# Wheel-Based MDM-PON System Incorporating OCDMA for Secure Network Resiliency
## 3 Results and Discussion
### Influence of FWM, Dispersion and Interference  
(a) Influence of FWM: By realizing a wheel-based MDM-PON scheme utilizing MWZCC OCDMA code, the high bandwidth and secure and protected network can be obtained, but some limitations also exist in the proposed scheme. However, as the number of channels (\(N_{c}\)) increases in the proposed scheme, there is an increase in system capacity by \(N_{c}\) times, but it also causes a major non-linear effect, i.e., FWM. The FWM effect generates unwanted wavelengths because of the interference of at least three distinct wavelengths in the fiber medium. The interactions of primary wavelengths cause unwanted FWM wavelengths in the transmission link. Mathematically, the generated FWM wavelengths can be expressed as [34]:  
\[\lambda_{abc}=\lambda_{a}\pm\lambda_{b}\pm\lambda_{c} \tag{1}\]  
Figure 8: Measured BER vs. received optical power at 10/2.5 Gbit/s data rate over 1 km range for modes 0 and 1 for different codes in (**a**) downstream and (**b**) upstream transmission. where \(\lambda_{a}\), \(\lambda_{b}\) and \(\lambda_{c}\) are three primary wavelengths in the fiber link. The number of generated FWM wavelengths are expressed as [34]:  
\[M=\frac{N_{c}^{2}}{2(N_{c}-1)} \tag{2}\]  
In the proposed scheme, a total of eighteen wavelengths were utilized. Thus, the total numbers of generated FWM wavelengths are 10 using Expression (2). Additionally, the decrease in channel spacing and increase in data rate in the system further increases the FWM side lobes. This impact can be minimized by using adequate channel spacing, data rate and optimum multiplexing techniques to handle multiple wavelengths. Therefore, in the proposed scheme, the MDM technique was used. (b) Influence of Dispersion: Fiber dispersion is another parameter that decreases the system performance. However, chromatic dispersion (CD) is the main cause of restricted bandwidth in fiber. Additionally, the CD tolerance of 18,817 ps/nm and 1176 ps/nm for uplink at 2.5 Gbit/s and downlink transmission at 10 Gbit/s, respectively, is defined in [40]. Therefore, the CD present in the proposed wheel architecture, at 1550 nm reference wavelength, is calculated as [34]:  
\[D_{Fiber}=L[D+S(\lambda-1550)] \tag{3}\]  
where \(D_{Fiberlink}\) implies CD in fiber, \(L\) represents fiber range, \(\lambda\) indicates transmission wavelength, \(D\) presents dispersion coefficient and \(S\) indicates slope coefficient. Table 3 represents the calculated CD in fiber link at different transmission lengths of the proposed scheme for uplink and downlink wavelength. The obtained results in Table 3 present that the achieved CD values are lower than the tolerance range for downlink and uplink wavelengths over 0.2\(\sim\)1.6 km at 10/2.5 Gbit/s data rate in the wheel-based MDM-PON with MWZCC code. However, uplink transmission shows less CD than downlink as uplink wavelength operates at a low data rate of 2.5 Gbit/s than downlink wavelength. Figure 9: Measured BER vs. number of ONUs at 10/2.5 Gbit/s data rate over 1 km range for modes 0 and 1 for different codes in (**a**) downstream and (**b**) upstream transmission. (c) Influence of interference: However, for low data rate signals, the CD does not notably broaden the propagating pulses into contiguous bit periods in fiber cable. Therefore, the CD does not influence the transmission of the system at a low data rate. Furthermore, at a high data rate, the pulses are shorter and closer. It prompts pulse overlapping into neighboring bit intervals, also known as inter-symbol interference (ISI). The expression for pulse broadening in ps is given as [34]:  
\[\Delta t=DL\Delta\lambda \tag{4}\]  
where \(\Delta t\) implies pulse spread and \(\Delta\lambda\) means pulse spectral linewidth, i.e., 1 nm. Additionally, the bandwidth of fiber cable is limited by dispersion and interference. Thence, the maximum supported bit rate in Gbit/s is evaluated as [34]:  
\[B_{r}\Delta t<1 \tag{5}\]  
where \(B_{r}\) indicates the bit rate in the system.