# Optical Code Construction of 2D Spectral/Spatial BIBD Codes for SAC-OCDMA Systems
## 5 Results and Analysis  
### Numerical Analysis  
The parameters used for theoretical and simulation analysis of the 2D-BIBD code based OCDMA system are listed in Table 4. The effective source power (\(P_{sr}\)) was set to \(-10\) dBm, and simulations were carried out at a bit rate of 622 Mbps. The SNR is a relevant term as it demonstrates the received signal quality. BER performance improves with the increase in SNR. Therefore, 2D-BIBD code performance uses multiple parameters, such as the number of supportable users and received output power for various types of noises. Figure 3 shows the BER performance for the proposed code concerning the number of supportable users. As the number of users increases, the quality of the received signal decreases due to MAL. Thus, SNR and BER degrade. Moreover, BER values of the 2D-BIBD (\(N_{max}=63\), \(N_{max}^{\prime}=3\)) code were compared with existing techniques such as DPD (\(M=63\), \(P=3\)) and DEU (\(M=63\), \(P=3\)) codes. It was observed that supported users were 90, 70, and 25 for 2D-BIBD, 2D-DPD, and 2D-DEU codes, respectively, at the minimum allowed BER value of \(10^{-9}\). Further, a large code cardinality is achieved due to the improved cross-correlation properties (Table 3) of the proposed code. Figure 4 represents the relationship between BER and \(P_{sr}\) at a bit rate of 622 Mb/s. We selected 20 active users for performance comparison, and the BER changed due to variations in the received power. However, it was observed that the BER's performance could not be enhanced with an increase of the transmitted power. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters Used** & **Value** \\ \hline LED bandwidth (\(B\)) & 30 nm \\ FBG filter bandwidth (\(\Delta v\)) & 0.4 nm \\ Electron charge (\(e\)) & \(1.6\times 10^{-19}\) coulombs \\ Electrical bandwidth (\(B_{rec}\)) & 311 MHz \\ Broadband effective power (\(P_{sr}\)) & \(-10\) dBm \\ Operating wavelength (\(\lambda_{\text{o}}\)) & 1550 nm \\ Boltzmann constant (\(K_{b}\)) & \(1.38\times 10^{-23}\) W/K/Hz \\ Receiver noise temperature (\(T_{n}\)) & 300 K \\ Receiver load resistor (\(R_{L}\)) & 1030 \(\Omega\) \\ LED quantum efficiency (\(\eta\)) & 0.6 \\ Width of broadband source (\(\Delta f\)) & 3.75 THz \\ Photodiode responsivity (\(\Re\)) & 0.75 \\ Data transmission rate (\(R_{b}\)) & 622 Mbps \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters used for numerical analysis and simulations of the SAC system with the 2D-BIBD code. Figure 4: 2D-BIBD code’s performance in terms of BER and effective source power (\(P_{sr}\)) at a data rate of 622 Mbps and the number of users K = 20. Figure 3: Dependence of BER on the maximum number of simultaneous users (\(K\)) at input transmitted power (\(P_{sr}=-10\) dBm) for 2D-BIBD (\(N_{max}=63\), \(N^{\prime}_{max}=3\)), 2D-DEU code (M = 63, \(P=3\)), and 2D-DPD (\(M=63\), \(P=3\)). The 2D-BIBD (\(N_{max}=63\), \(N^{\prime}_{max}=3\)) code outperformed the 2D-DPD (\(M=63\), \(P=3\)) and 2D-DEU (\(M=63\), \(P=3\)) codes. This system achieved the desired optical transmission performance at the smallest effective transmitted 2D-BIBD power (\(P_{sr}=-27.5\) dBm) when compared to 2D-DEU (\(-26.8\) dBm) and 2D-DPD (\(-25.8\) dBm) codes, respectively. The main factor in 2D code design is spatial code length. Due to its optimal spatial code length, the system with 2D-BIBD code requires a smaller effective transmitted power. Additionally, interference from other users is decreased by increasing the number of star couplers and filters required for spatial encoding purposes. PIN is introduced in the system with the mixing of the incoherent light fields, and it further affects the photodiode detector, which leads to high-intensity noise. Further, higher weight in the 2D code adds more intensity noise in the system. The relation between BER and \(P_{sr}\) for different noise combinations such as PINN-shot-thermal for 2D-BIBD and PINN-Shot for 2D-DEU and 2D-DPD is shown in Figure 5. We selected 20 active users and a 622 Mbps data rate for performance comparison.