## 4 Results and Discussion  
In this section, we will discuss the performance of the CS M-ary SVM NLE scheme in compensating the nonlinear effects of the 120 Gb/s PS-64 QAM coherent optical communication system. Figure 9 shows the Q factor and the number of SVs versus the ratio of training data when launched optical power is 0 dBm. The size of the data set is 32,768. With the increase of the ratio of training data, both the Q factor and the number of SVs are increasing. The complexity of SVM only depends on the number of SVs. Therefore, the complexity increases with the increase of the ratio of training data. When the ratio of training data is greater than 0.6, although the number of SVs is increasing, the performance of the system is no longer improved. The Q factor of the system has been convergent. Therefore, we pick 60% data as training data while 40% of data are testing data. Figure 10 shows the Q factor as a function of launched optical power for 120 Gb/s PS-64 QAM with CS M-ary SVM NLE, M-ary SVM NLE, and without (w/o) employing NLE. The Q factor of the soft-decision FEC (SD-FEC) limit is 6.25 dB, which corresponds to the BER of \(2\times 10^{-2}\)[26]. As shown in Figure 10, when the launched optical power is in the range of \(-5\) dBm to \(-3\) dBm, the Q factor increases with the increase of launched optical power. This is because in this range, the OSNR of the received signal is increasing  
Figure 8: (**a**) The experimental setup for the 120 Gb/s PS-64 QAM coherent optical communication system; (**b**) offline DSP flow chart. Figure 9: Q factor and the number of support vectors versus the ratio of training data. with the increase of the launched optical power. In this situation, amplified spontaneous emission (ASE) is the main element affecting the performance of the system. However, when the launched optical power is higher than \(-3\) dBm, the Q factor will decrease as the increase of launched optical power. In this launched optical power range, the system is mainly affected by the fiber nonlinearity instead of ASE. The nonlinearity of the system is more and more serious as the launched optical power increasing, especially for the outer constellation points with higher power. The LOPDR, which represents the difference between the two power values corresponding to the points where Q factors are equal to the Q factor of the SD-FEC limit (6.25 dB) is employed to evaluate the performance of the NLE schemes. As for the results shown in Figure 10, the LOPDR is 9.2 dBm (\(-5\) dBm \(\sim+4.2\) dBm) under CS M-ary SVM NLE. In addition, the LOPDRs are 8.6 dBm (\(-5\) dBm \(\sim+3.6\) dBm) and 7.6 dBm (\(-4.8\) dBm \(\sim+2.8\) dBm) under M-ary SVM NLE and without NLE, respectively. Therefore, when employing the proposed scheme, the LOPDR is 0.6 dBm larger than when the M-ary SVM NLE scheme is employed. In addition, with the aid of the proposed scheme, the LOPDR of PS-64 QAM is 1.6 dBm larger than without the NLE situation. At the optimal launched optical power of \(-3\) dBm, compared with employing M-ary SVM NLE and without employing NLE, the proposed CS M-ary SVM scheme can obtain about 0.50 dB and 0.96 dB Q factor gain, respectively. The constellation diagrams of PS-64 QAM detected by CS M-ary SVM NLE and without employing NLE are illustrated in Figure 10a,b, respectively. The complexity of the SVM algorithm is only dependent on the number of support vectors (SVs). The number ofSVs is measured to compare the complexity of the two NLE schemes. The number ofSVs for the two NLE schemes is shown in Figure 11a. As can be seen in the results, the number ofSVs is the least at the optimal launched optical power of \(-3\) dBm. Due to the ASE noise, the number ofSVs is increasing with the decrease of the launched optical power when the optical power is lower than \(-3\) dBm. However, when the launched optical power is higher than \(-3\) dBm, the number ofSVs is gradually increasing as the launched optical power is increasing.