accuracy of training results, it is not applied to different models of optical fiber transmission links. In this paper, the SSMF model is used to transfer the training parameters to the MCF link for modulation pattern recognition. However, optimization of model parameters based on machine learning requires a large number of training samples, so the performance largely depends on the number of training samples [20]. In SDM, the amount of training is multiplied if multiple channels are trained simultaneously. Therefore, a better recognition scheme is needed that can recognize multiple modulation formats in SDM transmission systems with a low training sample size.
In this paper, we propose a novel MFR scheme for MCF transmission systems. Different sectional planes images are made according to different modulation formats, and the number of training samples is reduced while the recognition rate is guaranteed. PDM-BPSK, PDM-QPSK and PDM-8PSK can achieve recognition results well by using only a sectional planes image, thus reducing the amount of sample training. Compared with the above methods, the recognition efficiency of sectional method is higher. At the same time, high recognition rate can be obtained by fine-tuning the parameters of the target source through transfer learning and transfer on the transmission model. Using transfer learning (TL), the format recognition is realized in a single - core to multi-core optical communication transmission system. At the same time, it can also identify the probabilistically shaped signal. Firstly, the signal received by a SSMF system is used to generate multiple Stokes sectional planes images and input into convolutional neural network (CNN) to train the pre-training model. Then, a small amount of data from the receiver of a MCF system is used to fine-tune the pre-training model. The scheme recognized nine signal modulation formats, including PDM-BPSK, PDM-QPSK, PDM-8PSK, PDM-uniformly shaped (US)-8QAM, PDM-US-16QAM, PDM-US-32QAM, PDM-PS-8QAM, PDM-PS-16QAM, PDM-PS-32QAM. The data transmission of the proposed scheme in 5 km 7-core optical fiber is successfully demonstrated in the experiment. Results show that the transfer learning-convolutional neural network (TL-CNN) model not only requires less training data and training cycles, but also has a higher tolerance to link damage inherent in MCF system. After 45/epochs in core 1, the recognition accuracy of all modulation formats can reach more than 95%. The minimum optical signal-to-noise ratio (OSNR) required for PDM-16QAM to achieve more than 99% MFR success rate is 17 dB. This scheme has good generalization ability for different modulation schemes.
2. Principles of modulation format recognition schemes
2.1 Generation of PS-QAM signals
In traditional optical communication systems, points in QAM signal constellation are transmitted with the same probability, while PS technology aims to improve the transmission probability of internal constellation points and reduce the transmission probability of external constellation points, forming a finely tuned probability distribution of constellation points. This technique can significantly reduce the average constellation power and improve system performance. It is a promising modulation format optimization technique and has been applied to high-speed optical transmission systems to obtain better bit error rate and transmission length performance. The probability distribution of constellation points obeys the Maxwell-Boltzmann distribution, as shown in the following formula [21]:
where ν is the probability distribution factor, which is used to determine the information entropy of the distribution mode and modulation format of the constellation. When ν is equal to 0, the constellation points are evenly distributed, and the information entropy reaches the maximum. In this paper, the method based on sub-label probability formation is adopted to achieve non-uniform probability distribution to generate PS signals through fixed symbol-level labels. In the scheme, the probability distribution of PS-8QAM has the entropy of 2.78 bits/symbol. In the case of PS-16QAM, we implemented the entropy of 3.56 bits/symbol. When the entropy of 4.12 bits/symbol with PS-32QAM, we realize high accuracy recognition. The constellation diagram of 8QAM, 16QAM and 32QAM US signals and PS signals is shown in Fig. 1.2.2 Stokes mapping and images generation
After chromatic dispersion (CD) compensation and timing recovery of a modulation format independent algorithm, the signal is converted into a four-dimensional Stokes vector and mapped into Stokes space according to the following formula (2) [22]:
The sectional images of signals in different planes are selected in Stokes space and grayed as the classification features of different modulation format of signals. In the process of mapping, the amplitude and relative phase of the signal remain unchanged, while the phase noise and frequency offset disappear. Therefore, the Stokes vector of the signal after mapping can be used as a good signal classification feature, which provides a very good signal feature basis for the subsequent MFR using TL-CNN. The three-dimensional Stokes space constellation and its sectional planes images in signal modulation format are shown in Fig. 2. The three-dimensional coordinate system is established based on the stokes space vectors S1, S2 and S3. With a plane parallel to S2-S3, it can be intercepted by means of clustering distribution points on axis S1. There are more than three planes formed by clustering distribution points of US/PS 16QAM and US/PS 32QAM, and they are symmetric. Therefore, part of sections can be selected as recognition objects, and three planes can be selected for recognition training.
Fig. 2. Signal three-dimensional Stokes space constellation and its corresponding sectional images of 12800 symbols (a) BPSK, QPSK, 8PSK, (b) US-8QAM, US-16QAM, US-32QAM, (c) PS-8QAM, PS-16QAM, PS-32QAM.
2.3 TL-CNN structure
As show in Fig. 3, we propose a TL-CNN model by designing training datasets and introducing transfer learning. The training datasets are divided into two parts, namely, SSMF datasets (multi-Stokes sectional images of all modulation formats at the receiver of a SSMF transmission system) and MCF datasets (multi-Stokes sectional images of all modulation formats at the receiver of a MCF transmission system). Firstly, the SSMF datasets are used as the source domain of transfer learning to train the network in the classical deep learning method. After several network iterations and parameter adjustment, when the training loss value and the accuracy of the test set tend to be stable, the pre-training model is obtained [23,24]. Then the MCF datasets are used as the target domain input to the pre-training model for fine-tuning the model. Finally, the MCF datasets are divided into 80% training datasets and 20% testing datasets. The test datasets are used to test the performance of the model, and the test results are evaluated by the accuracy of MFR.
Figure 4 shows the structure of CNN. Table 1 describes the specific architectural layers of the network. The input layer feeds the Stokes sectional images into the neural network. The convolution layer abstracts the relevance implied in the input data by extracting features from the convolution kernel. The batch normalization layer normalizes the input channel of the network to speed up training. The rectified liner unit (ReLU) layer adds nonlinear factors to increase the fitting ability of the network. The maximum pooling layer compresses the features to simplify the network complexity and expand the perception field. The dropout layer prevents overfitting by reducing the actual capacity of the model. The global average pooling layer integrates global spatial information, integrates multidimensional data into one dimension, reduces the number of parameters, and facilitates information processing into the dense layer. The dense layer combines all the features of images learned from the previous layer and classified images. The softmax layer is used for multi-classification activation function to classify 9 modulation formats and output the results. In addition, Adam was selected as the gradient descent optimization algorithm, and the CrossEntropy loss was selected for the loss function, as shown:
where p(x) is the real probability distribution and q(x) is the predicted probability distribution [25]. The initial learning rate is set to 0.001.
Table 1. The specific architecture layer of CNN model
2.4 Proposed scheme
The digital signal processing (DSP) algorithm flow of the multi-core fiber transmission system is shown in Fig. 5. Before MFR, the received signals need to be processed though certain DSP algorithms independent of modulation format, including IQ imbalance compensation, CD compensation and timing recovery. Then, the applied scheme is processed to recognize different modulation formats. The scheme includes four parts: power normalization, Stokes space mapping, CNN and TL. After the modulation format is determined successfully, the back-end DSP algorithms dependent of modulation format, such as carrier phase recovery, channel equalization, can flexibly choose their best parameters for effective operation, and finally achieve signal demodulation.
Figure 6 illustrates two main steps to realize the proposed TL-CNN-MFR scheme. In the first step, the X and Y polarization signals received by the receiver of the SSMF transmission system are mapped to the Poincare sphere in Stokes space. Then the corresponding sectional images are selectively selected as signal features and input into the CNN to train the pre-training model. The second step is to fine-tune the pre-training model with a small amount of data from the receiver of the MCF transmission system to realize the successful MFR.
3. Experiment setup
The experimental setup of the proposed MFR scheme is shown in Fig. 7. At the transmitter, a laser generates light with a central wavelength of 1550 nm and a sampling rate of 12.5 GS /s. An arbitrary waveform generator (AWG, TekAWG70002A) generates electrical signals using 9 modulation formats. An I and Q modulator is used to modulate the electrical signals to light, and then the optical signals which pass through 1:8 the beam splitter is sent to the 7-core optical fiber for transmission. An erbium doped fiber amplifier (EDFA) and a variable optical attenuator (VOA) were utilized to alter the OSNR value so that they are adjustable in the 15-25 dB range. The transmission length of the 7-core optical fiber link was set as 5/km. At the receiver, an optical bandpass filter (OBPF) with a bandwidth of 0.8/nm is used to filter out the out-of-band noise, and the received optical power is adjusted by VOA. The integrated coherent receiver detects the received signal by means of a photoelectric detector (PD) and 50 GS/s analog digital sampling of the real-time oscilloscope, and then uses the offline DSP processing proposed MFR scheme. After the modulation format is determined successfully, the optimal parameters of carrier phase recovery, channel equalization and demodulation can be flexibly selected for effective operation. In the experiment, in order to reduce the signal correlation between each core, we added delay line to each core after the fan-out. The length of the delay line is respectively 2 km, 4 km, 6 km, 8 km, 10 km, 12 km.
Fig. 7. Experimental setup (AWG: arbitrary waveform generator; EDFA: erbium doped fiber amplifier; VOA: variable optical attenuator; OBPF: optical band pass filter; LO: local oscillator).
The distribution diagram between cores used in this paper is shown in Fig. 7(a). It can be seen that evenly cores distribute in honeycomb shape. Its performance index parameters are shown in Table 2. The isolation degree between cores is high, and there is almost no cross-talk between cores.
Table 2. performance index
The length of the seven-core fiber adopted in this paper is 5 km. After testing, the isolation degree between the cores is shown in Table 3, and the minimum isolation degree between cores can reach 34.9 dB. The transmitting terminal adopts the same wavelength, and after the seven-core transmission system, the receiving terminal can recover the information carried by each wavelength.
Table 3. seven core fiber isolation degree (unit: dBm)
To train the network, we established training datasets by MATLAB simulation of 57,600 sectional images of different modulation formats in Stokes space under the additive white gaussian noise (AWGN) channel. Each modulation format has 6400 sets of sectional images. The image size is 256 ${\times} $ 256. The parameters of TL-CNN were trained offline on the jupyter notebook using NVIDIA Quadro P2200. In addition, an additional 1600 sets of Stokes space sectional images were generated for each modulation format as testing datasets to evaluate the generalization ability of the final model and the feasibility of the proposed scheme. The confusion matrix in Fig. 8 gives the classification performance. Each column of the confusion matrix represents the instances in the target modulation format, and each row represents the instances in the actual modulation. The figure shows that the accuracy of MFR in the test datasets can reach more than 98%, indicating that the model has strong generalization ability and good recognition performance.
Fig. 8. Classification results of testing datasets for the proposed scheme (image size is 256${\times} $256; epoch = 50).
4. Results and discussion
Figure 9 shows the recognition accuracy results of the proposed MFR scheme in core-1 when OSNR was 16 dB. The results of the experiment are averages of five measurements and the error range between the values of five experimental and the average of multiple trials is within 1%. During the training, the accuracy of MFR improved with the increase of epoch. When the epoch was 18, the recognition accuracy of m-PSK signal is more than 98%. When the epoch was 48, the recognition accuracy of US-mQAM and PS-mQAM signals reached a stable value of more than 98%, and the overall recognition rate of PS modulated signal was higher than that of US modulated signal. The results show that the lower training epoch of m-PSK signal can achieve fast convergence. While the higher order modulation format can achieve stable recognition, it requires relatively high training epochs. This is because the constellation points and positions of different modulation formats are different in Stokes space, while the constellation points of higher-order modulation formats are densely distributed in Stokes space, showing a certain similarity. The scheme has high MFR accuracy, and to our knowledge, it is the first time that a TL-CNN method has been demonstrated to recognize MPSK, US-MQAM and PS-MQAM signals in MCF.
We fixed the transmission channel as core-1 and trained the model for 30 epochs. The MFR accuracy of different modulation formats at 10-25 dB SNR is given, as shown in Fig. 10. This value is the average of five experiments, and its fluctuation range is within 1%. The recognition accuracy increases with the rise of OSNR values generally. When OSNR is 19 dB, the recognition accuracy of all modulation schemes reaches a stable value. For BPSK, QPSK, 8PSK, US-8QAM, US-16QAM, US-32QAM, PS-8QAM, PS-16QAM and PS-32QAM, the minimum OSNR values required to achieve more than 98% accuracy of MFR is 11 dB, 12 dB, 13 dB, 16 dB, 17 dB, 19 dB, 14 dB, 16 dB and 17 dB respectively.
Besides, we also analyzed the MFR accuracy of US-16QAM with or without TL in core-1 when the training epoch was 30 and the training data was 2500-25000. It can be seen from Fig. 11 that the more training samples, the higher the recognition accuracy. The result is the average of five experiments and the numerical fluctuation range is below 0.8%. The recognition accuracy of traditional CNN network is close to 90% when the training sample is 25,000, while TL-CNN achieves more than 90% recognition accuracy when the training sample is only 10,000. Compared with traditional CNN, the model of TL-CNN effectively reduces the amount of training data, and achieves better recognition performance while using fewer samples. As shown in Fig. 12, in the case of the same parameter, this paper also analyzes the training time cost. The numerical fluctuation range is within 10s for the values of five experiments. It can be seen from the results that the time of TL-CNN model is much faster than CNN when reaching the same recognition accuracy.
In MCF transmission system, inter-core crosstalk is the damage caused by the crosstalk of signals between different transmission channels. In order to verify the feasibility of the TL in the MCF transmission system, we analyzed the classification performance of the proposed scheme for US-16QAM signal in core-1, core-2, core-3, core-4, core-5, core-6, core-7 transmission channels. When OSNR was set as 16 dB, the results are shown in Fig. 13. The experiment was carried out for five times and the results were averaged. The deviation between the mean and the value of each experiment is within 1%. When OSNR was set as 16 dB, the results are shown in Fig. 13. Within about 40 training epochs, the recognition accuracy of signals can reach over 95% in all transmission channels, which demonstrates the feasibility and effectiveness of transfer learning-assisted CNN in a MCF transmission system.
5. Conclusion
This paper proposed a novel MFR scheme for a MCF transmission system. Firstly, the signal received by a SSMF system is used to generate Stokes multi-sectional images and input into CNN to train the pre-training model. Then, a small amount of data from the receiver of the MCF system is used to fine-tune the pre-training model. We evaluated the capability of our proposed MFR scheme in a 7-core optical fiber system transmitting 12.5/Gbaud signals. The results successfully show that the proposed scheme can achieve high recognition accuracy (>98%) at relatively low OSNR values (>11 dB) in MCF. Compared with traditional CNN, TL-CNN not only reduces the computational complexity and training time, but also improves the tolerance of MCF itself to crosstalk. Our findings promote the application of deep learning in multi-core optical fiber transmission systems.
Funding
National Key Research and Development Program of China (2018YFB1800901); National Natural Science Foundation of China (U2001601, 61835005, 61727817, 61875248, 62035018, 61975084, 61720106015, 61935011, 61935005); Open Fund of IPOC (BUPT); Opened Fund of the State Key Laboratory of Integrated Optoelectronics (IOSKL2020KF17); Jiangsu team of innovation and entrepreneurship; The Startup Foundation for Introducing Talent of NUIST.
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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