## 3 Simulation Demonstration and Performance Evaluation  
The simulation platform of a 10 Gbps QPSK CFSO communication system is shown in Figure 4. Firstly, the PRBS data source was mapped to QPSK symbols in the mapping module and then converted to corresponding electrical pulse signals. The transmitter side used a polarization beam splitter (PBS) to split the external cavity laser (ECL), with a linewidth of 50 kHz, into two orthogonally polarized lights. The four electrical pulse signals of the two polarization states drove two dual parallel Mach-Zehnder modulators (MZMs) to complete the up-light modulations of the two orthogonally polarized lights. The modulated optical signals of the two polarization states were coupled with a polarization beam combiner (PBC) to form a signal beam and were then integrated into a computer-simulated free-space turbulence channel. To simulate different transmitting optical powers, we used a variable optical attenuator (VOA) to adjust the appropriate input power on the transmitter side. On the receiver side, a continuous wave laser with a linewidth of 50 kHz was used as the LO laser, with a frequency offset of 300 MHz from the transmitter-side laser. Finally, the four electrical signals were mixed and balanced with the integrated optical coherent receiver. The detector was sampled with an analog-to-digital converter (ADC) and processed in an offline DSP module. The offline DSP module included IQ quadrature imbalance compensation, clock recovery, polarization demultiplexing, JCSCR, QPSK de-mapping, and BER counting. In computer simulations of free-space turbulence channels, the McGlamery atmospheric-turbulence phase-screen model based on the Fourier transform is used to simulate atmospheric turbulence [13]. The simulation parameters were as follows: wavelength \(\lambda=1550\) nm; the internal scale of atmospheric turbulence, \(l_{0}\), was negligible; the external scale of atmospheric turbulence, \(L_{0}\), was infinite [20]; z (the atmospheric turbulence range) = 10 km, considering that atmospheric turbulence mainly occurs within the range of about 10 km from the ground [21]; and the refractive index structure parameters, \(C_{n}^{2}\), were \(6.5\times 10^{-14}\) m\({}^{-2/3}\), \(5\times 10^{-15}\) m\({}^{-2/3}\) and \(6\times 10^{-16}\) m\({}^{-2/3}\) (three kinds of classical refractive index structure parameters corresponding to strong-, medium-, and weak-turbulence channels, respectively) [19; 20; 21; 22; 23; 24]. The insets (a), (b), (c), and (d) in Figure 4 show the light-field distribution in its initial state and after being disturbed by the strong-, medium-, and weak-turbulence atmospheric channels, respectively. For the carrier recovery module, shorter estimated symbol-block lengths (N1, N2) could achieve fast carrier phase tracking, but this was limited by DSP speed. On the contrary, longer estimated symbol-block lengths (N1, N2) could better suppress the effect of noise on the carrier's estimated symbol block and achieve higher noise tolerance. Therefore, the optimal estimated symbol-block lengths (N1, N2) needed to be obtained after balancing the two factors [25]. Figure 5 shows the effect of FOE symbol-block length N1 on the normalized mean square error (MSE) in a medium-turbulence channel. The FOE accuracy  
Figure 4: Simulation setup for a 10 Gbps QPSK CFSO transmission system. increased with increases in the transmitting power and the length of the estimated symbol block. Meanwhile, the difference between the MSEs of different FOE symbol blocks decreased as N1 increased to 512. Based on the present simulation platform, we consider N1 = 512 the optimal symbol-block length for this system. On this basis, we compared the effects of phase-offset-estimation symbol-block length N2 on the receiver sensitivity of the proposed JCSCR in a medium-turbulence channel. In this simulation, FOE symbol-block length N1 = 512 and the laser linewidth was 50 kHz.