## 3 Adaptive Compensation through Digital Filters
Figure 6: The direct current (DC) gain of the FIR filter should be optimized to minimize the bit error ratio (BER). In the subplot of the back-to-back scenario, the penalty of the Q\({}^{2}\) factor under the strong FIR setting is always zero, since this is chosen as the baseline. With the signal's bandwidth larger than 40 GHz, we obtain a negative penalty for the mild setting, which indicates a better BER performance. However, when the signal's bandwidth is smaller than 30 GHz, we obtain a positive penalty for the mild setting, which indicates a worse BER performance. In the other scenarios, the penalty in the Q\({}^{2}\) factor is always positive due to the fact that the transmission impairments such as CD, PMD, and PDL cause the degradation in the BER. Still, we can notice that the mild FIR setting performs better with the signal's bandwidth larger than 40 GHz, while the strong FIR setting performs better with the signal's bandwidth smaller than 30 GHz. Those experimental results agree with the analysis above. In the scenarios of back-to-back, 3-dB PDL, and combined impairment, as shown in Figure 7a-c, a coherent receiver using a strong FIR setting can still recover the signal with 20-GHz signal's bandwidth; however, a coherent receiver using the mild FIR setting fails to recover this signal. This indicates that the operation range of the coherent receiver using 4-dB peaking at 19 GHz (strong FIR setting) is 5 GHz larger than that of the coherent receiver using 2-dB peaking at 13 GHz (mild FIR setting). A 5-GHz improvement on the tolerance to the bandwidth narrowing effect will allow the coherent signal to pass 10 additional ROADMs [16]. In the data path of the coherent receiver, there is another adaptive equalizer (AEQ) to track the state of polarization (SoP), de-multiplex the orthogonal polarizations, and compensate the PMD. It is illustrated as the \"PMD Comp\" block in Figure 1. The AEQ also has multiple taps, thus a large amount of PMD can be compensated. To some degree, the bandwidth-narrowing effect can be partially compensated by this AEQ. The advantages of AEQ are high loop bandwidth and small response time. Thus, the equalizer can quickly track and dynamically compensate the bandwidth narrowing effect. However, there are certain limitations associated with the AEQ. The first limitation from AEQ is its  
Figure 7: The penalty in Q\({}^{2}\) factor versus the receiver bandwidth under different scenarios of the transmission impairments. (**a**) Result in back-to-back setup. (**b**) Result with 40 ps/nm CD. (**c**) Result with combined impairment. (**d**) Result with 25 ps PMD. (**e**) Result with 3 dB PDL. The Combined impairments are 3-dB polarization dependent loss (PDL), 18-ps polarization mode dispersion (PMD), and 40-ns/nm chromatic dispersion (CD). complexity. The AEQ is a \(2\times 2\) equalizer with tap coefficients being complex numbers. It has large power consumption and long latency as well. The second limitation is that AEQ is placed after the CD compensation block. Thus, the bandwidth narrowing effect will increase the noise floor of the CD compensation block. The third limitation is that the quality of the signal impacts whether AEQ converges. When the bandwidth of the signal is severely narrowed down to <20 GHz, we notice that the coherent receiver cannot lock due to the fact that the AEQ cannot converge anymore. This can be seen from Figure 7a,c,e, where there are no data points for the mild FIR setting. When we apply the strong FIR setting to partially compensate the bandwidth narrowing effect, the AEQ converges, and the coherent receiver locks. We summarize the difference between two types of equalizers in Figure 4:0  
The influence of these two types of equalizers on the optical performance of the coherent transponder can also be viewed in the experimental results above.