## 2 Adaptive Optics Enabled Free-Space Optical Communication  
### Experimental Setup  
Figure 1 shows the experimental setup for an AO enabled FSO communication system. The five continuous wave (CW) laser beams are generated with the inter-channel spacing of 50 GHz (1549.32-1550.92 nm). The wavelength channels are multiplexed together and used as the optical input of an I/Q modulator. The pseudorandom binary sequence (PRBS) signals are encoded using a binary LDPC code with the code rate of 0.8. The data streams pass to the arbitrary waveform generator (AWG) and drive the I/Q modulator to generate a 15.6 GBaud optical QPSK signal. An optical interleaver (IL) is applied to separate odd and even channel signals, which are then decorrelated by 350 symbols and recombined together. The resulting WDM QPSK optical signals with the decorrelated adjacent wavelength channels are boosted by an Erbium-doped fiber amplifier (EDFA), followed by an optical tunable filter (OTF) to suppress amplified spontaneous emission (ASE) noise. The optical signals are separated by a coupler, and one path is later decorrelated before recombination. The optical Gaussian modes are collimated by fixed fiber optic collimator and converted to OAM modes (OAM states \(\pm 2\) and \(\pm 6\)) by using a high-resolution spatial light modulator (SLM). The resulting OAM modes are then centrally aligned by a beam splitter (BS). Another 1548.9 nm Gaussian probe beam is used to assist AO compensation. The Gaussian probe beam is expanded using a beam expander (BE) to reach a diameter larger than the widest OAM beams (OAM states \(\pm 6\)) generated in this experiment. At this stage, the probe beam is also centrally aligned with the data-carrying OAM modes. The expanding telescope is applied to adjust the diameters of the collimated OAM beam and Gaussian probe beam, which are then sent to the turbulence emulator. The SLM2 and SLM3 are continuously and randomly updating phase patterns to be modelled on the dynamic atmospheric turbulence environment [22]. The accuracy of the turbulence model can be validated in terms of on-axis Gamma-Gamma intensity distribution and intensity correlation function. The atmospheric turbulence emulator used here is designed according to the Rytov variance [32] of \(\sigma_{R}^{2}=2\). The size of the distorted OAM and probe beams are decreased by a compressing telescope. The distorted beams then pass to the DM for wavefront correction. The distorted Gaussian probe beam functions as a stimulus in this wavefront sensorless AO setup, with the assumption that the probe beam and OAM beams are affected by the similar wavefront distortion. Partial optical beams are segregated via a BS and collected by a single-mode fiber (SMF) patch cable. In this experiment, the OTF3 with a central wavelength of 1548.9 nm is implemented to only capture the Gaussian probe beam, followed by a photodiode (PD) for power monitoring. The detected analog voltage is digitized by an analog-to-digital converter (ADC) to update the DM pixels based on stochastic parallel gradient descent algorithm [33]. It is noteworthy that the performance of the FSO transmission system is dominated by linear mode crosstalk. within comparison to fiber-optic transmission systems, FSO links will not have notable nonlinear effects in principle. The AO used in our experiment will not bring nonlinear distortions, since the processing time of the AO is far longer than the data rate. Following AO compensation, the less distorted OAM modes are detected by SLM4. This is used to convert one OAM mode back to the Gaussian-like mode, which is then collected by another SMF patch cable. The collected optical signals are pre-amplified by EDFA2, followed by a variable optical attenuator (VOA) for optical power tuning. Additional ASE noise is generated and adjusted via a sub-system configured by EDFA3, EDFA4, and VOA2.