## 3 Simulation and Results  
In this section, we will further demonstrate the superiority of the proposed scheme in terms of anti-dispersion performance through the two different filter AO-OFDM systems' transmission simulation. By analyzing the bit error rate of the AO-OFDM system with 8, 16, and 32 carrier numbers after 10 to 80 km of SMF transmission without dispersion compensation, it is possible to clearly compare the anti-dispersion capabilities of the two AO-OFDM systems. We used the iterative split-step Fourier method to simulate the chromatic dispersion and nonlinear effects of optical signal transmission in the optical fiber. When considering nonlinear effects, we considered self-phase modulation, cross-phase modulation, and four-wave mixing effects. When considering the influence of dispersion on the system, we not only analyzed the second-order dispersion coefficient, but also considered the walk-off effect of the sub-carriers produced by the first-order dispersion coefficient. CPs of different sizes were inserted, and the symbol rate of the 4\(-\)level pulse-amplitude-modulation (PAM-4) signals or 16-quadrature amplitude modulation (16 QAM) signals carried by the subcarriers was 10G baud with a signal length of \(2^{17}-1\). The power of each sub-carrier was \(-10\) dBm. Figure 1 shows the simulation of AO-OFDM system setup. An optical frequency comb with 10 GHz spacing was generated by a MLL and then broadened in a 400 m dispersion-flattened highly nonlinear fiber (DF-HNLF) (\(\gamma=10.7\)/W/km, \(\beta^{\prime\prime}=-0.446\) ps\({}^{2}\)/km, and \(\beta^{\prime\prime\prime}=0.0057\) ps\({}^{3}\)/km at 1550 nm). When the iterative split-step Fourier method was used to simulate the transmission of optical signals in the optical fiber, each symbol period was sampled 500 times, the step length was 100 m, and each iteration had five individual steps. The fiber was a standard single-mode fiber (SSMF) with attenuation \(\alpha=0.2\) dB/km, nonlinear coefficient \(\gamma=1.3\)/W/km, and \(\beta^{\prime\prime}=-20\) ps\({}^{2}\)/km. The filter used to separate the sub-carriers at the receiving end was a Sinc-shaped filter, and the bandwidth was the same as the symbol rate of each sub-carrier, which was 10 Gbaud. The center frequency of each filter was the same as the filter corresponding to the transmitting end. The greater the CP inserted, the greater the center frequency interval. The signal underwent clock synchronization and signal demodulation after being converted from an optical signal to an electrical signal by the PD. The dispersion chromatic was left uncompensated at the receiving end in order to reflect the anti-dispersion capabilities of the two systems. In Figure 9, the dashed and solid lines of pink, light blue, blue, green, and red represent BER with \(2^{4-8}\) subcarriers, respectively, for the all-optical OFDM systems based on Sinc-shaped filters and Gauss-shaped filters, respectively, at different accumulated dispersion, and it can be seen that, when the accumulated dispersion was 1000 ps/nm, the BER of an all-optical OFDM system based on a sinc-shaped filter with \(2^{4-8}\) subcarriers was higher than \(10^{-2}\). When the number of subcarriers was 16, the BER was 4.214 \(\times\)\(10^{-2}\); when the number of subcarriers was 256, the BER was 6.870 \(\times\)\(10^{-2}\), and the BER of Gauss-shaped filters-based systems was less than \(10^{-2}\). BER = 4.425 \(\times\)\(10^{-3}\) when the number of subcarriers was 16, and 7.858 \(\times\)\(10^{-3}\) when the number of subcarriers was 256. That is to say, when the cumulative CD was 1000 ps/nm, the BER of the all-optical OFDM system based on the Gauss-shaped filter was reduced by more than eight times compared with the system based on the Sinc filter.