## 4 Equalization Technologies
### Ffe/Dfe
#### 4.1.2 Improved Algorithms Based on FFE/DFE  
\(\bullet\) DD-FTN  
When the FFE tries to amplify the power of high-frequency components to compensate for the low-pass effects, it boosts the noise power at high-frequency components as well. To address this phenomenon, a DD-FTN algorithm is proposed [33] and the principle is shown in Figure 9.  
Figure 8: The structure of **(a)** DFE; **(b)** FFE and DFE combined. Figure 9: **(a)** The components and **(b)** the structure of DD-FTN (reprinted from [33] with permission from authors and reprinted from [7] with permission from IEEE). First, the signal after synchronization is equalized by a FFE, adapted by the LMS algorithm. Then, a balanced digital filter is placed behind to suppress the enhanced in-band noise by the equalizer. The transfer function of the balanced filter in \(z\)-transform is \(H(z)=1+az^{-1}\), where the tap coefficient \(\alpha\) is employed to optimize the frequency response of the post filter. Finally, the maximum likelihood sequence estimation (MLSE) is utilized behind to eliminate the strong ISI induced by the balanced filter. Although two more DSP blocks are contained in DD-FTN compared to traditional equalizers, the increase in complexity is relatively small and the overall complexity is not high compared to other DSP techniques. The BER performance as a function of received optical power for 112 Gbps PAM4 signal after 2 km SSMF transmission is depicted in Figure 10a [33]. With conventional FFE, the enhanced noise significantly degrades the system performance and a BER floor at \(5\times 10^{-2}\) can be observed. By using DD-FTN, the noise enhancement is effectively mitigated by the balanced filter and the induced ISI can be processed by the MLSE. The performance is improved and the BER can reach \(3\times 10^{-4}\) when received power is \(-7.1\) dBm. Figure 10b shows the BER performance versus received optical power for 140 Gbit/s PAM-4 system after back-to-back transmission [35]. It can be found that the traditional FFE updated by DD-LMS exhibits the worst performance, while the BER can reach the hard decision FEC (HD-FEC) threshold of \(3.8\times 10^{-3}\) with DD-FTN. Therefore, DD-FTN can make a big difference in enhanced noise mitigation. \(\bullet\) ID-FFE/ID-DFE  
In C-band transmission, low-cost modulator like DML will introduce an additional impairment due to the interaction between frequency chirp and chromatic dispersion. Recently, a low complexity intensity directed equalizer based on FFE and DFE is proposed to suppress the chirp induced distortions. Different from the traditional FFE/DFE that utilizes one set of coefficients, the proposed algorithm first divides the symbol into different sets according to its intensity level, as shown in Figure 11a [37]. Then the coefficients of different groups are applied accordingly. Four sets of coefficients for PAM4 symbol are selected according to the three thresholds for ID-FFE and four levels for ID-DFE. After classification, the desired tap coefficients from different sets are used and the following procedures are the same as the traditional FFE/DFE. In terms of complexity, only a few simple decision circuits are added to the original FFE/DFE and the complexity increment is negligible considering the operations of multiplication in the equalizer. Figure 10: (**a**) The bit error rate (BER) performance versus received optical power for 112 Gbps PAM4 signal after 2 km SSMF transmission (reprinted from [33] with permission from authors). (**b**) The BER performance versus received optical power for different tap coefficient of balanced filter for 140 Gbit/s PAM4 system after back-to-back transmission (reprinted from [35] with permission from IEEE). The effectiveness of ID-FFE/ID-DFE greatly depends on the accuracy of the decision in the classification. Thus, a conventional FFE is employed to equalize the severe impairments and enhance the decision accuracy before the intensity directed equalizer as shown in Figure 11b.