# Machine Learning Applications for Short Reach Optical Communication
## 3 Machine Learning for Short-Reach Optical Communication System Signal Processing
### Machine-Learning-Based Equalizer for Short-Reach Optical Communications  
With the increasing demand for higher speed and longer transmission distance, the impact of ISI, which can be caused by the bandwidth limitation of various devices/components and fiber dispersion, has become a critical limit in short-reach optical communication systems that leads to detection errors [82]. Therefore, a powerful equalizer is needed for high data rate applications. The digital feed-forward equalizers (FFEs) and decision-feedback linear equalizers (DFEs) are typically used. However, in IM/DD systems, due to the interaction among the square-law detection of PD, the laser/modulator chirp, the fiber dispersion and the additive noise, the overall channel response becomes nonlinear, making it difficult for the linear equalizer to perform accurate channel estimation and impairment compensation [103].  
As a result, more complex approaches such as the maximum likelihood sequence estimation (MLSE) [112] and ML-based equalizers have been studied. ML techniques, especially neural networks, are now considered as a powerful equalization tool to compensate both linear and nonlinear distortions in optical communications. Some of them use neural networks as an aid to other signal processing steps, while others use the neural network directly as a one-stop equalizer. In these studies, the neural network has shown better performance than traditional equalizers, and hence, it becomes a very useful and popular technology for short-reach applications [113]. Among various proposed neural network architectures, the feedforward neural network (FFNN) [104; 103; 114], reservoir computing (RC) [115; 116; 117; 82; 111; 118; 111; 115; 116; 117; 118], and RNN [54; 105] allow time-dependent processes (e.g., ISI) to be captured and learned effectively. Therefore, they are good candidates for the linear and nonlinear equalization of memory communication systems such as IM/DD systems [82]. Hence, this section will focus on the recent studies of using these neural network techniques for signal equalization in short-reach systems.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Applications** & **Features Type** & **ML Techniques** & **System Info.** & **Ref.** \\ \hline Signal detection and classification & Time domain Analogue pattern & ELM \& RC & 25 Gb/s NRZ-PAM, 56 Gb/s PAM-4, 17–55 km & [106] \\ \hline Carrier recovery based on nonlinear equalization & Phase \& frequency noise & Bayesian inference & 50 MBaud CV-QKD system, 500 MSa/s sampling rate, 20 km & [107] \\ \hline Digital predistortion & Frequency-domain sampled signal & ELM & 100 GSa/s sampling rate, 40 GHz bandwidth, 40 km SSMF & [108] \\ \hline Auto-encoder & Time domain signal & LSTM & PAM2 and PAM4 20–80 km & [109] \\ \hline Soft-demapping for nonlinear channels & Soft decision mapping relationship & DNN & 800 Gb/s BtB coherent system, DP-32 QAM & [110] \\ \hline CD compensation & Frequency domain spectrum & DNN & 32 GBd QPSK 16 QAM, 12 km 25 km SSMF & [74] \\ \hline CD mitigation & Time domain digital signal & RC & 32 GBd, OOK, 80 km & [111] \\ \hline PMD compensation & Frequency domain sampled data & LDBP & 128 Csa/s sampling, MIMO-FIR filter, 100 km SSMF & [53] \\ \hline  & FFNN: feed-forward neural network, SSMF: standard single mode fiber, SMF: single mode fiber, DSO: digital storage oscilloscope, MMFs: multi-mode fibers, SUI: Stanford University Interim, ELM: extreme learning machines, RC: reservoir computing, CV-QKD: continuous-variable quantum key distribution, BtB: back to back, DP: dual polarization, LDBP: learned digital back propagation, FIR: finite impulse response. \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._