## 4 Performance Evaluation  
Figure 4 illustrates a comparison of Q-factor versus HNLF length for HNLF A-D, which are obtained by simulations using \"OPTISYSTEM 15.0\" [21]. On other hand, Q-factor can be calculated from the measured BER using Equation (2), which is provided by [11]. \[Q(dB)=20\text{lg}[\sqrt{2}\times erfcinv(2\times BER)] \tag{2}\]  
Note that the numerical results illustrated in Figure 4 are obtained under the conditions that the input signal power and the pump signal power of OPC are set to the optimum values obtained by Figures 2 and 3 for HNLF A-D, respectively. Figure 4 shows that the HNLF length corresponding to the optimum Q-factor value for HNLF A-D is 550, 500, 750, and 800 m, respectively. Equation (3) shows that the deterioration power of OPC is sensitive to HNLF length [2]. \[P_{\text{deterioration}}=3N_{\text{SC}}^{2}(\gamma L)^{4}P_{pump}^{2}P_{\text{SC}}^ {3} \tag{3}\]  
where, \(N_{SC}\) is the number of sub-carriers, \(\gamma=\frac{2\pi n_{2}}{\lambda_{Q}\lambda_{eff}}\) is the non-linearity factor in the HNLF, L is the length of HNLF, \(P_{pump}\) is the pump signal power, \(P_{\text{SC}}\) is the power of a single sub-carrier. Figure 5 illustrates the received 16-QAM signal constellation diagrams at the receiver end for different scenarios, where received OSNR is set up to 34 dB. The aim is to evaluate the OPC compensation capability. It is known that fiber nonlinear effect, dispersion effect, and ASE noise accumulated within the transmission bandwidth are the major interference in optical transmission systems, especially in long haul transmission. After an optical BPF of 0.32 nm is adapted for reducing the out-band ASE noise effect, it can be seen that constellation rotation obviously due to fiber nonlinearity in Figure 5a. The constellation diagram of OPC with different HNLF scenarios as shown in Figure 5b-e demonstrates that OPC can effectively compensate the fiber dispersion and nonlinearity. In contrast, as shown in Figure 5a, although DCF is used for dispersion compensation, the constellation points are still scattered compared to that of using OPC. It clearly demonstrates that dispersion compensation using OPC is better than that of using DCF [9]. Figure 4: A comparison of Q-factor versus HNLFs length. Figure 6 shows Q-factor versus OSNR for different HNLF scenarios. Table 3 presents the numerical results of conversion efficiency, Q-factor gain, and BER, where received OSNR is 34 dB. It can be observed that the mid-link OPC with 550 m HNLF A has Q-factor of 9.8 dB, BER of 6.1 \(\times\) 10\({}^{-4}\) and conversion efficiency of \(-\)22 dB. In contrast, the mid-link OPC with 800 m HNLF D has Q-factor gain of 8.9 dB, BER of 2.7 \(\times\) 10\({}^{-3}\), and conversion efficiency of \(-\)22.6 dB. This can be explained by Equation (4), that the power spectrum of OPC, denoted as \(P_{OPC}\), is in direct proportion to the term \(\left(\gamma L\right)^{2}\)[2]. \[P_{OPC}=\left(\gamma L\right)^{2}P_{pump}P_{SC} \tag{4}\]  
The mid-link OPC improves Q-factor of 3 dB in average and enhances the BER performance nearly two orders magnitude comparing to the case of no OPC. Figure 5: Received 16-QAM signal constellation diagram after 800 km transmission: (**a**) Dispersion compensation using dispersion compensated fiber (DCF); (**b**) mid-link OPC using 550 m HNLF A; (**c**) mid-link OPC using 500 m HNLF B; (**d**) mid-link OPC using 750 m HNLF C; (**e**) mid-link OPC using 800 m HNLF D.  
Figure 6: A comparison of Q-factor gains versus optical signal-to-noise ratio (OSNR) after 800 km transmission.