## 3 Results and Discussion
### BER Performance  
Finally, the simulation results on the bit-error-rate (BER) performance of the multi-twin-SSB system with 16-QAM modulation after 50-km SSMF transmission with and without KK-receiver are presented in Figure 4a. In the simulations, the guard band was set to 3 GHz and the OMI was 0.08. The two inner sub-bands for ONU2 and ONU3 were found to have worse BER performance than the two outer sub-bands for ONU1 and ONU4 since the ONU2 and ONU3 were closer to the optical carrier and the BERs were deteriorated mainly by the SSBI of the desired sideband. For example, ONU2 and ONU3 showed an error floor about 8.84 \(\times\) 10\({}^{-3}\) for a conventional receiver without a KK-scheme. This high error floor made the system fail to work with the BER threshold of 3.8 \(\times\) 10\({}^{-3}\) for the commonly-used hard-decision forward-error-correction (HD-FEC) code with 7% redundancy ratio. However, if KK-receiver was available, the error floor could be reduced to 1.44 \(\times\) 10\({}^{-3}\), which was lower than the 7% redundancy ratio HD-FEC BER threshold. If the BER threshold of 2.4 \(\times\) 10\({}^{-2}\) for a soft-decision FEC (SD-FEC) code with 20% redundancy ratio was used instead, the KK-receiver could provide about 1 dB received optical power (ROP) gain over the receiver without a KK-scheme for ONU2 and ONU3. Compared with ONU2 and ONU3, the two outer sub-bands for ONU1 and ONU4 showed better BER performance because the SSBI only overlapped the desired signals partially as discussed in Section 3.1. As a result, the BER floors of ONU1 and ONU4 with a KK-receiver and without a KK-receiver were about 2.55 \(\times\) 10\({}^{-4}\) and 9.12 \(\times\) 10\({}^{-4}\). About 0.7 dB ROP gain could be obtained for the KK-receiver at 7% redundancy ratio HD-FEC BER threshold for ONU1 and ONU4.  
From Figure 4a, it was also observed that the ONU2 and ONU3 had worse BER performance compared with the ONU1 and ONU4 because of the residual SSBI effect. In order to balance the performance between the ONUs, the power of different sub-band signals could be pre-equalized in the transmitter-side DSP. To do this, we increased the signal power of the two inner sub-bands while decreasing that for the two outer sub-bands. Figure 4b shows the simulation results on BER performance after power pre-equalization.  
Figure 3: SNR versus OMI for 12.5 Gbaud per sub-band 16-QAM modulation after 50-km transmission. Insets: (a) and (b) represent the constellation diagrams for the outer sub-bands with and without KK-receiver at the optimum OMI, respectively; (c) and (d) represent the constellation diagrams for the inner sub-bands with and without a KK-receiver at the optimum optical modulation index (OMI) respectively.  
Comparing the results from Figure 4b with Figure 4a, the four ONUs were found to have a similar performance for the KK-receiver. For example, for the case without pre-equalization, if the 7% redundancy ratio HD-FEC BER threshold was used, the required ROP was about \(-10.2\) dBm for ONU1 and ONU4, while a higher ROP of about \(-8.8\) dBm was required for ONU2, ONU3. After pre-equalization, the required ROP became \(-9.5\) dBm for all ONUs. Note that the pre-equalization could be dynamically controlled via the centralized SDN controller and easily implemented in the DSP-based transmitters.