# Machine Learning Applications for Short Reach Optical Communication
## 2 Machine Learning for OPM and MFI in Short Reach Optical Communications
### Coherent Detection System  
With the rapid technology development, the cost of coherent receivers is declining. In recent years, the application of coherent detection in short-reach optical communication systems and networks to improve spectral efficiency and data rate has also become a new development direction. For example, due to the high receiver sensitivity, frequency selectivity, and scalability, the coherent long-reach PON (LRPON) is regarded as a good choice for providing beyond 100 Gbit/s access, which typically targets at up to 20 km distance connection between the OLT and the ONU [59]. Several reported studies are showing the capability of ANN-based OPM and MFI for short-reach coherent systems [100,101]. In [101], the authors proposed a method based on the combination of ANN and AAH evaluation for OPM, and it can also identify the symbol rate and modulation format at the same time. The ANN model of this work consists of three layers, where there are 200 neurons and 25 neurons in the input layer and the hidden layer, respectively. The MSE was used to train the neural network to improve classification performance. The results reveal that this scheme can monitor CD in the range of 200-1600 ps/nm, with a DP-QPSK OSNR of 9-19 dB and a DP-16 QAM OSNR of 14-26 dB. The estimation accuracy can reach \(1.317\times 10^{-6}\) after 40 training epochs. However, the data set for training typical ANN-based OPM techniques is often manually selected [93,101], which limits the scalability to more broad signal sets with different symbol rates and modulation formats. The authors of [49] compared the effectiveness of various ML models for OSNR estimation and center wavelength detection of a QPSK coherent system with up to 80 km transmission distance by analyzing the OSA detected optical spectrum. Thirty optical pre-processed spectral data from 1551 to 1554 nm are collected as the training data set. Each spectral consists of 4096 samples. This work compared the training time and detection accuracy of four ML algorithms (k-nearest neighbor (KNN), decision tree (DT), SVM, ANN) with the same parameters. Results show that SVM has the highest estimation accuracy and lowest training time compared with KNN, ANN and DT. However, the author did not give the details of these ML models, such as the number of nodes in each layer of ANN and the loss function used. In order to save the cost of feature extraction, a WDM system using the DNN trained with time-domain raw data for OSNR monitoring is proposed [94]. Since the multiple hidden layer units of DNN can automatically extract the input features for modeling complex data, the asynchronously sampled raw data from the coherent receiver is used as a feature vector for DNN training. The five layer DNN contains 2048 neurons in the input layer and is trained with 400,000 data obtained through experiments. Results show that the OSNR of a 16 GBaud/s DP-QPSK signal is successfully estimated with an average error of 1.23 dB and a range of 12 to 32 dB [94]. However, compared with the method based on the eye-diagram [101], the OSNR estimation error of this method is higher. In addition to the time domain data, the frequency domain raw data has also been explored for OSNR monitoring directly [66], where a CNN model is utilized in a single channel cohere system. The total number of training data is 1,000,000. The structure is a typical CNN consisting of an input layer, two convolutional layers, two pooling layers, and two fully connected layers (2048 nodes). The loss function for training is based on MSE. For different combinations of modulation formats and symbol rates (14- and 16-GBaud/s DP-QPSK, 16-QAM, and 64-QAM signals), the bias errors and standard deviations of the OSNR estimator are analyzed. Results show that the proposed OSNR estimator can achieve accurate estimation results with a 0.4 dB average error. However, many ANN-, DNN- or CNN-based studies only considered the ASE noise or CD without the effects of fiber nonlinearity, such as SPM, XPM and FWM [66; 84; 94].