## 4 Equalization Technologies
### Summary of Recent Work  
Various equalization technologies mentioned above are summarized and compared as shown in Table 3. The FFE/DFE is widely used in short-reach PAM4 optical links due to simple architecture and low complexity, however, it can only eliminate the linear ISI induced by bandwidth limitation and CD. In [26], a single-channel 56 Gbit/s PAM4 optical transmission over 60 km is experimentally demonstrated with receiver sensitivities of \(-19.9\) dBm using 35 taps FFE. Meanwhile, with the help of 17 taps FFE, the 40 km error-free transmission is achieved for 106 Gbit/s PAM4 using APD receiver [27]. The THP is a transmitter-side DFE without suffering from error-propagation, which is proposed recently to resist against power fading and bandwidth limitation. For the first time, the THP is applied to 100 Gbit/s FTN PAM4 transmission over 40 km through a 20 GHz low-pass channel [72]. With similar or a low addition of complexity, the novel DD-FTN, ID-FFE/ID-DFE and CR-FFE can compensate for the weakness of conventional linear equalizers and achieve better performance for specific issues. In [35], the DD-FTN is experimentally demonstrated for a 140 Gbit/s PAM4 signal over 20 km transmission with a receiver sensitivity of \(-5.5\) dBm. [PERSON] et al. firstly demonstrate a C-band 56 Gbit/s PAM4 system over 43 km transmission with the proposed ID-FFE/ID-DFE [37]. In [39], the CR-FFE resist SCO up to 1000-ppm after 40 km transmission for 50 Gbit PAM4 system based on 10 GHz DML. While bandwidth limitation can be efficiently compensated for by using FFE/DFE, the nonlinearity of devices is difficult to eliminate effectively. VNLE is the most popular nonlinear equalization while the high computational complexity can be reduced by removing the less important kernels. Using 1722 taps VNLE, the C-band \(2\times 56\) Gbit/s PAM4 transmission over 100 km is experimentally demonstrated in [92]. A sparse VNLE with half computational complexity achieves similar performance for \(2\times 64\) Gbit/s PAM4 transmission over 70 km SSMF using 18 GHz DML [93]. As for machine learning algorithms, SVM and NN including artificial NN (ANN), deep NN (DNN), and convolutional NN (CNN) are the mainstream to further eliminate nonlinear distortions of PAM4 optical links with higher complexity. When the SVM is applied to PAM4 signal, sensitivity gain of 2.5 dB is obtained for 60 Gbit/s VCSEL-MMF short-reach optical links [40]. [PERSON] et al. experimentally demonstrate a C-band \(4\times 50\) Gbit/s PAM4 transmission over 80 km SSMF employing a radial basis function ANN [44]. In [46], with the help of CNN, a 112 Gbit/s PAM4 transmission over 40 km SSMF is accomplished and the BER performance outperforms traditional VNLE. For more complicated DNN, the BER of \(4.41\times 10^{-5}\) is obtained for a 64 Gbit/s PAM4 transmission over 4 km MMF based on 850 nm VCSEL [47]. Note that some equalization methods such as look-up table (LUT) are not mentioned in this paper due to less implementation. Figure 20: **(a)** BER vs. fiber length with NN for 112 Gbps SSB-PAM4 transmission. **(b)** BER vs. OSNR after 80 km dispersion uncompensated SSMF (reprinted from [49] with open access from OSA). At present, the standard to evaluate the equalization technologies is considering both the performance improvement and the computational complexity. The high complexity will occupy massive resources for computation, thus increasing the computational cost. The score to judge the equalization technologies can be described as:  
\[\text{score}=\frac{a*\text{performance improvement}}{b*\text{computational cost}} \tag{7}\]  
where \(a\) and \(b\) are the influence factors of performance improvement and computational cost, respectively. The comparison of the computational complexity and performance improvement for different equalization technologies is summarized in Table 4. Note that the main limited factor for the short-reach PAM4 system is the cost, and the goal for equalization technologies is to achieve better performance at the same computation cost.