## 4 Results and Discussions  
Using Equations (4) and (7)-(13), we shall investigate the BER performance of the proposed FSO link using different modulation techniques discussed previously. The performance of the link was analyzed for turbulence conditions ranging from weak to strong. The investigation reported in this section can be broadly divided into two cases, links without spatial diversity and links with spatial diversity. Although it is well established from the reported literature that OOK modulated links are simple to design but lack the necessary fidelity, especially when the turbulence conditions vary from moderate to strong, however for the sake of quantitative comparison, we have considered the OOK scheme apart from other modulation techniques as well. Various link parameters that were used during the design and analysis of the proposed link are listed in Table 1.  
For single-channel FSO link operating in weak turbulence conditions, the BER performance of different modulation techniques for varying receiver SNR (dB) is shown in Figure 4. Similar investigation has also been extended to moderate and strong turbulence conditions as shown in Figures 5 and 6, respectively. For all the cases of FSO link without space diversity reception technique (SDRT) shown in Figures 4-6, we observe that out of all the investigated modulation formats, BPSK exhibits outstanding BER performance, followed very closely by 256-QAM and GMSK. Table 2 provides greater insight into the performance of different modulation formats in FSO links for weak, moderate and strong turbulence link conditions. Table 2 and Figure 4 shows that to achieve target BER of \(10^{-8}\), OOK requires 19.9 dB SNR at the receiver, while the observed SNR requirements for DPSK, GMSK, 256-QAM, and BPSK are 10 dB, 9.2 dB, 8.4 dB, and 8 dB, respectively. The performance improvement of BPSK over OOK in a \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Range/Value** \\ \hline Link length [26; 27] & \(1.25\) km \\ \hline \multirow{3}{*}{Refractive index structure (\(C_{n}^{2}\)) [28; 29; 30]} & \(10^{-12}\) m\({}^{-2/3}\) (strong turbulence) \\ \cline{2-3}  & \(10^{-15}\) m\({}^{-2/3}\) (moderate turbulence) \\ \cline{2-3}  & \(10^{-17}\) m\({}^{-2/3}\) (weak turbulence) \\ \hline Spatial diversity order [26; 31] & \(2\times 2\) \\ \hline Photodetector responsivity [27; 32] & 1 A/W \\ \hline Operating wavelength [27; 30; 32; 33] & 1550 nm \\ \hline data rate (\(\text{r}_{\text{b}}\)) [3] & 155 Mbps \\ \hline Transmitter aperture [27; 34] & 20 cm \\ \hline Receiver aperture [34; 35] & 20 cm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Link design parameters. weak turbulence scenario is approximately 59%. Figure 5 shows the BER performance of different modulation techniques in the moderate turbulence channel. To achieve the BER of \(10^{-8}\), the SNR requirements for OOK, DPSK, BPSK, GMSK, and 256 QAM are 33 dB, 15.3 dB, 14.3 dB SNR, 16.8 dB SNR, and 15.1 dB, respectively. The performance improvement of BPSK over OOK in the moderate turbulence scenario is approximately 56%. A similar characteristic of BER performance is also seen in Figure 6, where, in the strong turbulence scenario to achieve the BER of \(10^{-8}\), the SNR requirements for BPSK were the least at 19.5 dB while DPSK, GMSK, and 256-QAM had their SNR requirements at 21.5 dB SNR, 23 dB SNR, and 21 dB SNR, respectively. Hence, BPSK performs better than all other modulation techniques in all turbulence regimes channels, providing a significant SNR gain of almost 25 dB over OOK, even under strong turbulence conditions. Hence, the performance improvement of BPSK over OOK in a weak turbulence scenario is approximately 54%. Figure 7 shows the BER performance of different modulation techniques with \(2\times 2\) SDRT order and streamline the BER comparison single-channel link, i.e., without SDRT, which has also been illustrated in this figure. Significant SNR gain is observed in Figure 7 when SDRT links are compared with/without SDRT ones.