# Fault Tolerant Spectral/Spatial Optical Code Division Multiple Access Passive Optical Network
## 3 Performance Analysis
However, a progressive increase in the BER is observed with growth in the reach of the OF media, demonstrating the cumulative effect of signal degradation. For instance, \(ONT_{1}\) nodes at \(RN_{1}\) are able to provide BER values of approximately \(5.11\times 10^{-13}\) at a fiber length of 10 km, indicating highly reliable transmission. However, as the length of the OF media increases to 16 km, the BER rises to as high as \(8.3\times 10^{-11}\). This indicates a drop in the transmission quality. This can be attributed to the fact that signal attenuation and dispersion increase along the length of the OF media, which increases the signal-to-noise ratio in the receiving photodiode. Correspondingly, the BER values are affected, and an increase in the BER is observed as the length of the OF media increases. Nevertheless, it can be observed from the graph patterns that the proposed 2D DW-ZCC with an efficient combination of spectral-spatial and temporal encoding systems is still able to support high transmission capacity in terms of data, reach, and the number of subscribers, owing to the utilization of the ideal cross-correlation property between adjacent codes. An analysis of Figure 6 shows a relatively steeper rise in the BER values for the ONT nodes at \(RN_{3}\) and \(RN_{4}\). For instance, BER values of 3.5 \(\times 10^{-15}\) and \(4.5\times 10^{-5}\) are observed for ONT1 of RN4 at 13 km and 19 km OF lengths, respectively. This shows a relatively greater decline in the system's performance, which can be attributed to the fact that the ONT nodes at \(RN_{3}\) and \(RN_{4}\) are experiencing higher signal attenuation and dispersion along the OF media as compared to the other nodes due to utilization of the ring topology at the feeder level, as the signal needs to traverse across all RNs and underlying OF media to reach  
Figure 5: BER vs. data rate for B2B model. its corresponding destination. Nevertheless, it can be observed that, for an acceptable BER value of \(10^{-9}\), the proposed system is still able to support 128 subscribers communicating at 10 Gbps of data across the OF span of 16\(\sim\)17 km, respectively. Figure 7 demonstrates the Q-factor (QF) at various ONT nodes of each RN for the proposed 2D DW-ZCC system with spectral-spatial and temporal encoding. The graph trends in Figure 7 demonstrate a decline in the QF with an increase in the length of the OF media. This can be attributed to an increase in the BER values at a longer reach of the OF media, owing to the reduction in power of the received signal. Figure 8 represents the analysis of the proposed system in terms of the BER against the received power at \(ONT_{1}\) of each RN. Since all ONTs exhibit relatively close BER values, a single ONT module is selected to facilitate clear visualization of the BER versus received power trends. It can be observed that a BER of approximately 5.11 \(\times 10^{-18}\) is observed at the \(ONT_{1}\) modules of \(RN_{1}\) at a received power of \(-9.2\) dBm for an OF length of 10 km. However, as the length of the OF media increases, the power received at the PIN photodiode decreases, resulting in a BER value of 8.3 \(\times 10^{-11}\), and the received power decreases to \(-19.4\) dBm, highlighting a significant reduction in signal integrity. This can be attributed to the fact that the signal-to-noise ratio decreases with a reduction in the received power, which in turn elevates the BER. A similar trend is observed for \(ONT_{1}\) of the \(RN_{2}\) module, where the BER increases from \(4\times 10^{-17}\) at \(-11.4\) dBm to \(8.5\times 10^{-9}\) at \(-20.6\) dBm, indicating the system becomes more error prone as the power decreases. In the case of the ONT nodes at \(RN_{3}\) and \(RN_{4}\), the impact is even more pronounced, with the BER reaching below the acceptable range at values of received power in the range of \(-19.4\sim\)\(-20.6\) dBm, respectively.