## 5 Simulation Results and Discussion  
We have carried out the Monte-Carlo simulations of the FSO system using the parameters listed in Table 1, unless otherwise specified. At transmitter, 6,553,600 symbols were transmitted with QAM-16 modulation format and 40 Gb/s symbol rate with the link distance 35,000 km to simulate the coherent and KK transceivers performance. The logarithm appearing in Equation (7) for the phase extraction in KK receivers leads to spectral broadening and hence, digital up-sampling of the received photocurrent is required. For the simulation of the transmitter and channel, a sampling rate of 20 GSa/s is used, and at the receiver digital signal processing (DSP), the sampling rate is increased to 40 GSa/s. Increasing the sampling rate beyond 40 GSa/s did not provide any performance improvement of the KK receiver. There are three types of atmospheric turbulence, i.e., beam wander, beam spreading, and beam scintillation. Out of these three types, for simplicity, we neglected the beam wandering in our simulations. Beam wander is caused mainly by large-scale turbulence near the transmitter and, therefore, can be typically neglected for downlink scenarios [4; 25]. For uplink, we assume that the beam is well tracked, and beam wander is mitigated [28; 29; 30; 31]. In our simulations, we have used the Hufnagel-Valley model for turbulence [4]. The normalized variance of scintillation is  
\[\sigma_{I}^{2}=\frac{\left\langle I^{2}\right\rangle}{\left\langle I\right\rangle ^{2}}-1 \tag{26}\]  
where \(\left\langle I\right\rangle\) and \(\left\langle I^{2}\right\rangle\) are the mean and second moment of the optical intensity at the receiver, respectively. When \(\sigma_{I}^{2}\leq 1\), it is considered as the weak turbulence and when \(\sigma_{I}^{2}\geq 1\) \begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Parameters** & **Value/Variable** \\ \hline Pre-amp. gain (Tx) & 30 (dB) \\ Post-amp. gain (Rx) & 30 (dB) \\ Noise figure (NF) pre-amp (Tx) & 5 \\ Noise figure (NF) post-amp (Rx) & 3.3 \\ Average transmit signal power (PT) & 30 (dBm) \\ Number transmitted symbols & 6,553,600 \\ Modulation format & 16 QAM \\ Telescope diameter (Tx) & 0.25 (m) \\ Telescope diameter (Rx) & 0.25 (m) \\ Data rate & 40 (Gb/s) \\ Over-sampling factor & 4 \\ Symbol rate & 10 (GS/s) \\ Pulse shape & Root-raised cosine \\ Roll-off factor & 0.1 \\ Link distance & 35,000 (km) \\ Zenith angle & 0 (deg) \\ PD responsivity & 0.8 (A/W) \\ Laser wavelength & 1550 (nm) \\ RMS of wind speed & 21 (m/s) \\ Wind speed close to ground & 5 (m/s) \\ Tropopause height & 9.4 (km) \\ Tropopause thickness & 4.8 (km) \\ Turbulence model [4] & Hufnagel-Valley model (H-V model) \\ Structure parameter at height & \(C_{n}^{2}\)(h) \\ \(C_{n}^{2}\)(0) Turbulence close to ground (weak) & \(1.7\times 10^{-14}\) (m\({}^{-2}/3\)) [4] \\ \(C_{n}^{2}\)(0) Turbulence close to ground (moderate) & \(1.0\times 10^{-13}\) (m\({}^{-2}/3\)) [4] \\ \(C_{n}^{2}\)(0) Turbulence close to ground (strong) & \(2.0\times 10^{-11}\) (m\({}^{-2}/3\)) [27] \\ Divergence factor (Tx) & 0.942 \\ Misalignment pointing, \(L_{P}\) & 0.2 \\ Tx efficiency, \(\eta_{T}\) & 0.8 \\ Rx efficiency, \(\eta_{R}\) & 0.8 \\ Rx telescope transmission factor, \(T_{R}\) & 0.8 \\ Tx telescope transmission factor, \(T_{T}\) & 0.8 \\ Responsivity R, & 1.1 (A/W) \\ Atmospheric loss (downlink/uplink), A\({}_{\rm atm}\) & 1.0 (dB) \\ Fried parameter, r0 (weak turbulence) & 200 (mm) \\ Fried parameter, r0 (moderate turbulence) & 80 (mm) \\ Fried parameter, r0 (strong turbulence) & 20 (mm) \\ Background noise (BN) (daytime, max sunlight, & \(1.544\times 10^{-25}\) (W/Hz) \\ clear sky) & \(12.5\) (GHz) \\ Optical filter bandwidth & \(290\) (\({}^{\rm K}\)) \\ Absolute temperature & \(22\) (kHz) \\ Laser linewidth (Tx) & \(22\) (kHz) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: FSO KK and coherent system simulation parameters. it is considered as moderate-to-strong turbulence [4].