## 5 Simulation Results and Discussion
### Comparison between KK and Coherent Systems in the Presence of Scintillation  
The sat-to-sat link can be assumed to be free from atmospheric turbulence. But the transceiver performance for downlink and uplink scenarios is impacted in the presence of turbulence. In this section, we compare the performance of coherent and KK transceivers for downlink and uplink scenarios in the presence of weak, moderate, and strong turbulence close to the ground station telescope. For simplicity, we assumed that the lens diameter of the Tx and Rx telescopes are equal. Figure 10: Comparison between KK and coherent transceiver uplink performance in the presence of scintillation versus telescopes lens diameter (Tx/Rx amplifier gains are 30 dB, Tx/Rx Lens diameters are assumed equal. Also, please see \(C_{n}^{2}(0)\) values in Table 1 for weak, moderate, and strong turbulence). Figure 9: Comparison between KK and coherent transceiver downlink performance in the presence of scintillation versus telescopes lens diameter (Tx/Rx amplifier gains are 30 dB, Tx/Rx lens diameters are assumed equal. Also, please see \(C_{n}^{2}(0)\) values in Table 1 for weak, moderate, and strong turbulence. To compute the mean BER in the presence of turbulence, we proceed as follows. The received optical intensity is divided into \(N\) blocks. Let the range of optical intensity in the \(n\)th block be (\(I_{n}\), \(I_{n+1}\)). This range is so selected that the BER is approximately constant. Monte-Carlo simulation of the FSO system with a constant path loss is carried out using 65,536 symbols assuming that the optical intensity is \((I_{n}+I_{n+1})/2\) and the corresponding bit error rate, \(BER_{n}\) is computed. This procedure is repeated for all the \(N\) blocks and a lookup table that maps the optical intensity to BER is formed. Using the H-V turbulence model [4], let the chance of the optical intensity lying in the range (\(I_{n}\), \(I_{n+1}\)) be \(p(n)\). The mean BER is computed as  
\[<\text{BER}>=\sum_{n}p(n)\text{BER}_{n} \tag{30}\]  
Figures 9 and 10 show the mean BER performance of coherent and KK systems, respectively (Tx/Rx amplifier gains are 30 dB). In general, the mean BER decreases as the lens diameter increases since a large diameter leads to a lower path loss. For both downlink and uplink scenarios, in the presence of weak and moderate turbulence, the required lens diameter of telescopes in coherent transceiver is lower to achieve the same mean BER performance in comparison to KK transceiver. For example, for uplink, in the presence of weak turbulence, the required lens diameter to achieve \(<\)BER\(>=10^{-3}\) is \(\sim\)35 cm and \(\sim\)44 cm for coherent and KK transceivers, respectively (see Figure 10). This translates into a SNR penalty of 2.0 dB for KK transceiver. For downlink, in the presence of strong turbulence, the required lens diameter to achieve \(<\)BER\(>=10^{-3}\) is \(\sim\)27.5 cm and \(\sim\)28.8 cm for coherent and KK transceivers, respectively (see Figure 9). This translates into a SNR 0.4 dB penalty for KK transceiver. It may be noted that the SNR penalty at a BER of \(10^{-3}\) for KK receiver is 2.9 dB (see Figure 8) in the absence of turbulence which is much larger than 0.4 dB in the presence of strong turbulence. In other words, the coherent receiver loses one of its main advantages in the presence of strong turbulence. In Figure 10, in the presence of moderate and strong turbulence, for the lens diameter less than 62.5 cm (20 cm) for strong (moderate) turbulence, KK transceiver performs slightly better than the coherent transceiver. The reason is that in the presence of strong/moderate turbulence, path loss is so high for uplink that the SNR is very low and the performance of laser phase noise compensator decreases at lower SNR for coherent receiver (it happens in Figure 8 too) whereas the phase noise is not an issue for KK receiver. Due to turbulence, the optical intensity at the receiver is time variant, which leads to a time-varying SNR.