## 4 Results and Discussion
From the graph, one can find that raising the propagation rate would increase BER values. Note that all values are lower than the forward error correction (FEC) threshold of \(3.8\times 10^{-3}\). Thus, future improvements to the MMF may lead to lower crosstalk and better system performance. Figure 8: BER curves with (**a**) single OAM mode versus multiplexed OAM modes; (**b**) 10 Gbps versus 20 Gbps single channel data rate in the OAM-DM-WDM-OFDM-PON system upstream link. Figure 7: Eye diagrams of (**a**) downstream; (**b**) upstream link after 10 km transmission distance. Table 2 shows the BER and Q factor with CW laser power of \(-8\) dBm, \(0\) dBm, and \(3\) dBm under \(10\) Gbits transmission rate, respectively. The performance of the system is degraded with the input power reduction, which is caused by the low power efficiency of each channel and thermal noise. In addition, the main limitation to the system performance is fiber mode crosstalk. We measure the power before and after transmission through MMF, as depicted in Table 3. As a consequence, different OAM modes would suffer little mode crosstalk (<0.01 dB). In Figure 9, simulated investigations are undertaken for the OAM-DM-PON system over a single wavelength, 2 wavelengths, and 4 wavelengths channel. For transmission distances varying from \(10\) km to \(80\) km, the BERs of the hybrid system with single and 2 wavelengths fluctuate around \(10^{-14}\) and \(10^{-30}\), respectively. It can be seen that the performance of 2 wavelengths system is similar to the 4 wavelengths system. It shows that the system with 2 wavelengths as well as 4 wavelengths has a better performance compared with the single wavelength transmission. Furthermore, it can also be seen from Figure 9 that as the transmission distance increases, the BER performance of the three systems is deteriorated. To investigate the influence of optical fiber dispersion on system performance, the eye diagrams are measured in back-to-back (B2B) transmission and \(50\) km fiber links, respectively. As can be seen in Figure 10, the performance of the system will decrease with the influence of the dispersion. The BER of the system under back-to-back and \(50\) km MMF transmission is \(2.8\times 10^{-73}\) and \(2.3\times 10^{-30}\). Besides, modal dispersion also affects \begin{table}
\begin{tabular}{c c c} \hline \hline
**Power** & **BER** & **Q Factor** \\ \hline \(-8\) dBm & \(2.31201\times 10^{-30}\) & \(11.3421\) \\ \(0\) dBm & \(1.50521\times 10^{-30}\) & \(11.3798\) \\ \(3\) dBm & \(1.50344\times 10^{-30}\) & \(11.3824\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: CW power versus BER and Q factor with \(10\) Gbit/s for OAM-DM-WDM-OFDM-PON upstream transmission. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Channel 1** & **Channel 2** \\ \hline
**0** & **10 km** & **0** & **20 km** \\ \hline SNR & 35.938069 dB & 35.932641 dB & 36.181936 & 36.174332 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The signal-noise ratio (SNR) versus transmission distance before and after MMF. Figure 9: BER versus transmission distance of the hybrid OAM-DM-WDM-OFDM-PON system with different wavelengths. the power of the signal. For B2B transmission, the received power of OAM is \(-13.13\) dBm, while the power of OAM is \(-27\) dBm after \(50\) km MMF. The comparative analysis of the BER features based on the OOK and QPSK modulation is plotted in Figure 11a,b. Especially, it only takes a low data rate with \(5\) Gbps and \(10\) Gbps in the system. As shown in Figure 11a, the BER values of the two systems are relatively large under \(10\) Gbps transmission rate. One possible reason is that the signal carriers from downstream links suffer from modal crosstalk, which reduces the optical power. Another possible reason is that the limitation of SMF leads to the attenuation of signals. Figure 11b also depicts the BER of the downstream link versus the transmission distance and a total capacity of \(10/20\) Gbps below the FEC limit is achieved.