# Machine Learning Applications for Short Reach Optical Communication
## 2 Machine Learning for OPM and MFI in Short Reach Optical Communications
### Direct Detection System  
Direct detection is commonly used in short-reach optical communications, such as intra-/inter-datacenter linkages, metro, and access networks, due to its convenience for large-scale deployment, low-cost optical transceivers, and low power consumption [1; 98]. The initial attempt to apply ML technology to the OPM in short-reach communications can be dated back to 2006. The authors apply the SVM and pattern recognition methods on eye diagrams to diagnose optical impairments, including CD, PMD and non-coherent crosstalk [50]. However, this approach requires noise filtering on the eye diagram before training, which increases the system's complexity. Then in 2009, ref. [84] proposed a ML application on a direct detection system using ANN for OPM. 40 Gb/s RZ-OOK/RZ-DPSK signal is transmitted over a direct detection system. Eye diagrams of the received signal sampled by the oscilloscope are then generated, which are used as the input to the ML model. The ML model is based on the ANN, which has one hidden layer with 8 hidden  
Figure 7: Typical application of ML models for MFI and OPM in short-reach optical systems and networks; MUX: multiplexer; EDFA: erbium-doped fiber amplifier; ADC: analog to digital converter XPM: cross-phase modulation; FWM: four-wave mixing; SPM: self-phase modulation. neurons. The eye diagram is used to estimate OSNR, CD, and PMD. The mean squared error (MSE) is used during the training process, which can be expressed as [84]:  
\[E_{T_{r}}(\omega)=\frac{1}{2}\sum_{n\in T_{r}}\sum_{k=1}^{K}|y_{k}(x_{n},\omega)-d _{kn}|^{2} \tag{10}\]  
where \(x_{n}\) and \(d_{n}\) are the inputs and the desired outputs of the neural network, \(T_{r}\) is the index sequence of the training data, \(d_{kn}\) is the \(k^{th}\) element of \(d_{n}\) and \(y_{k}(x_{n},\omega)\) is the neural network output for input \(x_{n}\). Based on the experimental verification, the authors extended this approach to a WDM system for OSNR, fiber nonlinearity and dispersion measurement, where the average measurement errors of OSNR, CD and DGD are 0.77 dB, 4.74 ps/nm and 0.92 ps Gb/s for 40 Gb/s RZ-DPSK signal, respectively [84]. However, the input of the ANN comes from the eye diagram, which requires clock recovery and feature extraction, resulting in higher cost and complexity. Based on prior studies that verified the feasibility of applying ML techniques for OPM and MFI, several multi-functional models that can provide both OPM and MFI simultaneously have been proposed. Ref. [99] proposed a multi-task model using SVM to perform MFI and ANN for OSNR monitoring on a 32 GBaud/s 64-QAM direct detection system. The SVM part for MFI is trained by the direct detected data, due to its kernel-based functions, which capture the similarities between any two pairings of raw input data. Meanwhile, the neural network part for OSNR monitoring is trained by eye-diagrams. Results show that the MFI accuracy is 94% and within the OSNR range of 4-17 dB, the mean OSNR estimation error is 0.2 dB. Works like [99] require different ML models to implement MFI and OSNR monitoring separately. Hence, they have the drawbacks of high computational complexity and slow response. In [95], a multi-task deep neutral network (MT-DNN) has been proposed to monitor multiple optical performances in the system simultaneously. In this work, polarization division multiplexed QAM (PDM-QAM) signals are considered, and the asynchronous amplitude histogram after direct detection is selected as the feature input to the ML model. Using MT-DNN, simultaneous MFI, baud rate identification (BRI) and OSNR monitoring are realized.