# High-Speed, High-Performance DQPSK Optical Links with Reduced Complexity VDEE Equalizers
## 4 Optical Layer Simulation
The rOSNR deterioration is saturated at 600 ps/nm, indicating that the equalizer is slowly reaching its full potential in terms of alleviating the residual CD. Although every equalizer succeeds in ensuring the proper operation of the system (by achieving a BER of \(10^{-3}\)), for a certain amount of additional dispersion there is point where the increase in the required OSNR becomes dramatic and the performance is deteriorated. From Figure 8 it becomes evident that although the best efficiency is achieved by the four-input joint single-ended VDFE and SVDFE, all three-input partially-joint alternatives exhibit marginal differences in performance. Figure 8: Required OSNR performance of comparison between the joint single-ended configurations (4I-) and the partially-joint three-input ones (3I) for the cases of (**a**) SVDFE[5,3]; (**b**) VDFE[9,5], (**c**) SVDFE[9,5]; and (**d**) VDFE[9,5]. All of the aforementioned conclusions can also be verified by the results that are derived by the numerical modeling of the multi-span transmission system shown in Figure 7b and are depicted in summary in Figure 9. The OSNR of this specific transmission system is approximately 18 dB measured at a bandwidth of 12.5 GHz. In this case the BER of the signal received after equalization is estimated and presented with respect to the variable amount of chromatic dispersion that emerges due to the partial optical compensation (OCR = 80%-99%). These performances are presented along with the case where no electronic equalization is used (without equalizer) and the FEC (Forward Error Correction) limit = 10\({}^{-3}\). Nonetheless, apart from the minor differences in the performance of all of the possible candidates, one can conclude that the solution of utilizing an equalization scheme that ignores branch \(Q_{d}\) can offer the best trade-off between complexity and efficiency. On the contrary, all equalizers that ignore \(Q_{c}\) output seems to experience the worst performance although its difference in efficiency is still marginal. Similarly, regarding the I channel of information, ignoring the \(I_{d}\) port instead of the \(I_{c}\) port presents better performance. This feature can be justified by noting that the constructive output port resembles a duobinary (DB) signal, while the destructive output port resembles an alternating-mark-inversion (AMI) signal [27; 28]. The intrinsic high tolerance of the DB modulation format in chromatic dispersion originates from its narrow spectrum [29] and can explain the better performance of every equalizer when the constructive, rather than the destructive, port (of each channel) is maintained to undergo the process of equalization [30]. Since ignoring the destructive output port of each channel (\(I\) or \(Q\)) seems to be the most efficient solution among the partially joint configurations in terms of alleviating the CD effect, it becomes of interest to investigate the performance of a degenerated equalizer in which the destructive outputs of both \(I\) and \(Q\) channel are ignored, resulting in a two-input partially-joint equalizer (denoted here after  
Figure 9: Estimated BER of optical links that utilize (**a**) SVDFE[5,3]; (**b**) VDFE[5,3]; (**c**) SVDFE[9,5]; and (**d**) VDFE[9,5] equalizers depending on the ignored input signal (\(I_{c}\), \(J_{d}\), \(Q_{c}\), \(Q_{d}\)). 41 and 3\(I\) denote the number of inputs. as 2_I_). The two-input partially-joint equalizer offers the lowest complexity among all of the different single-ended receiver configurations. In order to provide a fair comparison in terms of efficiency, the performance of the two-input partially-joint equalizer is presented along with the performance of the balanced receiver/equalizer combination [2], considering that the complexity of the configurations are also comparable. In Figure 10 the estimated BER of the two-input configuration for every equalizer is depicted, along with the performance of balanced configuration, in respect to variable amounts of residual dispersion.