## 3 Link Margin of FSO System and SMF Coupling Efficiency of Signal Light and Sunlight  
For better integration in practice, an actual FSO communication system was considered; the link margin was calculated to determine whether the receiver sensitivity met the requirements. In this study, a satellite-ground laser communication system was considered. The coupling efficiency of the signal light and AL to the SMF is important. In this study, sunlight was considered as major AL; the analysis is presented as follows. Figure 6: Measured and theoretical curves of coherent OOK BER and received signal power with a communication rate of \(1\) Gbit/s. Figure 7: Simple block diagram of FSO communication. A simple block diagram of FSO communication is shown in Figure 7. The differences between an FSO system and an optical fiber system are mainly as follows. An FSO system includes received optical power fluctuation, Doppler frequency shift, tracking error, platform jitter, and coupling of space light to receiver SMF. The main difference considered in this paper is the coupling of space light to a receiver SMF. In this design, the laser wavelength \(\lambda\) was 1555.74 nm; the effective transmitting aperture \(D_{\mathrm{T}}\) was 20 cm; the corresponding beam divergence angle was \(\theta_{\mathrm{T}}=1.22\lambda/D_{\mathrm{T}}=9.49\ (\mathrm{\mu rad})\); and the transmitting antenna gain was \(\mathrm{G_{T}}=10\log 10\left(16/\left(\theta_{\mathrm{T}}\right)^{2} \right)=112.49\ (\mathrm{dB})\). For the receiving antenna gain, in satellite-ground laser communication, the communication distance is long and the spot size reaching the receiving terminal is much larger than the receiving antenna aperture; thus, it can be considered that the beam reaching the receiving antenna is a plane wave. When the communication distance \(z\) was 40,000 km; the free space loss was \(\mathrm{FSL}=10\times\log 10\left(\left(\lambda/4\pi z\right)^{2}\right)=-290.19\ (\mathrm{dB})\). When the effective aperture of the receiver \(D_{R}\) was 20 cm, the receiving antenna gain was \(\mathrm{G_{R}}=10\times\log 10\left(\left(\pi D_{R}/\lambda\right)^{2} \right)=112.12\ (\mathrm{dB})\). Assuming that the transmission efficiency loss was 1.5 dB and the reception efficiency loss was 3 dB, the total link loss was \(290.19+1.5+3-112.49-112.12=70.08\ (\mathrm{dB})\), regardless of the atmosphere, alignment, and coupling losses. When the transmission power was 33 dBm, the residual power was \(-37.08\ \mathrm{dBm}\). When the BER was \(10^{-3}\), the link margins for coherent reception and non-coherent reception were 17.52 dB and 14.17 dB, respectively. In this study, we considered the coupling of the signal light and AL to the receiver SMF. In an FSO system, when a signal light enters the receiver, it can be regarded as a plane wave. When there is no alignment error, the coupling efficiency of the signal light to SMF can be expressed as [42]  
\[\eta=2\left[\frac{\exp\left(-\beta^{2}\alpha^{2}\right)-\exp\left(-\beta^{2} \right)}{\beta\sqrt{1-\alpha^{2}}}\right]^{2}, \tag{11}\]  
where \(\beta\) is the coupling parameter, \(\beta=\pi D_{R}\omega_{0}/2\lambda f\); \(D_{R}\) is the receiver lens diameter or the effective aperture of the receiver; \(\omega_{0}\) is the mode field radius of the SMF, \(\omega_{0}=5\ \upmu\)m in this study; \(f\) is the focal length of the receiving lens; \(\alpha\) is the linear central obstruction, \(\alpha=0\) in this study. When \(\beta=1.12\) was used, the optimum coupling efficiency of the 1555.74 nm signal light was 0.81 [43]. To achieve the optimum coupling efficiency, the focal length of the receiver lens should be 0.90 m when the receiver lens diameter is 20 cm. In other words, each receiver lens diameter can uniquely determine a lens focal length so that 1550.74 nm signal light has the optimum coupling efficiency to an SMF.