## 3 Simulation Setup  
Atmospheric turbulence induces phase distortions and intensity fluctuations, which result in noise. These noise effects are observed at the receiver as variations in signal strength and phase, significantly impacting system performance. Additionally, due to limitations in the laser manufacturing processes, the center frequencies of the signal laser and the local oscillator (LO) laser cannot be perfectly aligned. This misalignment, especially after transmission through the atmospheric channel, leads to further degradation of the  
Figure 6: Calculation and compensation of accumulated frequency offset. signal's coherence, resulting in frequency offsets and phase distortions, and introducing phase noise. To address these issues, this study utilizes the spatial diversity reception simulation platform for the 10 GBaud PM 16 QAM free-space optical (FSO) system, as shown in Figure 7. The simulation system incorporates different atmospheric structure constants (\(C_{n}^{2}\)) to represent varying levels of turbulence intensity. Specifically, \(C_{n}^{2}=1\times 10^{-14}\) m\({}^{-2/3}\) is used to simulate strong turbulence, while \(C_{n}^{2}=1\times 10^{-16}\) m\({}^{-2/3}\) represents weak turbulence. To model the impact of laser manufacturing process quality, different frequency offset values are configured accordingly. The following sections provide a detailed description of the relevant configurations of the simulation platform. At the transmitter, the polarization beam splitter (PBS) splits the external carrier laser with a linewidth of 50 kHz into two orthogonal polarizations. Subsequently, 16 QAM data symbols are generated from the PRBS, corresponding to the real and imaginary parts of the X and Y polarizations. They are then converted into electrical signals using a digital-to-analog converter (DAC), and the two orthogonally polarized optical signals are modulated using a dual-polarization IQ modulator. Finally, the signal is combined into a single signal beam using a polarization beam combiner and emitted into a simulated free space turbulent channel. The free space turbulent channel is simulated using a Fourier transform-based phase screen model, assuming that the outer scale of the atmospheric turbulence tends to infinity and the inner scale tends to zero. The range of atmospheric turbulence is 10 km. The light field distribution before passing through the phase screen is shown in Figure 7a, and the light field distribution after passing through strong and weak atmospheric turbulences is shown in Figure 7b,c, respectively. The refractive indexes of weak and strong turbulences are \(C_{n}^{2}=1\times 10^{-16}\) m\({}^{-2/3}\) and \(C_{n}^{2}=1\times 10^{-14}\) m\({}^{-2/3}\), respectively [24]. At the receiver end, multiple receiving telescopes receive independent, attenuated optical signals and couple them into a single-mode optical fiber. In the receiver, the received optical field is mixed with a local oscillator (LO) laser and the photoelectric conversion is completed by the balanced photodiodes (BPDs). Each receiving branch shares a common LO laser, with a linewidth of 50 kHz and an optical power of 7.5 dBm. After I/Q imbalance compensation, frame synchronization and diversity branch phase correction are performed on each branch, Maximum Ratio Combining (MRC) can be performed. The combined signals share a set of DSPs to reduce the complexity of the diversity receiving system. The  
Figure 7: Simulation platform for a spatial diversity coherent FSO communication system. Insets: Light field distributions (**a**) before and (**b**) and (**c**) after passing through the phase screen. simulation verifications conducted in this paper all use the four-branch received MRC. The main modules of the simulation system include I/Q imbalance recovery, diversity branch phase correction, MRC, polarization demultiplexing, TTQP carrier FOE, carrier phase recovery, decision-directed least-mean-square (DD-LMS), and bit error rate (BER) counting [30].