# Analysis of Scintillation Effects on Free Space Optical Communication Links in South Africa
## 7 Average Bit Error Rate (BER) Analysis
### Return-to-Zero On-Off Keying (RZ-OOK) FSOC Links
\bigg{]}\] (69) Inserting Equations (52) and (69) into Equation (56) gives: \[P_{RZ-\mathrm{OOK}}=\frac{\xi^{2}}{4\Gamma(\alpha)\Gamma(\beta)\pi^{0.5}} \bullet\int\limits_{0}^{\infty}\gamma^{-1}\bullet G_{1,2}^{2,0}\bigg{[}0.25 \gamma\bigg{|} \begin{matrix}1\\ 0,0.5\end{matrix} \bigg{]}\bullet G_{1,3}^{3,0}\bigg{[}\frac{\alpha\beta\xi^{ 2}}{\xi^{2}+1}\bigg{(}\frac{\gamma}{\gamma}\bigg{)}^{0.5}\bigg{|} \begin{matrix} \xi^{2}+1\\ \xi^{2},\alpha,\beta\end{matrix} \bigg{]}d\gamma\] (70) Applying equation (07.34.21.0013.01) in [53] to evaluate Equation (70) yields: \[P_{RZ-\mathrm{OOK}}=\frac{\xi^{2}2^{\alpha+\beta-4}}{\pi^{1.5}\Gamma(\alpha) \Gamma(\beta)}G_{4,7}^{6,2}\bigg{[}\bigg{(}\frac{\alpha\beta\xi^{2}}{\xi^{2}+ 1}\bigg{)}^{2}\frac{1}{4\gamma}\bigg{|} \begin{matrix}1,0.5,\frac{\xi^{2}+1}{2 },\frac{\xi^{2}+2}{2}\\ \frac{\xi^{2}}{2},\frac{\xi^{2}+1}{2},\frac{\alpha}{2},\frac{\beta}{2},\frac{ \beta+1}{2},0\end{matrix} \bigg{]}\] (71) Further simplification of Equation (71) gives: \[P_{RZ-\mathrm{OOK}}=\frac{\xi^{2}2^{\alpha+\beta-4}}{\pi^{1.5}\Gamma(\alpha) \Gamma(\beta)}G_{3,6}^{5,2}\bigg{[}\bigg{(}\frac{\alpha\beta\xi^{2}}{\xi^{2}+ 1}\bigg{)}^{2}\frac{1}{4\gamma}\bigg{|} \begin{matrix}1,0.5,\frac{\xi^{2}+2}{2 }\\ \frac{\xi^{2}}{2},\frac{\alpha+1}{2},\frac{\beta}{2},\frac{\beta+1}{2},0 \end{matrix} \bigg{]}\] (72)  
In Figure 6b-d, the BER results of the FSOC links in all the cities of interest are generated using Equations (1)-(3), (15), (35), (38), (40), (41), (46), and (67) because the scintillation parameters in those locations fall within the weak atmospheric turbulence regime over a link distance of 1.5, 1, and 0.5 km, respectively. The BER results of the cities in Figure 6a are computed using Equations (1)-(3), (15), (30), (31), (35), (46), and (72). Figure 6a-d present the BERs computed for the zero inner scale and infinite outer scale model and finite inner and finite outer scale model for different receive SNRs, and are based on the numerical values in Table 2, Table 3, Table 4, and Table 5, respectively. It is imperative to state that the presence of misalignment errors (\(\frac{\sigma_{e}}{\tau}=2\)) in Figure 5(a,b) strongly impacts on the BER performance of the FSOC links, while the low presence of pointing errors (\(\frac{\sigma_{e}}{\tau}=1\)) in Figure 5(c,d) indicate better BERs for all the locations investigated. Additionally, the presence of the inner and outer scales of turbulence where \(l_{o}=0.005\) m  
Figure 6: BER of OOK FSOC links vs. Average SNR (dB) over weak and moderate to strong atmospheric turbulence channels for various cities in South Africa. and \(L_{o}=10\) m, cause poorer BERs when compared to the results of the zero inner scale and infinite outer scale model. It is also important to note that the inner scale bump is responsible for the higher values of scintillation obtained when the modified atmospheric spectrum is employed. The BER performances of the FSOC links deployed in the cities investigated are quite similar, as shown in the four figures.