## 4 Results and Discussion  
In this section, the performance of the proposed OAM-DM-WDM-OFDM-PON system is characterized. Especially, some key parameters adopted in this study are listed in Table 1. Under the same parameter conditions, the system with QPSK and OOK modulation formats is also investigated. In the meantime, the electrical constellation diagram, eye diagram, Q factor, and BER are measured. Figure 4: Spectrum diagram of (**a**) OFDM modulated signal, (**b**) signal after the LiNbO3 MZM, (**c**) the multiplexed signal, (**d**) signal after 50 km MMF, (**e**) the de-multiplexed signal at 193.1 THz; (**f**) the received OFDM signal. Figure 5: The upstream spectrum of the re-modulated signal (**a**) before; (**b**) after SMF transmission. To start, the received OFDM constellation diagrams of the proposed OAM-DM-WDM-OFDM-PON system at 10 Gbps and 20 Gbps are presented in Figure 6a,b, respectively. It can be seen that the quality of the constellation diagram degrades with the data rate increases, which means the stronger attenuation introduces distortion into the signal. As shown in Figure 7, under 10 Gbps data rate, the eye diagrams of upstream and downstream links after 10 km propagation distance are successfully demonstrated with favorable transmission performance. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Parameter** & **Value** & **Unit** \\ \hline \multirow{3}{*}{CW laser} & power & \(-8\) & dBm \\  & wavelength & 193.1, 193.2 & THz \\  & linewidth & 0.01 & MHz \\ \hline \multirow{2}{*}{PRBS generator} & bit rate & \(10,20\) & Gbits \\ \hline \multirow{2}{*}{LG mode generator} & power ratio array & 1 & - \\  & pox. m. n index & 0.2, 0.4 & - \\ \hline \multirow{2}{*}{QAM sequence generator} & bits per symbol & 2 & bits \\ \hline \multirow{2}{*}{LiNbO3 MZM} & extinction & 30 & dB \\ \hline \multirow{3}{*}{OFDM de/modulator} & number of subcarriers & 512 & - \\  & number of FFT points & 1024 & - \\  & number of cyclic prefix points & 64 & - \\ \hline \multirow{3}{*}{Quadrature de/modulator} & frequency & 7.5 & GHz \\ \hline \multirow{9}{*}{MMF} & length & 10–80 & km \\  & attenuation & 0.2 & dB/km \\  & refractive index profile & step-index & - \\  & core radius & 3.4 & μm \\  & core refractive index & 1.45 & - \\  & dispersion slope & 0.075 & ps/nm\({}^{2}\)/km \\ \hline \multirow{2}{*}{WDM de/mux} & frequency & 193.1, 193.2 & THz \\ \hline \multirow{2}{*}{Spatial de-multiplexer} & number of spatial modes & 1 & \\ \hline \multirow{2}{*}{Optical amplifier} & gain & 15 & dB \\ \hline \multirow{2}{*}{Global parameter} & sequence length & 16,384 & - \\  & sample per bit & 32 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The Main Parameters of the OAM-DM-WDM-OFDM-PON System. Figure 6: Constellation diagrams of received OFDM at (**a**) 10 Gbps; (**b**) 20 Gbps data rate after 80 km transmission distance. As shown in Figure 8a, the influence of OAM mode number and different transmission distances on BER is investigated in the hybrid OAM-DM-WDM-OFDM-PON system. Here, we mainly focus on the performance of the upstream link. The black dots show the BER of single OAM mode (\(LG_{l=0,p=2}\)) whereas the red dots and the blue dots show the 2 multiplexed OAM mode (\(LG_{l=0,p=2}\),\(LG_{l=0,p=4}\)) and 4 multiplexed OAM mode (\(LG_{l=0,p=2}\), \(LG_{l=0,p=4}\), \(LG_{l=0,p=6}\), \(LG_{l=0,p=8}\)), respectively. It is observed that with the transmission distance increased, the BER performance is getting worse. The system performance of a single mode is better than multiple modes in short-distance transmission case, which is caused by mode crosstalk. Under the same BER, the 2 multiplexed OAM mode system shows significant advantages in transmission capacity thanks to its orthogonal property and low crosstalk. For the 4 multiplexed mode system, the performance deteriorates significantly over long distances owing to the mode crosstalk. With example constellation diagrams, two curves of BER under the data rate with 10 Gbps and 20 Gbps are displayed in Figure 8b.