# Fault Tolerant Spectral/Spatial Optical Code Division Multiple Access Passive Optical Network
## 5 Reliability Analysis  
The convergence of wireless and optical communication technologies has become one of the significant steps in facilitating the 6G network infrastructure. Higher throughput and cardinality, lower latencies, substantially high data rates, and reliability have become the fundamental characteristics of future communication networks. Consequently, this section will analyze the reliability of the proposed ring-based architecture in comparison with the tree-based counterpart proposed in [5]. The reliability analysis is performed in terms of connection availability that can be expressed as follows [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]:  
\[CA=1-\sum_{i=1}^{i}UA_{i} \tag{1}\] \begin{table}
\begin{tabular}{l c c c} \hline \hline
**RN** & \(RN_{1}\) & \(RN_{2}\) & \(RN_{3}\) & \(RN_{4}\) \\ \hline \hline \multirow{2}{*}{Eye Diagram} & \multirow{2}{*}{\(\begin{bmatrix}\text{Eye Diagram}\\ \text{Eye Diagram}\end{bmatrix}\)} & \multirow{2}{*}{\(\begin{bmatrix}\text{Eye Diagram}\\ \text{Eye Diagram}\end{bmatrix}\)} & \multirow{2}{*}{\(\begin{bmatrix}\text{Eye Diagram}\\ \text{Eye Diagram}\end{bmatrix}\)} \\ \hline \hline BER & \(3.7\times 10^{-18}\) & \(2.6\times 10^{-15}\) & \(1.6\times 10^{-14}\) & \(3.2\times 10^{-16}\) \\ \hline \hline \multirow{2}{*}{Received Power} & \(-9.8\) dBm & \(-14.3\) dBm & \(-16.2\) dBm & \(-13\) dBm \\ \hline \end{tabular}
\end{table} 
Table 4: BER and eye diagrams for clockwise and counterclockwise flow of traffic. Figure 9: Simulation setup for failure recovery analysis (blue lines show clockwise flow of traffic, red lines show counterclockwise flow of traffic after failure at point of failure (PoF). \(CA\) in Equation (1) represents the connection availability of the entire network, and \(UA_{i}\) is used to give the unavailability of the system components \(i\) inside the network. Accordingly, the proposed architecture can be divided into the following blocks to analyze the connection availability of the entire network:  
\[UA_{i}=UA_{CO}+UA_{FF}+UA_{RNs}+UA_{DF}+UA_{ONTs} \tag{2}\]  
Here, CO is used to represent the central office of the network, and \(UA_{CO}\) refers to the overall unavailability of the components employed at the CO. The same can be further elaborated as follows:  
\[UA_{CO}=UA_{OLT}+UA_{2:1 CP_{SE}}+UA_{1:2 CP_{SLE}}+UA_{2:1 CP_{SLE}}+UA_{TDU}+UA _{1:ICP}+UA_{CP_{SA}}+UA_{SW_{SA}} \tag{3}\]  
Here, \(UA_{OLT}\) gives the unavailability of the system components that are employed at the OLT module, including laser diodes, modulators, filters, data sources, etc. The unavailability of the coupler that is employed to implement the spatial encoding operation is given as \(UA_{2:1 CP_{SE}}\). Similarly, \(UA_{1:2 CP_{SLE}}\) and \(UA_{2:1 CP_{SLE}}\) are used to represent the total unavailability over a given span for the couplers utilized in spatial encoding at the CO. \(UA_{TDU}\), _and_\(UA_{1:ICP}\) are used to give the unavailability of the time delay units and 1:t optical coupler that is used to combine all signals for the feeder level. Switching arrangement components unavailability figures are given as \(UA_{CP_{SA}}\) and \(UA_{SW_{SA}}\), respectively. Now, the unavailability of the feeder fiber \(UA_{FF}\) can be expressed as follows:  
\[UA_{FF}=(D_{FF}UA_{OF})^{2} \tag{4}\]  
Here, \(D_{FF}\) is used to represent the overall span of the OF medium deployed along the feeder level. \(UA_{OF}\) is used to employ the unavailability factor of the OF medium. The superscript 2 is utilized in the equation to incorporate the redundant feature of the ring-based topology that provides protection against failures or cuts at the feeder level. The unavailability of the components employed at the RNs can be expressed as follows:  
\[UA_{RNs}=UA_{CP_{RNs}}+UA_{2:2 CP_{RNsLD1,1}}+UA_{1:2 CP_{RNsLD2,1}}+UA_{1:2 CP_{ RNsLD2,2}} \tag{5}\]  
It can be observed from Figure 3 that each remote node employed four optical couplers.