# Error Probability of a Coherent \(M\)-ary PSK FSO System Influenced by Phase Noise
## 5 Conclusions  
We have analyzed the performance of a coherent FSO system when turbulence is modeled by general Malaga (\(\mathcal{M}\)) distribution including misalignment fading. Taking into account the imperfect compensation of the phase error that occurs in the coherent receiver when mixing the optical signal and the signal of the local laser, we have derived an analytical expression for the error probability in detecting multilevel PSK signals.  
The results have shown that turbulence conditions significantly affect the SEP in the range of mean SNR values. The influence of pointing errors is stronger when the phase noise is weaker, i.e., when the standard deviation of the phase noise is smaller. In the case of applying higher-order modulation, the receiver becomes significantly less tolerant to the influence of the phase noise. For example, in the case of 8 PSK, there is already a significant deterioration of the SEP when standard deviation of phase noise is around 2.5 degrees, while BPSK modulation format is insensitive for values of phase noise standard deviation even up to 16 degrees. The results have also illustrated that the effect of phase noise on SEP values is stronger when atmospheric turbulence is weaker.  
The results show that the phase noise causes the appearance of a floor, which only depends on the standard deviation of the phase noise, and not on the signal power and turbulence conditions over the channel. The higher the standard deviation of phase noise is, the lower the value of the floor. For example, in the case of 16 PSK transmission, increasing of standard deviation of phase noise from 2.5 degrees to 3 degrees will cause the BER floor to increase by more than one order of magnitude.  
The results presented here show that SEP floor cannot be decreased by increasing the signal power. In our further work, we will design quasi-cyclic low-density parity-check codes to downscale this SEP floor. Our aim will be to examine if those powerful error correction codes have error floors under given scenarios.  
Conceptualization, G.T.D.; methodology, G.T.D., M.P., G.V.M., Z.M., J.M.; software, M.P., G.T.D.; validation, G.T.D., M.P., G.V.M., Z.M., J.M.; formal analysis, M.P., G.T.D., G.V.M.; investigation, G.T.D., M.P., G.V.M., Z.M., J.M.; resources, G.T.D, M.P.; data curation, G.T.D.; writing--original draft preparation, G.T.D., M.P., G.V.M.; writing--review and editing, G.T.D., G.V.M.; visualization, M.P., G.T.D.; supervision, G.T.D., G.V.M.; project administration, G.T.D.; funding acquisition, Z.M. All authors have read and agreed to the published version of the manuscript.  
The work of [PERSON] has received funding from the European Union Horizon 2020 research and innovation program under Grant No. 856967. The work of [PERSON] and [PERSON] are supported by the Polish National Agency for Academic Exchange (NAWA) under Grant No. PPN/ULM/2020/1/00256. A part of paper was also supported by the Science Fund of the Republic of Serbia under grant no. 7750284 (hi-STAR), and by the Ministry of Education, Science and Technological Development of the Republic of Serbia. This publication was based upon work from COST Action NEWFORCUS CA19111, supported by COST (European Cooperation in Science and Technology).  
Not applicable.  
The authors would like to thank five reviewers for their helpful comments that significantly improved the initial version of the paper. [PERSON] would like to thank [PERSON] for discussions during the preparation of the second version of the manuscript.