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Abstract
A novel modulation format recognition (MFR) scheme based on multiple Stokes sectional planes images by generative adversarial network (GAN) is proposed and demonstrated to adapt to next-generation elastic optical network (EON). The application of the encoder, along with the suitable loss function, is able to achieve better performance with regards to MFR of GAN. Experimental verifications were performed for the polarization division multiplexing (PDM)-EON system at a symbol rate of 12.5GBaud. Five modulation formats, including PDM-BPSK, PDM-QPSK, PDM-8PSK, PDM-8QAM, PDM-16QAM, were recognized by our scheme under the condition of practical optical signal-to-noise ratio (OSNR) over both back-to-back transmission and 25km standard signal-mode fiber (SSMF). Specifically, the minimum required OSNR of PDM-16QAM signal to achieve 100% MFR success rate is 18 dB, which is lower than its corresponding 7% forward error correction (FEC) threshold. Results show that, compared with three other machine learning algorithms, the proposed scheme obtains the higher recognition accuracy in the case of the same OSNR. Moreover, the training data required by the proposed scheme is less than the traditional convolutional neural network (CNN) in MFR task, which means the training cost of the neural network is greatly reduced by using GAN.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, the landscape of data transmission has changed a lot while the optical communication system becomes more complex, with the booming advancement of bandwidth intensive services as clouding computing, 5G, Internet of Things (IoT) and virtual reality (VR) [1–5]. The next generation optical transmitter network is envisioned to be more cognitive. The elastic optical network (EON) can dynamically adjust the modulation format according to different channel conditions for increasing the utilization efficiency of bandwidth resources [6–7]. Furthermore, for the sake of mastering the transmission state of the physical layer, the EON applies optical performance monitoring (OPM) technology to monitor various optical network parameters and estimate the damage of various channels in the dynamic optical network [8]. To allocate system resources reasonably and satisfy the diversified requirements of users, the transmitter terminals of EON adaptively adjust various network parameters, such as modulation format, symbol rate, spectrum planning and forward error correction (FEC) codes [9]. Due to the frequency offset compensation, carrier phase recovery and other algorithms in the receiver digital signal process (DSP) depending on the modulation format of the signal, receivers need to automatically identify the modulation format of the receives signal. Therefore, MFR at the coherent receiver is essential to cope with the variety of instantaneous service transmission requests for EON and plays a fundamental role in it [10].
When it comes to MFR, various methods based on signal characteristic to classify unknown signals are widely used, roughly divided into three categories. The first is maximum likelihood estimate recognition based on hypothesis testing [11]. Through the theoretical analysis of the statistical characteristic of the signals, the likelihood function of the samples is obtained. The modulation format of the signal is determined by comparing the value of likelihood function with the suitable threshold according to the decision criterion. The second recognition scheme is based on the signal amplitude statistics, which takes the asynchronous amplitude histogram (AAH) as the signal characteristic [12–14]. In this scheme, AAH depended on the modulation format can obtained by sampling the signal at a lower sampling rate. Then, artificial neural network (ANN), support vector machine (SVM) and other algorithms are used as the classifier to realize the MFR. Due to the characteristic of insensitivity to carrier phase noise, frequency offset and polarization mixing, the third scheme based on Stokes space, combined with clustering algorithm, stands out to attract more and more momentum [15]. Compared with the supervised learning algorithm in machine learning, clustering algorithm belonging to unsupervised learning requires less training data than ANN or SVM [16–17]. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers [18]. It has high computational complexity when the data set is larger, which limits the recognition accuracy. Consequently, there is a vacancy for coordinated and unified orchestration between the system reliability and complexity, which calls for a better recognition scheme aimed at better interference immunity and high recognition accuracy.
In this paper, a novel MFR technique based on multiple Stokes sectional planes images using GAN is proposed for EON. The proposed scheme maps the signals into the Stokes space at the receiver. Then we extract multiple sectional images in the Poincaré sphere as the classification feature of the signal. In this work, a GAN is used to recognize the signal’s modulation format according to those sectional images for its powerful ability to free from the inference of hidden variables and the computation of Markov chains. GAN offers a distinct and promising approach that focuses on a game-theoretic formulation for training an image synthesis model [19]. Recent work has shown that GAN can produce convincing image samples on datasets with low variability and low resolution [20–21]. Furthermore, we modify the loss function of the GAN to make it more suitable for the recognition task, which mainly improves the discriminator’s ability of the feature extraction in the training process of adversarial. Accompanying the introduction of the new loss function, GAN process the input images as the signal feature efficiently. In addition, an encoder is used to reconstruct the input images to enrich the categories of input data, which means the training cost is cut down and generalization ability is heighten. Then the recognition results are given to select the appropriate DSP algorithms. The joint implementation of Stokes sectional images and GAN can effectively improve the accuracy of the MFR scheme and greatly reduce the training data of neural network. In doing so, not only can the marvelous recognize ability of network model be enhanced, but also low training cost can be achieved. In this paper, an experiment demonstrating five aforesaid modulation formats over 25 km SSMF is successfully carried out, which confirm the feasibility of our proposed MFR scheme. Results show that the minimum required optical signal-to-noise ratio (OSNR) of PDM-16QAM to achieve 100% MFR success rate is 18 dB, which is lower than its corresponding 7% forward error correction (FEC) threshold.
2. Principle
2.1 Stokes mapping and feature images generation
Figure 1 depicts the DSP algorithms of EON communication system. Before MFR, the received signals need to be processed by certain DSP algorithms independent of modulation format, including chromatic dispersion (CD) equalization, time phase recovery and IQ imbalance compensation. Then MFR results are given by the proposed scheme. Afterwards, the system chooses the appropriate algorithms to carry out frequency offset compensation, carrier recovery and decoding accordingly.
As is shown in Fig. 2, three operating steps are included in our proposed scheme: 1) normalizing the power of the pre-processed signals; 2) mapping the signal into Stokes space accordingly and generating the sectional images in different planes; 3) inputting the images to GAN with coding function and giving the results. The proposed scheme based on Stokes high-dimensional mapping the neural network model has the characteristics of fast convergence speed and high accuracy, which enables the receiver to distinguish the modulation format under the condition of low OSNR and low launched power of optical fiber communication link.
Fig. 2. Identifying the modulation format by converting signals to an image combination of multiple sectional images and classifying the images with GAN.
The pre-processed signals are transformed into a four-dimensional Stokes vector S through formula (1), which are mapped into Stokes space:
Before the feature images are generated, the power normalization of the pre-processed signals is carried out according to formula (2). The mapping rule operates on the basis of the energy differences and phase differences of the mutually polarized signals, with the received signals still retaining their amplitudes and relative phases. Thus, it turns out that the proposed scheme can differentiate the signal characteristic of different modulation formats.
The constellation points in the 2-D constellation diagram distribute on different places in the Poincaré sphere after power normalization and Stokes mapping [15]. The clustering distribution is closely related to the amplitude modulation and phase modulation of the signals, and the signals with different modulation formats have different clustering distributions in the Stokes space. Among them, the m-PSK signals have only one amplitude, so the S1 component representing the difference of the signal energy is 0. In this way, the constellation points are only distributed on the S2-S3 plane. Additionally, m-QAM signals contain not only phase information but also a variety of amplitude information, so its constellation points are distributed on multiple planes of Stokes space.
As is shown in Table 1, the constellation points of BPSK signal have only one amplitude value and two phases values, so the vectors in Stokes space are distributed on the plane S1=0. In the meantime, there are two phase differences on the plane S2-S3, so there are two clustering distribution points in generated images. The other phase-shift keying modulated signals also follow a similar distribution principle. As is depicted in Table 2, the constellation points of 8QAM signals contain two kinds of amplitude, among which the phase of the smaller amplitude of the first amplitude has four kinds of phase differences, while the phase of the second amplitude also includes four kinds of phase differences. At this point, the difference of energy of the Stokes vector of the signal has three values; in other words, 8QAM signals contain three different planes in the Poincaré sphere, including 16 clustering distributions. The distribution principle of other QAM signals is similar.
Table 1. Images of PDM-BPSK, PDM-QPSK, PDM-8PSK signals in Stokes space with their corresponding Stokes sectional image
Table 2. Images of PDM-8QAM, PDM-16QAM signals in Stokes space with their corresponding Stokes sectional images
The region of each cross-section is divided into a sub-region grid of 512 rows and 512 columns, and the number of clustering points under each sub-region is calculated. Then, the number of constellation points in each subregion is normalized by dividing by the maximum number of all subregions. Finally, we take the normalized value of each subregion as the gray value of the corresponding pixels in the image with a size of 512 × 512 to get the feature images for classification. According to the above properties, we use multiple sectional planes images in Stokes space as the input of neural network to carry out the corresponding training network parameters.
2.2 Structure of GAN with coding function
GAN is used to recognize modulation format of received signals through those sectional images. GAN consists of two neural network models trained in opposition to one another: a generator G that extracts the data distribution and a discriminator D that distinguishes whether an image is from G or training datasets by predicting label [22]. The training process of GAN, is shown in Fig. 3. Both the generator G and the discriminator D have six neural layers, where 256 neurons in input layer of generator G and six neurons in output layer of discriminator D. In generator G, there are 288, 256, 64, 8 neurons in the hidden layers, respectively, which are trained by a controlled learning rate by Adam optimizer. Leaky ReLU is used as the activation function. In discriminator D, there are 256, 256, 64, 8 neurons in the hidden layers, respectively. The learning rates of two neural networks are both 0.0001, and warm up technology is used in the training process. All the biases are initialized to 0, while the batch size is set to 500. Besides, we find that the fixed learning rate is difficult for neural network to start converging. So we use 0.0001 to warm up the training until the training loss is below 0.75, and then transfer to 0.001 and continue training, which helps to make the neural model converge faster. The input of the generator G has two parts: random noise Z and labels C. Fake images G(Z) are generated by generator G through random noise sampling. Each generated image has a related category label C as auxiliary information to assist its data generation process. The input to the discriminator D may be the generated images G(Z), or it may be the real images X. The discriminator D receives as input either a real image from training set or a fake image from the generator G. Then the discriminator D outputs a probability distribution over sources and a probability distribution over the class labels. The networks are trained on the label prediction loss in a mini-max fashion: simultaneously optimizing generator G to minimize the loss while also training discriminator D to maximize the probability of assigning the correct label.
Furthermore, the output of generator G is shown in Table 3. The first row images in Table 3 are the generated images from generator, while the second line images are the real images. Table 3 demonstrates the fact that the generated images are similar to the real images after adversarial training.
Table 3. The fake images of BPSK, QPSK, and 8PSK signals and the real images of BPSK, QPSK, and 8PSK signals
The generated samples obey distribution PZ(Z), and the real data obeys distribution Pdata(X). The function D output by the discriminator represents the probability that X is a true image, from which the loss function V (D, G) of GAN can be established:
λKL(D’||C) denotes the relative entropy between the discriminator’s recognition results D’ and the labels C. It narrows the probability distribution discrepancy between the recognition results and the target labels. As a result, the ability of discriminator to extract the features of the data is enhanced. Meanwhile, an auxiliary encoder E is added to reconstruct the real data to enrich the categories of the input images. More concretely, the discriminator D can learn more image characteristic form the reconstructed images. On the test dataset, we study the model performance with different number of training data. As shown in Fig. 4, compared with CNN, GAN needs less training data to achieve better performance in recognition due to its image generation ability. The GAN tends to be convergent with only 50000 training data, while the CNN requires about 75000 training data to achieve the same accuracy. Despite the fact that CNN can realize 100% recognition accuracy in MFR task after training. However, CNN require more data for training, which means consuming more computational resources. In this work, the CNN model is based on ResNet-34 framework, which is a deep neural network adept at image classification [23].
However, if the gradient of the generator is too small, the decoded image generated by the generator is unrecognizable noise. Due to the discriminator failing to acquire satisfactory ability of recognition, although it can quickly identify the difference between the generated image and the real image, it cannot distinguish different modulation formats. Hence, the mean square error (MSE) of the coding images and generated images are added to the generator loss function. In this way, the generator not only acts as the decoder, but also provides the gradient optimization path for the encoder, which ensures the encoding function of the encoder and the decoding function of the generator.
In this work, we demonstrate that adding an encoder E to the GAN structure results in alleviating the mode collapse. The conventional GAN can easily cause instability in the training process because the optimization objectives of the two networks are completely opposite. In the course of training, a common problem, mode collapse, may be encountered. Mode collapse problem refers to that generator only produces some mode of the data in the training set and neglects other modes. As shown in Fig. 5, the red line represents the probability distribution of the conventional GAN, and the blue line represents the probability distribution of the proposed GAN. There are five main modes of the target distribution. However, the generated data by conventional GAN only contains three modes. In this case, the generator only needs to generate few specific modes of data to deceive the discriminator. In contrast, the encoder in our proposed scheme encourages the generator to learn the representations of different categories of samples through overall true samples [24]. It turns out that increasing training dataset is always useful to improve the learning ability of GAN [25]. The introduction of encoder enlarges the type of input images under the same label and makes the dataset become more diverse. By enhancing parallelly the capabilities of the generator and discriminator, we reduce the training cost of GAN while avoiding the phenomenon of mode collapse.
3. Experimental setup
With the view of training the network, we established our dataset by MATLAB simulation of 60000 sectional images of different modulation formats in Stokes space under AWGN (Additive White Gaussian Noise) channel. Each modulation format contains 12000 sets of data, which are divided into 66.67%, 16.66% and 16.67% for training, validation and testing, respectively. K-fold cross validation was applied where k is set to 4, and the hyperparameters for neural network training is selected accordingly. The size of the images was 512×512. The parameters of GAN were trained offline on the PyTorch platform using NVIDIA GeForce RTX 2060.
On the test dataset, the confusion matrix in Table 4 gives the performance of recognition. Each column of the matrix represents the instances in a target class while each row represents the instances in a predicted class. Due to the capability of data generation and reconstruction, the trained model has a 100% recognition success rate for the test set, which means that this model has strong generalization ability and excellent recognition performance.
Table 4. Number of test set and result of recognition for the proposed scheme with image size 512×512
The performance of the proposed MFR scheme is investigated in detail under the scenarios of both back-to-back and fiber transmission, and the experimental setup is illustrated as Fig. 6. At the transmitter, four channel 12.5GS/s electronic signals generated by arbitrary waveform generator (AWG, TekAWG70002A) were fed into dual-polarization I and Q modulator. A continuous wave laser operated at 1550nm served as the light source. Then the modulated optical signals in both cases were sent into fiber and coupled with the noise signals by a coupler with a ratio of 50:50, while in the fiber transmission scene, the transmission length of SSMF link was set as 25km. Subsequently, an erbium doped fiber amplifier (EDFA) and variable optical attenuator (VOA) were utilized to alter OSNR value of the input optical signals. After fiber transmission, EDFA was used to compensate for the fiber loss. The launched power was adjusted with the step size of 1 dBm within a range of [−6,4] dBm. OSNR values were adjusted within a range of 7 dB to 25 dB by employing EDFA and VOA as amplified spontaneous emission (ASE) source. At the receiver side, an optical bandpass filter (OBPF) was adopted to filter the out-of-band noise. After the clock recovery and CD compensation, the received signals were mapped into Stokes space and characteristic images were generated as the input data of neural network. The experimental data set contains 20000 samples, which are randomly divided into 75% and 25% for training and testing, respectively. Then, the discriminator of GAN extracted the features from the images, and the final MFR result was given. When the modulation format of the signal is known, different algorithms can be selected according to different modulation formats to carry out MMA (Multi-modulus Algorithm) equalization, frequency offset compensation, carrier phase recovery and demodulation.
Fig. 6. Experimental setup (AWG: arbitrary waveform generator; EDFA: erbium doped fiber amplifier; VOA: variable optical attenuator; BTB: back-to-back; OSA: optical spectrum analyzer; OC: optical coupler; OBPF: optical band pass filter; LO: local oscillator).
4. Results and discussion
The other machine learning algorithms, including decision trees, k-nearest neighbors (KNN) and SVM, are limited on their ability of feature extraction, which means they cannot process the natural data directly. However, the proposed scheme can automatically extract features of Stokes sectional images. To demonstrate the comparative advantage of the proposed scheme, all those algorithms are conducted for MFR. As shown in Fig. 7, we fixed the OSNR with around 10 dB, the proposed scheme achieves better accuracy than the three other algorithms when recognizing aforesaid modulation formats.
Fig. 7. Performance comparison between GAN and other machine learning algorithms under the same OSNR.
When the launched power is 3 dBm and training epochs are 20, the recognition results are shown in Fig. 8. Form the Fig. 8, it can be observed that the minimum required OSNR values to achieve 100% MFR success rate are 9 dB, 11 dB, 15 dB, 16 dB and 18 dB for PDM-BPSK, PDM-QPSK, PDM-8PSK, PDM-8QAM and PDM-16QAM, respectively. The recognition accuracy of the proposed scheme increases with the rise of OSNR values generally, as shown in Fig. 8. Furthermore, the results demonstrate that the minimum required OSNR to achieve 100% MFR success rate of five aforesaid modulation formats is less than their respective 7% FEC thresholds. When the order of QAM signals are higher, the performance of the recognition of QAM signals might be deteriorated slightly.
Fig. 8. The MFR performance versus OSNR. The dot lines represent OSNR thresholds corresponding to 7% FEC of the corresponding modulation formats.
Figure 9 illustrates that the proposed scheme has high MFR accuracy for PDM-BPSK, PDM-QPSK, PDM-8QAM and PDM-16QAM over wide launched power ranges. When the training epochs are 20, the recognition accuracy is shown in Fig. 9. And the OSNR in Fig. 9 is changed with the emitted launched power. With respect to the results after fiber transmission, nearly 100% correct identification is realized for both the m-PSK and m-QAM signals within practical optical power ranges launched to the fiber, indicating the proposed MFR technique is resilient to fiber impairments. Figure 8 and Fig. 9 prove that the proposed scheme can achieve 100% MFR success rate at low OSNR and low launched power.
We found that the modulation format recognition accuracy varies with the epoch in the training process. As a result, we also investigated the impact of the training epoch on neural network performance. The trained model at different epochs performs different recognition capabilities. For recognition of m-PSK signals, convergence is quickly achieved by a few epochs whereas the training epoch required to achieve 100% recognition success rate in the high-order modulation format is relatively high. With epochs of 9, the proposed scheme can recognize both m-PSK and m-QAM signals correctly, as depicted in Fig. 10. The results are given when the launched power and OSNR are 3 dBm and 20 dB, respectively.
Besides, we also analyzed the effect of the resolution of input images on the recognition accuracy of the proposed scheme, while the launched power and OSNR are 3 dBm and 20 dB, respectively. It can be seen from Fig. 11 that more training epochs are required for smaller image size to achieve the same accuracy. When the resolution of the input image is 64 × 64, the accuracy of the proposed scheme may not very high even if the training epoch reaches 15. This is because neural networks have difficulty in learning images characteristics when many characteristics coincide in one pixel. When the resolution is high, the recognition accuracy is much higher than that of lower resolution ones. However, for images with high resolution, the recognition accuracy will not increase when the train epoch reaches 15. Otherwise, the computational complexity will increase with the resolution. In order to balance the recognition accuracy and the computational complexity, the input image resolution of 512× 512 is selected.
5. Conclusion
This paper proposed a novel method to identify the modulation format in EON. The scheme was verified by 12.5GBaud PDM-EON experiments of five modulation formats recognition under the condition of low OSNR and low launched power. Via performing recognition in the Stokes space, the proposed scheme is insensitive to polarization mixing, carrier phase noise and frequency offset. Moreover, compared with other machine-learning-based algorithms, GAN needs less training data when they achieve the same recognition accuracy. In addition to the five modulation formats described in this paper, other modulation formats can also be recognized by the proposed MFR scheme owing to the fact that the Stokes sectional images of different modulation formats are discriminative. Therefore, with the attractive recognition performance, the proposed scheme is a competitive solution for OPM in next generation EON.
Funding
National Key Research and Development Program of China (No. 2018YFB1800905); National Natural Science Foundation of China (61775098, 61822507, 61835005, 61875248, 61727817, U2001601, 62035018, 61975084, 61720106015, 61935011, 61935005); Open Fund of IPOC (BUPT); Jiangsu talent of innovation and entrepreneurship; Jiangsu team of innovation and entrepreneurship.
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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