# Frequency Comb-Based WDM Transmission Systems Enabling Joint Signal Processing
## 4 Joint Digital Signal Processing Schemes for Carrier Recovery
### Experimental Evaluation
#### 4.3.2 Joint Estimation  
We evaluated joint phase estimation with the same setup as in [66], but with a distributed feedback (DFB) laser as the seed for the transmitter. The DFB laser had a specified linewidth of 1 MHz and  
Figure 8: (**a**) Phase traces from channels spaced \(\Delta f=25\) GHz apart, together with their difference; (**b**) phase traces from channels spaced \(\Delta f=275\) GHz apart, together with their difference; (**c**) phase difference standard deviation (STD) as a function of channel frequency spacing. was chosen to evaluate the phase noise tolerance of the joint phase estimation. The algorithm used was the modified BPS described in Section 4.1.2. Frequency offset compensation was performed in a master-slave fashion as illustrated in Figure 7a. To align the phase before joint estimation, a feedback-based phase-aligner as described in Figure 7b was applied. The phase alignment was implemented as a one-tap decision-directed equalizer, where the tap was updated every 128 th symbol. The phase-estimation algorithms were evaluated for channel separations of up to \(\pm 275\,\mathrm{GHz}\). We compared independent phase estimation, joint-polarization and joint-wavelength phase estimation, which means that the phase estimation is performed on 1, 2 and 4 polarization channels, respectively. To make a fair comparison, the feedback-based phase alignment was applied in all cases. In Figure 9a,b, the bit-error rate (BER) for the center channel is plotted as a function of averaging filter time window for the three cases, with frequency spacing of \(125\,\mathrm{GHz}\) and \(275\,\mathrm{GHz}\) away. This corresponds to five and 11 wavelength channels away, respectively. For the same averaging time window, the joint schemes used two- or four-times more symbols for averaging due to having access to more channels. Both the joint-polarization and joint-wavelength phase-estimation schemes consistently performed better than the single-polarization phase estimation in terms of BER and had a shorter optimum averaging time window, which is expected. The catastrophic failures for short block lengths seen in Figure 9a,b were caused by cycle slip events, and an increased number of jointly-processed channels improve the resilience against these events. In terms of BER, the joint-wavelength scheme performed better than the joint-polarization scheme with 125-GHz frequency spacing, but for a spacing of \(275\,\mathrm{GHz}\), which was the furthest tested, the BER performance of the two joint schemes is similar. The higher resilience against cycle slips was however retained also for the higher spacing. In Figure 9c, the ratio between the BER achieved by the joint-polarization and the joint-wavelength schemes is plotted as a function of the frequency spacing. Up to a frequency spacing of \(175\,\mathrm{GHz}\), the joint-wavelength scheme performed better than the joint-polarization, but for larger frequency spacings, this gain is diminished. This was likely due to the frequency-spacing-dependent phase-noise differences between the comb lines observed in [66]. In Figure 9d, the BER is plotted as a function of the OSNR for a frequency spacing of \(125\,\mathrm{GHz}\). We observe a 0.25-dB lower required OSNR for  
Figure 9: **(a,b)** Bit-error rate (BER) of the center channel as a function of the filter block-length, with either independent, joint-polarization or joint-wavelength phase estimation for different frequency spacings to the other wavelength channel. The optical signal-to-noise ratio (OSNR) is 20.3 dB. **(c)** The ratio between the BER for joint-polarization and joint-wavelength phase estimation as a function of frequency spacing. The optimal block length is used in all cases. OSNR \(\cong 20\,\mathrm{dB}\). **(d)** BER vs. OSNR for a frequency spacing of \(125\,\mathrm{GHz}\). The block lengths are 96, 48 and 32 for independent, joint polarization and joint wavelength, respectively, which are close to the optimum values.