## 4 Simulation Results
### The BER Performance  
The BER performance of the proposed scheme based on different training SNRs are investigated in this section under the LOS and NLOS conditions, respectively. For simplicity, only the special optical links in terms of one LOS and three NLOS links are adopted in the testing stage to evaluate the system performance. For convenience, the three NLOS links with the root mean square (RMS) delaying the spread by 7.92, 8.2, and 8.9 ns are marked as \(U_{1,5}\),\(U_{1,1}\), and \(U_{2,1}\), respectively. In addition, the BER of the original received signal and the ideal equalized signal are also depicted here for the convenience of comparison. Note that the original case does not have any equalization, and the ideal case has the CSI perfectly known to a receiver that employs a zero-forcing (ZF) equalizer.  
Figure 6 shows the BER performance comparison of the proposed DL-NPE over a LOS link with different \(\lambda\). In general, we can observe from the figure that all of the BER curves have obvious performance improvements compared with the original case and can achieve an acceptable target BER of less than \(1\times 10^{-3}\). Nevertheless, the proposed scheme for \(\lambda=5\) and 30 dB can achieve similar BERs because they both converge to a similar loss in the training procedure. In addition, the BER curves of these two curves seem to be saturated when the testing SNR is above 20 dB. However, they still have the ability to reduce the BER with increasing testing SNR since the corresponding value is lower than \(5.2\times 10^{-4}\). Comparatively speaking, the proposed scheme for \(\lambda=15\) dB can provide the best BER performance, and the required power can be reduced by at least 2 dB compared with that of \(\lambda=20\) and 25 dB for the same BER level. If the DL-NPE was trained with a small noise level, the model only learns the small decision region near the original symbol location in the constellation plane, which is unfavorable for the learning of signal demapping. Note that the BER performance reaches the performance floor at high SNR levels, and the main reason is that the DL-NPE configured with this parameter reached their maximum performance capacity; thus, there is still residual nonlinear noise in the equalized signal. Although the BER curve for \(\lambda=15\) dB is not exactly the same as the ideal case, the power gap is small, e.g., 1.9 dB for a BER of \(1\times 10^{-4}\), which indicates that the overall channel nonlinearity can be compensated efficiently to a certain degree because the CSI of the IM/DD channel can be approximately learned by the DL approach from the training data.  
Figure 7 demonstrates the corresponding BERs for different \(\lambda\) under the NLOS case \(U_{1,5}\). As seen from the figure, the proposed scheme can still provide acceptable equalization as \(\lambda\) varied from 15 to 30 dB. Note the fact that the performance of the scheme with  
Figure 6: BER performance comparison of the proposed scheme under the LOS case.  
an excellent learning ability. This shows that we cannot select the learned DL model just only based on their learning ability. The optimal learned model should be the optimal trade-offs between the learning and the generalization ability. Under the consideration of convergence speed and training quality, the trained model with \(\lambda=15\) dB is employed in the following.