## 2 System Structure and Channel Model  
Figure 1 shows a schematic diagram of the proposed OFDM-based spatial diversity reception FSO communication system. At the transmitter, a radio frequency (RF) OFDM series carrying the initial data is modulated on an optical carrier through an IQM to generate the CO-OFDM signal, and it is launched into an atmospheric turbulence channel via a collimator. At the receiver, the signal is collected by multiple optical apertures, coupled into optical fibers, and demodulated by the coherent detectors. Then, these branched received signals are combined using an EGC algorithm after offline DSP processing. Figure 2a shows the schematic diagram of the modulating process of the CO-OFDM signal at the transmitter. The initial data are mapped into QPSK format, and then converted into a parallel sequence through serial-to-parallel conversion. The parallel sequence is modulated on the sub-carriers through inverse fast Fourier transform (IFFT), and a cyclic prefix (CP) is added. All sub-carriers are combined into an RF-OFDM-QPSK series through  
Figure 1: Schematic diagram of the spatial diversity reception FSO communication system using OFDM signals. parallel-serial conversion, which is modulated on the optical carrier through an IQM. Then, the CO-OFDM signal is sent to the atmospheric turbulence channel. In the FSO communication system, the transmission of the signal will be influenced by the atmospheric turbulence to cause light attenuation, power jitter, and phase distortion. The FSO link can be expressed as  
\[y=h\otimes s_{\text{OFDM}}+n, \tag{1}\]  
where \(s_{\text{OFDM}}(t)=\sum_{k=1}^{N}x_{k}exp(j2\pi f_{k}t)\) is the OFDM signal sent by the transmitter, \(N\) is the number of sub-carriers, \(f_{k}\) is the frequency of the \(k\)th sub-carrier, \(x_{k}\) is the complex data in the \(k\)th sub-carrier which is modulated in a QPSK format, \(y\) is the receiving signal at the receiver, \(n\) is the additive white Gaussian noise (AWGN), and \(h\) is the influence coefficient caused by the atmospheric turbulence channel. As shown in Figure 1, the OFDM-PSO system's performance can be evaluated by using a split-step beam propagation method based on phase screen theory [22]. The transmission distance \(L\) is divided into several segments, each of which has two parts: a vacuum transmission link of length \(\Delta z\) and a phase screen regardless of thickness. The effect of the atmospheric turbulence is superimposed on the optical carrier through the phase screen after the vacuum transmission. The phase screen is generated by the power spectrum inversion method. According to the von [PERSON] model, the phase power spectral density is described as  
\[\Phi(\kappa)=0.033C_{n}^{2}\frac{\exp\bigl{(}-\kappa^{2}/k_{m}^{2}\bigr{)}}{ \bigl{(}\kappa^{2}+\kappa_{0}^{2}\bigr{)}^{11/6}}, \tag{2}\]  
where \(\kappa=2\pi\bigl{(}f_{x}\hat{i}+f_{y}\hat{i}\bigr{)}\), \(\kappa_{m}=5.92/l_{0}\), \(k_{0}=2\pi/L_{0}\), and \(l_{0}\) and \(L_{0}\) are the inner and outer scales of the turbulence, respectively. \(C_{n}^{2}\) is the atmospheric refraction-index structure parameter, which can characterize the strength of atmospheric turbulence. The effect of the atmospheric turbulence on the CO-OFDM signal is simulated by transmitting it through a series of phase screens. The optical signal is collected by multiple apertures at the receiver after introducing the AWGN noise. As shown in Figure 2b, the CO-OFDM signal is down-converted to RF-OFDM by coherent photodetectors. After compensating for the frequency offset and the  
Figure 2: Processes of (**a**) the generation of the CO-OFDM-QPSK signal at the transmitter and (**b**) the demodulation of the signal at the receiver. phase noise of each receiver branch signal, and then sampled through an analog-to-digital converter. The initial data are reconstructed through serial-to-parallel conversion, CP removal, fast Fourier transform (FFT), parallel-to-serial conversion, and QPSK demodulation.