Open Access
Add to BibSonomy
Abstract
In this paper, a new method for the modulation format and bit rate recognition (MFR) is proposed. The method analyzes the asynchronously sampled signal data and uses the tools such as asynchronous delay tap plots (ADTP), principal component analysis (PCA), artificial neural network (ANN) and supported vector machine (SVM) to distinguish the different modulation format and bit rate. The mixed algorithm is able to provide accurate MFR for unprecedented number of signal modulation formats/bit rates. An example is demonstrated to recognize 18 different modulate formats/bit rates with higher than 96.17% accuracy. Such recognition performance is beyond the existing methods.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The rapid increasing demand for transmission capacity has called for the implementation of higher order modulation format in optical networks. In the fast evolutionary optical transmission networks, multiple modulation formats coexist. These modulation formats require different configurations at the receiver, e.g. constant modulus algorithm (CMA) is implemented for the PM-QPSK signal de-multiplexing/equalization while radius direction equalizer (RDE) is used for the PM-16QAM signal de-multiplexing/equalization. The carrier/phase offset compensation algorithms are also different for the QPSK signal and the 16QAM signal. In addition to that, different modulation formats have different OSNR requirement and the link configuration should be adjusted accordingly. Therefore, modulation format/bit rate recognition (MFR) is an important issue in the dynamic optical network configuration and management.
Most of the MFR technologies could be classified as two folds, the synchronous signal processing based techniques and the asynchronous signal processing based techniques. The synchronous signal processing techniques require coherent detection and clock recovery, which are non-trivial in a high speed transmission optical network [1–9]. An inexpensive alternative is to use the asynchronous signal processing technique, which can realize MFR by analyzing the statistical distribution characteristics of the signals.
There have been quite a few studies on the topic of MFR based on the asynchronously collected data and many methods have been proposed, such as the asynchronous amplitude histograms (AAHs) based method and the asynchronous delay tap plots (ADTPs) based method [10–15]. AAHs are generated by plotting the amplitude/power statistical distributions, while asynchronous delay tap plots (ADTPs) are generated by re-plotting the two asynchronously collected data tributaries on the two dimensional histograms. By analyzing the AAH or ADTP, one may realize MFR through tools like principal component analysis (PCA) [10–11], artificial neural network [12–13], or the combination of the both methods [15–16]. In comparison with the synchronous sampling based MFR techniques, the AAH and ADTP based methods do not need clock recovery and can implement a much lower sampling rate than the data transmission baud rate. Furthermore, only the power of the signal is measured for MFR which avoids coherent detection. All these factors greatly reduce the cost and the technical difficulty for MFR.
In comparison with AAH, the ADTP based MFR technique is able to recognize more signal types with higher accuracy as substantial statistical information is gathered in the two dimensional histogram. However, the performance of the ADTP based MFR method still needs improvement as more and more higher order modulation formats come into use. In most of the published works, the numbers of signal modulation format types to be recognized by ADTP are below 10. Hence, the ADTP based technique for MFR meets its capability bottleneck when the number of signal modulation format/bit rate further increases, which could be possible in a fast evolutionary optical network.
Supported vector machine (SVM) has been viewed as a powerful tool for pattern recognition. It is, however, quite time consuming to find the related coefficients and bias constants for the SVM when the number of the input parameters is large, which is the case while analyzing ADTP. Therefore, the implementation of SVM for MFR is usually accompanied by the higher order cumulants (HOC) [17] or the fractal dimension analysis [9], which require coherent detection. A method which combines ADTP based entropy and SVM is proposed in [18]. It is able to realize MFR for 15 different signal modulation formats/bit rates. However, further increase of signal types seems difficult for this method as quite significant information has been dropped while converting ADTP to its entropy.
In this paper, a novel method which combines ADTP, PCA, ANN, and SVM is proposed for MFR. By exploiting the advantage of the four techniques, it is possible to realize MFR for 18 different signal modulation format/bit rate. The proposed method is conducted in the following procedure. First of all, the asynchronously collected power data is processed to obtain the ADTPs for the two different polarization data streams. The calculated ADTPs are processed by PCA to reduce data dimension and this avoids the problem of the over-fitting. An ANN follows the PCA processor to classify the data into different groups. The SVM is used to further recognize the modulation format and bit rate with the lessened input data dimensions, which greatly reduces the difficulty to find the related coefficients and bias constants for the SVM. Comparing with the existing methods, the proposed method is more robust and accurate. With 18 different modulation formats/bit rates, the method is able to realize the recognition accuracy of 96.17%.
2. Methods
The data sampling scheme is shown in Fig. 1, which demonstrates the two asynchronous samples a and b with the sampling period as T and the asynchronous sampling delay as τ. Only the power information is used for MFR, and it is called asynchronous delay tap samples (ADTS) [10–15]. Since the transmission signals might have two polarizations, the asynchronous samples have three sampling pairs, i.e. (ax, bx), (ay, by), (ax +ay, ay +by), including the sampling on the powers of the x and y polarizations as well as the total power. Here, a and b refer to the powers of the signal at the corresponding sampling times. x and y refer to the two polarizations. Using these three pairs, it is possible to generate three two dimensional histograms, i.e. three ADTPs. Different signal realizations corresponds to different ADTPs, however, ADTPs of the same modulation format/bit rate demonstrate similar patterns.
2. 1 Principal component analysis (PCA)
The principal component analysis is a method which transforms the characteristic of the signals to the principal directions. The procedure is as follows. The calculated ADTPs are converted to a vector x, which is formed by piling up the rows of the three ADTP matrices [10]. The vectors will be used to generate a matrix C, which can be calculated by [10]
With the principal eigenvalues λk, one may find the corresponding principal eigenvectors vk. The signal character vector xi, which is the vector formed by the ADTPs of one signal modulation format realization, can be projected to the principal directions [10]
where K is the number of the selected principal vectors, which is determined by the principal ratio. In this way, the vector xi will be converted into a new vector wi, which has much less elements but more significant characteristics for recognition, and this resolves the problem of over-fitting for the ANN and reduces the data dimension. The vector can be represented by2. 2 Artificial neural network (ANN)
After calculating the new characteristic vectors wi for different signal realizations, one may use them to train the ANN for MFR. The ANN is formed by the input layer, hidden layer, and the output layer. The hyperbolic tangent function and the linear function are used for the transfer functions for the hidden layer and the output layer [19].
Each type of modulation format/bit rate will have a corresponding label at the output of the ANN. If the probability of being one type of modulation format is high, the label will be close to 1. Otherwise, it will be close to 0. Henceforth, the input vector w has been converted to a new vector z whose number of elements equals the number of possible signal modulation formats.
One may directly determine the signal modulation format/bit rate by finding the largest element in z. However, the performance is not promising when the number of signal modulation format/bit rates exceeds ten. A better way can be adopted to recover the full information hidden in z, which is to implement the supported vector machine (SVM).
2. 3 Supported vector machine (SVM)
The vector obtained from the ANN is further processed by SVM. The SVM based MFR is graphically shown in Fig. 2. Assuming two distinctive modulation formats/bit rates are to be recognized, a hyper plane is generated to separate them so that they are distinguished correctly.
The mathematical formulation of SVM is as follows. Supposing the data vector z and its label l has the form of (z, l) with l <(−1,1), the hyper plane has the form of
where ${\boldsymbol {\omega} },b$ is the coefficient vector and the bias constant, T the transpose of a vector. The SVM will try to find the parameter ${\boldsymbol {\omega} },b,\xi$ so that the following function is minimized [20].For the multi-class separation problem, one may reduce it to the binary separation problem by adopting the one against all approach or the one against one approach [20].
In this work, the authors have used the open source Matlab libsvm code written by Chih-Chung Chang and Chih-Jen Lin et. al [20] to implement the SVM. One against one approach is adopted in this case, and the kernel function is selected as the Gaussian kernel [20].
From the introduction above, the computational complexity of the SVM is dependent on the length of the data vector z and the number of the signal to be separated. For a SVM to recognize 18 signals, it takes about 12 hours to find the optimal coefficient vectors and bias constants if the inputs are three ADTPs with the 16×16 grid. Therefore, the direct implementation of SVM for MFR with ADTPs is computational intensive and impractical.
2. 4 Overall algorithm description
The overall schematic of the proposed MFR method is shown in Fig. 3. The algorithm has two modes, i.e. the training mode and the recognition mode. The signals are split into two polarizations and each of them experiences asynchronous delay tap sampling. The sampled data are processed to obtain the ADTPs.
In the training mode, the training signal data are used for the training of the ANN and the SVM. The ADTPs of the training data set is used to generate the PCA matrix and the principal directions are calculated. The vectors obtained from the ADTPs are projected onto those directions and are converted into the PCA weight vectors indicated by Eq. (3). The PCA weight vectors of the training signals form the library to train the ANN. After training, the ANN is able to convert the PCA weight vectors into the ANN labels which indicate the different types of signal. The ANN output labels of the training signal form the other library for SVM training. After training, the SVM is ready to distinguish different modulation formats/data rates. Since the number of SVM input equals the number of the signal types to be recognized, the training time for SVM is relatively fast, which is comparable with the ANN training time.
In the recognition mode, the signal undergoes the procedures to create the ADTPs, to calculate the PCA vector, to have the ANN output labels and to be recognized by the SVM.
3. Results and discussions
The proposed method has been verified numerically. In the simulation, the fiber link has the length of 1000km, which is divided into 20 spans and with each span as 50km. An optical amplifier is inserted between each of the two spans and fully compensates the fiber attenuation. The fiber has the chromatic dispersion as −20 ps2/km and the differential group delay (DGD) as 0.1 ps/sqrt(km). In order to incorporate the random fiber rotation, the fiber is divided into multiple sections with each section as 1000m. Random rotation matrix with the DGD term is multiplied on the propagating signal Jones vector. The optical schematic of the transmission link is shown in Fig. 4. In the simulation, 18 different types of signals with either different modulation format or bit rates are simulated. Each type of signal is simulated with 5000 realizations. 1000 of them are used for training, and the rest 4000 realizations are used to test the recognition accuracy. Due to the computational capacity limit, the fiber nonlinearity is not considered in the simulation. Fortunately, the statistical property of the nonlinear noise was found to be the same as the Gaussian noise [21] and therefore, one may tune the amplified spontaneous emission (ASE) noise of the optical amplifier to reflect the nonlinear noise contribution. Different dispersion map results in different nonlinear distortion and the impact can be characterized by the different tuned strength of the ASE noise source. At receiver side, the signals are asynchronously sampled with the delay as 15ps. The dispersion is assumed to be compensated either by the dispersion compensation fiber (DCF), the tunable dispersion compensator or the DSP. In the simulation, the DSP has been adopted to compensate the CD. The residual dispersion is assumed to be 0-400 ps/nm. The asynchronously sampled data is converted into the three ADTPs with the grid as 16×16. The ANN has 40 neurons in the hidden layer and the PCA principal ratio threshold is set as 99.9%.
The total 18 types of signals to be recognized are shown in Table 1, which includes the return-to-zero (RZ) and non-return-to-zero (NRZ) signals with OOK, QPSK, 16QAM, 64QAM, 256QAM modulation. Each modulation format can have multiple transmission bit rates. In the low bit rate transmission regime, the signals are not polarization multiplexed, while in the high bit rate transmission regime, the signals are polarization multiplexed with the indication of ‘PM’. In the 18 types of signals, OFDM signals are also included. The data transmission rates range from 10Gbps to 200Gbps which have included the main stream modulation formats/bit rates in the existing optical networks.
Table 1. 18 types of signals to be recognized.
Initially, the signal to noise ratio is tuned as 20dB, which is reasonable considering the number of propagation spans. The residual dispersion varies between 0-400 ps/nm. The proposed method achieves outstanding recognition accuracy for the 18 types of different signals. The results have been summarized in a large table, with its rows indicating the actual signals to be recognized and its columns indicating the identified signals. The number inside the blocks stands for the recognition probability. Since the 18×18 table is too huge to be placed in the paper, the contents of the table are partially shown in Fig. 5, Table 2 and Table 3.
Table 2. Part of the recognition results for the 18 types of signals (NRZ signals).
Table 3. Part of the recognition results for the 18 types of signals (OFDM signals).
The overall recognition accuracy results are summarized in Fig. 5 with the total MFR accuracy as 96.17%. The summarized results in Fig. 5 indicate that most of the 18 signals reach nearly 100% recognition accuracy. The worst cases are signal type 7 and 11, i.e. the PM-RZ-QPSK-100Gbps signal and the PM-RZ-16QAM-200Gbps signal, which have the recognition accuracies around 80% and 85%. They have been actually mistaken as signal type 11 and 7 respectively, i.e. they are mistaken by each other. One may further develop a two-signal-type recognizer to distinguish them more accurately.
Table 2 and Table 3 are parts of the large table. Table 2 demonstrates that the NRZ signals with different modulation schemes and the recognition accuracies are quite high. There is little misrecognition between the NRZ signals. Table 3 illustrates the recognition accuracy for the OFDM-NRZ signals, whose recognition accuracies are above 96%. Also there are almost no recognition errors among the OFDM-NRZ signals.
The robustness of the proposed method is investigated with respect to different residual chromatic dispersion values and different OSNRs. When the residual dispersion value changes between 0-400 ps/nm, the recognition accuracies vary accordingly, which is demonstrated in Table 4. As the residual chromatic dispersion increases, the accuracy decreases in most cases. However, there are some exceptions, e.g. the PM-RZ-QPSK-200Gbps signal. This is because the data with different residual dispersion have been combined together during the training stage, and the proposed method does not consider the signal with 0 residual dispersion as the “good” signal and the one with 400 ps/nm residual dispersion as the “bad” signal. The robustness of the method is also tested under different OSNRs, which is shown in Table 5. The results indicate that the performance of the proposed signal recognizer has been impacted by the OSNR degradation. In order to have a high recognition accuracy, one should maintain the OSNR above 15dB.
Table 4. Signal recognition accuracies under different residual dispersion values.
Table 5. Signal recognition accuracies under different OSNRs.
Finally, the proposed method is compared with other methods such as ANN, PCA based MFR method and the pure SVM based method with ADTPs, which is shown in Table 6. From Table 6, it can be clearly seen that the proposed method can significantly improve the MFR accuracy in comparison to the existing methods, such as the pure ANN and PCA + ANN. The performance of the proposed method is comparable with the pure SVM method, which is understandable, because both of the methods implement SVM at last. However, the computational costs of the two methods differ significantly, which are shown in Tables 7–8. From the tables, it can be seen that the training time and the recognition time per symbol for the proposed method is only 4% and 40% compared with the pure SVM method. This is due to the fact that the proposed method has significantly reduced the data size during the PCA-ANN processing steps, and thus decreases the time required for SVM training and symbol recognition.
Table 6. Signal recognition accuracies with different MFR methods under different OSNRs.
Table 7. Required training time for the different methods (the time unit is hour).
Table 8. Required recognition time per symbol for the different methods (the time unit is second).
4. Summary
A novel method for modulate format/bit rate identification is proposed, which combines multiple tools, such as ADTP, PCA, ANN, and SVM. The hybrid recognition method uses asynchronous samples and therefore it is of low cost and easy to implement. The proposed method avoids the limits of the individual tools, such as the over-fitting problem for ANN and the long training time for SVM, and achieves remarkable recognition performance. Over 96.17% recognition accuracy is demonstrated with 18 different modulation formats/bit rates.
Funding
National Natural Science Foundation of China (61775168).
Disclosures
The authors declare no conflicts of interest.
References
1. N. G. Gonzalez, D. Zibar, and I. T. Monroy., “Cognitive digital receiver for burst mode phase modulated radio over fiber links,” in 36th European Conference and Exhibition on Optical Communication (ECOC) 2010, Proc. ECOC’10, paper P6.11.
2. M. Zaerin and B. Seyfe, “Multiuser modulation classification based on cumulants in additive white Gaussian noise channel,” IET Signal Process 6(9), 815–823 (2012). [CrossRef]
3. J. Liu, Z. Dong, K. Zhong, A. P. T. Lau, C. Lu, and Y. Lu, “Modulation format identification based on received signal power distributions for digital coherent receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th4D.3.
4. S. M. Bilal, G. Bosco, Z. Dong, A. P. T. Lau, and C. Lu, “Blind modulation format identification for digital coherent receivers,” Opt. Express 23(20), 26769–26778 (2015). [CrossRef]
5. R. Borkowski, D. Zibar, A. Caballero, V. Arlunno, and I. T. Monroy, “Optical Modulation Format Recognition in Stokes Space for Digital Coherent Receivers,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh3B.3.
6. R. Boada, R. Borkowski, and I. T. Monroy, “Clustering algorithms for Stokes space modulation format recognition,” Opt. Express 23(12), 15521–15531 (2015). [CrossRef]
7. M. Xiang, Q. Zhuge, M. Qiu, X. Zhou, F. Zhang, M. Tang, D. Liu, S. Fu, and D. V. Plant, “Modulation format identification aided hitless flexible coherent transceiver,” Opt. Express 24(14), 15642–15655 (2016). [CrossRef]
8. S. Fu, Z. Xu, J. Lu, H. Jiang, Q. Wu, Z. Hu, M. Tang, D. Liu, and C. C.-K. Chan, “Modulation format identification enabled by the digital frequency-offset loading technique for hitless coherent transceiver,” Opt. Express 26(6), 7288–7296 (2018). [CrossRef]
9. H. Zhou, M. Tang, X. Chen, Z. Feng, Q. Wu, S. Fu, and D. Liu, “Fractal dimension aided modulation formats identification based on support vector machines,” in 43th European Conference and Exhibition on Optical Communication (ECOC) 2017, Proc. ECOC’17, pp. 1–3
10. M. C. Tan, F. N. Khan, W. H. Al-Arashi, Y. Zhou, and A. P. T. Lau, “Simultaneous Optical Performance Monitoring and Modulation Format/Bit-Rate Identification Using Principal Component Analysis,” J. Opt. Commun. Netw. 6(5), 441–448 (2014). [CrossRef]
11. F. N. Khan, Y. Yu, M. C. Tan, W. H. Al-Arashi, C. Yu, A. P. T. Lau, and C. Lu, “Experimental demonstration of joint OSNR monitoring and modulation format identification using asynchronous single channel sampling,” Opt. Express 23(23), 30337–30346 (2015). [CrossRef]
12. F. N. Khan, Y. Zhou, A. P. T. Lau, and C. Lu, “Modulation format identification in heterogeneous fiber-optic networks using artificial neural networks,” Opt. Express 20(11), 12422–12431 (2012). [CrossRef]
13. L. Guesmi, A. M. Ragheb, H. Fathallah, and M. Menif, “Experimental Demonstration of Simultaneous Modulation Format/Symbol Rate Identification and Optical Performance Monitoring for Coherent Optical Systems,” J. Lightwave Technol. 36(11), 2230–2239 (2018). [CrossRef]
14. B. Kozicki, A. Maruta, and K. Kitayama, “Transparent performance monitoring of RZ-DQPSK systems employing delay-tap sampling,” J. Opt. Netw. 6(11), 1257–1269 (2007). [CrossRef]
15. F. N. Khan, C. H. Teow, S. G. Kiu, M. C. Tan, Y. Zhou, W. H. Al-Arashie, A. P. T. Lau, and C. Lu, “Automatic modulation format/bit-rate classification and signal-to-noise ratio estimation using asynchronous delay-tap sampling,” Computers & Electrical Engineering 47, 126–133 (2015). [CrossRef]
16. J. Zhou and P. Fan, “Modulation format/bit rate recognition based on principal component analysis (PCA) and artificial neural networks (ANNs),” OSA Continuum 2(3), 923–937 (2019). [CrossRef]
17. G. Han, J. Li, and D. Lu, “Study of modulation recognition based on HOCs and SVM,” 2004 IEEE 59th Vehicular Technology Conference. VTC 2004-Spring, 898–902, 2004.
18. J. Wei, Z. Huang, S. Su, and Z. Zuo, “Using Multidimensional ADTPE and SVM for Optical Modulation Real-Time Recognition,” Entropy 18(1), 30 (2016). [CrossRef]
19. The MathWorks, Inc., Neural Network Toolbox User’s Guide version 4 (2004).
20. C.-C. Chang and C.-J. Lin, LIBSVM: A Library for Support Vector Machines, 2001, maintained at http://www.csie.ntu.edu.tw/∼cjlin/papers/libsvm.pdf.
21. P. Poggiolini, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri, “The GN-Model of Fiber Non-Linear Propagation and its Applications,” J. Lightwave Technol. 32(4), 694–721 (2014). [CrossRef]
