# Modulation Format Identification Based on Signal Constellation Diagrams and Support Vector Machine
## 1 Introduction  
With the rapid development of services such as 5G, cloud computing, high definition video, and cloud conferencing, the demand for bandwidth and spectrum utilization is increasing [1, 2, 3, 4, 5], and the channel capacity in optical communication systems is growing exponentially. The future fiber optic communication systems are expected to be dynamic and diverse, which can accommodate a wide variety of signals and have different modulation formats to meet the different needs of users [6, 7, 8, 9, 10]. In addition, optical signals are susceptible to various transmission impairments that change dynamically in time, which places new demands on optical receivers. At the digital receiver, demodulate the transmitted signal; it is necessary to know the type of modulation format; therefore, correctlyidentifying the modulation format is critical for high-quality communication [11; 12; 13].  
Currently, existing algorithms for modulation format identification (MFI) are broadly classified into two categories according to the identification principle of the algorithm. One is the likelihood-based (LB) method of hypothesis testing based on the likelihood function, which minimizes the probability of false identification and provides the optimal solution on Bayesian ideals [14; 15; 16]; however, this method contains higher computational complexity and is not easy to implement. Another category is the feature-based (FB) identification method, which is also the approach taken in this paper. This method has to extract significant features from the received signal and then identify the signal modulation format. Although FB is a sub-optimal method, it is usually more straightforward and easier to implement and can also provide near-optimal identification performance if properly designed [17; 18; 19; 20]. For example, an MFI scheme based on lightweight convolutional neural networks (CNN) in the 2D-Stokes planes is proposed in [17]. The authors in [18] proposed an MFI scheme that depends on using CNNs on constellation diagrams. A blind optical MFI scheme based on the Hough transform of the constellation diagram is proposed in [19], which is used to display phase and magnitude information. In [20], the authors proposed a modulation classification scheme based on signal constellation diagram and deep learning to identify different modulated signals. Most of the above MFI techniques can identify modulation formats such as QPSK, 16 QAM, and 64 QAM. To the authors' knowledge, MFI has not been considered in the literature for higher-order QAM signals.  
In this paper, an MFI scheme based on signal constellation diagrams and support vector machine (SVM) is proposed. Firstly, the signal constellation diagrams are divided by the fractal dimension of the weighted linear least squares (WLS-FD) algorithm, and each region's fractal dimension (FD) is calculated, regarded as one of the image features. Then, the feature values of the image in different directions are extracted by the gray-level co-occurrence matrix (GLCM), and their mean and variance are calculated, which is regarded as another feature. Finally, the two features are input into the modulation format classifier constructed by the SVM to achieve MFI in coherent optical communication systems. To verify the feasibility and superiority of the scheme, we compare it with the MFI scheme based on higher-order statistical (HOS) features, GLCM features, and FD features, respectively. Further, we built a 30 GBaud coherent optical communication system with fiber lengths of 80 km and 120 km, where the optical signal-to-noise ratio (OSNR) ranges from 0 dB to 30 dB. The proposed MFI scheme identifies seven modulation formats: QPSK, 8 QAM, 16 QAM, 32 QAM, 64 QAM, 128 QAM, and 256 QAM. The results show that compared with the other three schemes, our proposed scheme has a better identification accuracy at low OSNR. In addition, the identification accuracy of this scheme can reach 100% when the OSNR \(\geq\) 10 dB.