## 5 Simulation Results and Discussion
### Comparison of KK and Coherent Systems without Scintillation  
In this section, we study the KK and coherent transceivers performances by neglecting turbulence (see Section 5.2 for results in the presence of turbulence). However, for uplink and downlink configurations, the path losses due to turbulence are included (see Equations (13)-(15)). Figure 4 shows the BER versus the \(K\)-factor (i.e., \(K\) of Equation (1)) for three FSO scenarios (see Figure 1) that are sat-to-sat, downlink, and uplink FSO communications. As can shown in Figure 4, the BER decreases as the \(K\)-factor increases for all scenarios. As the K-factor increases, the penalty due to phase extraction using the Hilbert transform decreases, and when this penalty becomes zero, we see saturation of the BER for the uplink. Since the uplink has the lowest SNR among these three schemes, saturation of the BER occurs for relatively lower \(K\)-factor since the channel noise dominates over the noise associated with the phase extraction. Note that this saturation effect would happen to the other links at higher K-factors because of their higher OSNRs. Figure 5a,b show the transmitted spectra of the FSO system based on coherent and KK transceivers. In Figure 5b, there is a DC component (see Equation (1)) which is required to ensure the minimum phase property. An example of the received constellation diagram for coherent transceiver is shown in Figure 6 for the downlink scenario. Due to laser phase noise introduced by the transmitter and receiver (LO) lasers [32], constellations are lost (Figure 6a) which are recovered by digital phase noise compensation (Figure 6b). We have implemented the phase noise compensation technique developed in [33] for the case of a coherent transceiver. However, for the case of the KK transceiver, the received signal is not sensitive to transmitter laser phase noise because of the direct detection, and, hence, phase noise compensation is not required for this FSO system. Figure 7 shows the constellation diagram for the case of KK transceivers. Comparing Figures 6b and 7, we see that the impact of noise is higher in a system based on KK transceiver (electrical SNR is the same for both systems). However, there is residual phase noise in Figure 6b at the corners even after the phase noise compensation. It is due to the fact that as the channel noise and/or constellation size increases, the compensator cannot compensate for the phase noise exactly. Figure 4: KK transceiver performance versus \(K\)-factor for satellite-to-satellite, downlink, and uplink communications. Figure 5: Normalized spectrum of the transmitted signal (**a**) coherent communication system, and (**b**) KK communication system (\(K=10\)). Figure 6: Example of received constellation diagram for QAM-16 in FSO coherent system (downlink), (**a**) before phase noise compensation, and (**b**) after phase noise compensation. Next, we compare the BER of KK and coherent transceivers for the sat-to-sat scenario in Figure 8. In the case of KK receiver, the electrical SNR is calculated after the matched filter (see Figure 3). As shown, the electrical SNR required to achieve a BER of \(10^{-3}\) for KK receiver is 2.9 dB higher than that of coherent receiver. On the other hand, at a fixed SNR of 14.3 dB, the BER for KK transceiver is 1.03 \(\times\)\(10^{-2}\) (see Figure 8) and the required hard decision forward error correction (HD-FEC) overhead (OH) for BER < 1.03 \(\times\)\(10^{-2}\) is 14.3% [32; 33]. However, the required OH for coherent transceiver is as low as 6% [34] at the fixed SNR of 14.3 dB, since the BER is less than \(10^{-3}\) at this SNR. So, the 8.3% OH is the penalty for using KK system instead of coherent system, which is acceptable for reduction of the cost and complexity of FSO coherent communication system. It may be noted that this comparison is made for the laser linewidth of 22 kHz (see Table 1).