Startseite A performance study of an inter-UAV-based free space optical (FSO) system in the maritime environment
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A performance study of an inter-UAV-based free space optical (FSO) system in the maritime environment

  • Vijaya Ratnam Nallagonda EMAIL logo , N. Siva Nagaraju , Dantuluri Bhavani , Rajesh Gogineni , Suneel Mudunuru und Prabu Krishnan
Veröffentlicht/Copyright: 12. Juni 2025
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Journal of Optical Communications
Aus der Zeitschrift Journal of Optical Communications

Abstract

Recent advances in optical communication technology have enabled users to access high-data services on maritime links using the unmanned aerial vehicles (UAVs)-based free space optical (FSO) system. However, ensuring reliable data communication for maritime links is a significant challenge due to harsh weather conditions. To address the growing demand for maritime links, we have proposed a maritime UAV-based FSO communication system that can support high-speed data rates and provide extended communication coverage. This paper investigates various aspects of maritime UAV-based FSO systems, including the basic architecture, different channel characteristics, and application scenarios. The paper also includes an analysis of the outage probability of the Inter UAV-based FSO communication system, considering the lognormal distributed channel model for the maritime Inter UAV-based FSO link with heterodyne detection (hd). Additionally, it presents an accurate analytical channel model between UAVs. It compares analytical and simulation results, considering maritime turbulence, pointing error, and hovering UAV fluctuations.

Keywords: unmanned aerial vehicles; free-space optical; radio frequency; non-line-of-sight communicaiton; heterodyne detection; angle-of-arrival fluctuations
Corresponding author: Vijaya Ratnam Nallagonda, Electronics and Communication Engineering, Dhanekula Institute of Engineering and Technology, Vijayawada, Gangur, Andhra Pradesh – 521139, India, E-mail:

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Conflict of interest: All other authors state no conflict of interest.

  5. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  6. Research funding: None declared.

  7. Data availability: Yes. Based on request.

Appendix A

The Rytov variance of a Gaussian beam experiencing weak turbulence is defined as follows [46]:

(A.1) σ B 2 = 8 π 2 k 2 L ∫ 0 1 d ξ ∫ 0 ∞ κ Φ n ( κ ) exp − Λ L κ 2 ξ 2 / k 1 − cos κ 2 L k ξ 1 − Θ ¯ 1 ξ d κ

The normalized distance parameter is ξ, the spatial frequency magnitude is κ, and the turbulence power spectrum for the marine environment is Φ n (κ), [47].

(A.2) Φ n ( κ ) = 0.033 C n 2 κ 2 + κ 0 2 11 / 6 exp − κ 2 κ H 2 1 − 0.061 κ κ H + 2.836 κ 7 / 6 κ H 7 / 6 ,

where κ0 = 1/L0, and L0 is the outer scale length of the turbulence. By substituting the equation above, we can express it as follows

(A.3) σ B 2 = 0.264 π 2 k 2 C n 2 L × Re ∫ 0 1 d ξ ∫ 0 ∞ κ κ 2 + κ 0 2 11 / 6 e − 1 + Q L ξ 2 κ H 2 κ 2 d κ − ∫ 0 1 d ξ ∫ 0 ∞ 0.061 κ 2 κ H κ 2 + κ 0 2 11 / 6 e − 1 + Q 2 ξ 2 κ H 2 κ 2 d κ + ∫ 0 1 d ξ ∫ 0 ∞ 2.836 κ 13 / 6 κ H 7 / 6 κ 2 + κ 0 2 11 / 6 e − 1 + Q 1 ξ 2 κ H 2 κ 2 d κ − ∫ 0 1 d ξ ∫ 0 ∞ κ κ 2 + κ 0 2 11 / 6 e − 1 + Q 1 ξ 2 + i Q H ξ 1 − Q ¯ 1 ξ κ H 2 κ 2 d κ + ∫ 0 1 d ξ ∫ 0 ∞ 0.061 κ 2 κ H κ 2 + κ 0 2 11 / 6 e − 1 + Q I ξ 2 + i Q H ξ 1 − θ ¯ 1 ξ κ H 2 κ 2 d κ   − ∫ 0 1 d ξ ∫ 0 ∞ 2.836 κ 13 / 6 κ H 7 / 6 κ 2 + κ 0 2 11 / 6 e − 1 + Q l ξ 2 + i Q H ξ 1 − Θ ¯ 1 ξ κ H 2 κ 2 d κ .

To solve the integral that depends on κ, we can apply the confluent hypergeometric function U(a; c; x).

(A.4) U ( a ; c ; x ) = 1 Γ ( a ) ∫ 0 ∞ e − x t t a − 1 ( 1 + t ) c − a − 1 d t .

Changing variable as κ 2 / κ 0 2 = t

(A.5) σ B 2 = 0.132 π 2 k 2 C n 2 L × Re ∫ 0 1 κ 0 − 5 3 U 1 ; 1 6 ; κ 0 2 κ H 2 1 + Q l ξ 2 d ξ − ∫ 0 1 0.061 κ 0 − 2 3 Γ 3 2 κ H U 3 2 ; 2 3 ; κ 0 2 κ H 2 1 + Q l ξ 2 d ξ + ∫ 0 1 2.836 κ 0 − 1 2 Γ 19 12 κ H 7 / 6 U 19 12 ; 3 4 ; κ 0 2 κ H 2 1 + Q l ξ 2 d ξ − ∫ 0 1 κ 0 − 5 3 U 1 ; 1 6 ; κ 0 2 κ H 2 1 + Q l ξ 2 + i Q H ξ 1 − Θ ¯ 1 ξ d ξ + ∫ 0 1 0.061 κ 0 − 2 3 Γ 3 2 κ H U 3 2 ; 2 3 ; κ 0 2 κ H 2 1 + Q l ξ 2 + i Q H ξ 1 − Θ ¯ 1 ξ d ξ   − ∫ 0 1 2.836 κ 0 − 1 2 Γ 19 12 κ H 7 / 6 U 19 12 ; 3 4 ; κ 0 2 κ H 2 1 + Q l ξ 2 + i Q H ξ 1 − Θ ¯ 1 ξ d ξ .

Since κ 0 2 / κ H 2 ≪ 1 we can use the approximation for the confluent hypergeometric function

(A.6) U ( a ; c ; x ) ≈ Γ ( 1 − c ) Γ ( 1 + a − c ) + Γ ( c − 1 ) Γ ( a ) x 1 − c , | x | ≪ 1 .

Applying this approximation to the integrals simplifies them significantly. Finally, after simplifying the integrals and applying various approximations, we arrive at the following expression for the Rytov variance

(A.7) σ B 2 = 0.132 π 2 k 2 C n 2 L κ H 5 / 3 Re Γ ( − 5 / 6 ) 2 F 1 − 5 / 6,1 / 2 ; 3 / 2 ; − Q l − 0.061 Γ ( − 1 / 3 ) 2 F 1 − 1 / 3,1 / 2 ; 3 / 2 ; − Q l + 2.836 Γ ( − 1 / 4 ) 2 F 1 − 1 / 4,1 / 2 ; 3 / 2 ; − Q l − Γ ( − 5 / 6 ) Γ ( 2 ) 2 F 1 − 5 6 , 1 ; 2 ; δ 1 + 0.061 Γ ( − 1 / 3 ) Γ ( 2 ) 2 F 1 − 1 3 , 1 ; 2 ; δ 1   − 2.836 Γ ( − 1 / 4 ) Γ ( 2 ) 2 F 1 − 1 4 , 1 ; 2 ; δ 1 ,

where δ 1 = − i Q H + 2 3 i Q H Θ ¯ 1 − Q l .

(A.8) F 1 2 ( 1 − a , 1 ; 2 ; − x ) = ( 1 + x ) a − 1 a x .

By applying Eq. (A.8) to Eq. (A.7) and utilizing the polar form of a complex number, the Rytov variance for a Gaussian beam propagating through Kolmogorov maritime turbulence can ultimately be expressed as shown in Eq. (10).

References

1. Khalighi, MA, Uysal, M. Survey on free space optical communication: a communication theory perspective. IEEE Commun Surv Tutorials 2014;16:2231–58. https://doi.org/10.1109/comst.2014.2329501.Suche in Google Scholar

2. Alqurashi, FS, Trichili, A, Saeed, N, Ooi, BS, Alouini, MS. Maritime communications: a survey on enabling technologies, opportunities, and challenges. IEEE Internet Things J 2022;10:3525–47. https://doi.org/10.1109/jiot.2022.3219674.Suche in Google Scholar

3. Willitsford, A, Newell, KT, O’Toole, M, Patel, K. Maritime free space optical communications field test and link budget statistics. Opt Express 2024;32:13769–82. https://doi.org/10.1364/oe.518363.Suche in Google Scholar

4. Stotts, LB, Kolodzy, P, Pike, A, Graves, B, Dougherty, D, Douglass, J. Free-space optical communications link budget estimation. Appl Opt 2010;49:5333–43. https://doi.org/10.1364/ao.49.005333.Suche in Google Scholar

5. Wolfram, C. The wolfram functions site internet. IL, USA; 2007. [Online].Available: http://functions.wolfram.com.Suche in Google Scholar

6. Lionis, A, Peppas, K, Nistazakis, HE, Tsigopoulos, AD, Cohn, K. Experimental performance analysis of an optical communication channel over maritime environment. Electronics 2020;9:1109. https://doi.org/10.3390/electronics9071109.Suche in Google Scholar

7. Cheng, M, Guo, L, Zhang, Y. Scintillation and aperture averaging for Gaussian beams through non-Kolmogorov maritime atmospheric turbulence channels. Opt Express 2015;23:32606–21. https://doi.org/10.1364/oe.23.032606.Suche in Google Scholar PubMed

8. Rabinovich, WS, Mahon, R, Ferraro, MS. Optical scintillation in a maritime environment. Opt Express 2023;31:10217–36. https://doi.org/10.1364/oe.484922.Suche in Google Scholar

9. Zolich, A, Palma, D, Kansanen, K, Fjørtoft, K, Sousa, J, Johansson, KH, et al.. Survey on communication and networks for autonomous marine systems. J Intell Rob Syst 2019;95:789–813. https://doi.org/10.1007/s10846-018-0833-5.Suche in Google Scholar

10. Yang, T, Shen, XS. Maritime wideband communication networks: video transmission scheduling. Berlin, Germany: Springer; 2014.10.1007/978-3-319-07362-0Suche in Google Scholar

11. Awan, MS, Leitgeb, E, Muhammad, SS, Nadeem, F, Khan, MS, Capsoni, C. Distribution function for continental and maritime fog environments for optical wireless communication. In: 2008 6th International Symposium on Communication Systems, Networks and Digital Signal Processing. IEEE; 2008.10.1109/CSNDSP.2008.4610728Suche in Google Scholar

12. Cvijetic, M, Li, M. Characterization of free space optical channels for terrestrial and maritime air conditions. In: 2017 19th International Conference on Transparent Optical Networks (ICTON). IEEE; 2017.10.1109/ICTON.2017.8024760Suche in Google Scholar

13. Gadwal, V, Hammel, S. Free-space optical communication links in a marine environment. Free-Space Laser Commun VI 2006;6304. https://doi.org/10.1117/12.682474.Suche in Google Scholar

14. Vetelino, FS, Grayshan, KJ, Young, CY, Grant, KJ, Wasiczko, L, Burris, HR, et al.. A new marine atmospheric spectrum for laser propagation. Atmos Propag IV 2007;6551. https://doi.org/10.1117/12.720903.Suche in Google Scholar

15. Juarez, JC, Sluz, JE, Nelson, C, Airola, MB, Fitch, MJ, Young, DW, et al.. Free-space optical channel characterization in the maritime environment. Atmos Propag VII 2010;7685. https://doi.org/10.1117/12.852645.Suche in Google Scholar

16. Djordjevic, IB. Advanced optical and wireless communications systems. Adv Opt Wirel Commun Syst 2017:1–942. https://doi.org/10.1007/978-3-319-63151-6.Suche in Google Scholar

17. Yuan-zhe, Lu, Z, Yan, B, Li, C, Zhang, H, Lin, W, et al.. Performance of differential phase shift keying maritime laser communication over log-normal distribution turbulence channel. Optoelectron Lett 2021;17:90–5. https://doi.org/10.1007/s11801-021-9211-9.Suche in Google Scholar

18. Li, M, Cvijetic, M. Coherent free space optics communications over the maritime atmosphere with use of adaptive optics for beam wavefront correction. Appl Opt 2015;54:1453–62. https://doi.org/10.1364/ao.54.001453.Suche in Google Scholar

19. Ghassemlooy, Z, Popoola, W, Rajbhandari, S. Optical wireless communications: system and channel modelling with Matlab®. Boca Raton: CRC Press; 2019.10.1201/9781315151724Suche in Google Scholar

20. Vetelino, FS, Young, C, Grant, K, Wasiczko, L, Burris, H, Moore, C, et al.. Initial measurements of atmospheric parameters in a marine environment. Atmos Propag VII 2006;6215. https://doi.org/10.1117/12.668026.Suche in Google Scholar

21. Han, JE, Nam, SS, Yoon, C, Hwang, DD, Alouini, MS. Asymptotic ergodic capacity analysis for FSO communication between mobile platforms in maritime environments. Appl Sci 2023;13:6978. https://doi.org/10.3390/app13126978.Suche in Google Scholar

22. Tsiftsis, TA. Performance of heterodyne wireless optical communication systems over gamma-gamma atmospheric turbulence channels. Electron Lett 2008;44:372–3. https://doi.org/10.1049/el:20083028.10.1049/el:20083028Suche in Google Scholar

23. Kaadan, A, Refai, HH, LoPresti, PG. Multielement FSO transceivers alignment for inter-UAV communications. J Lightwave Technol 2014;32:4785–95. https://doi.org/10.1109/jlt.2014.2364795.Suche in Google Scholar

24. Kaadan, A, Refai, H, Lopresti, P. Spherical FSO receivers for UAV communication: geometric coverage models. IEEE Trans Aero Electron Syst 2016;52:2157–67. https://doi.org/10.1109/taes.2016.150346.Suche in Google Scholar

25. Fawaz, W, Abou-Rjeily, C, Assi, C. UAV-aided cooperation for FSO communication systems. IEEE Commun Mag 2018;56:70–5. https://doi.org/10.1109/mcom.2017.1700320.Suche in Google Scholar

26. Alzenad, M, Shakir, MZ, Yanikomeroglu, H, Alouini, M-S. FSO-based vertical backhaul/fronthaul framework for 5G+ wireless networks. IEEE Commun Mag 2018;56:218–24. https://doi.org/10.1109/mcom.2017.1600735.Suche in Google Scholar

27. Dabiri, MT, Sadough, SMS, Khalighi, MA. Channel modeling and parameter optimization for hovering UAV-based free-space optical links. IEEE J Sel Area Commun 2018;36:2104–13. https://doi.org/10.1109/jsac.2018.2864416.Suche in Google Scholar

28. Dabiri, MT, Sadough, SMS, Ansari, IS. Tractable optical channel modeling between UAVs. IEEE Trans Veh Technol 2019;68:11543–50. https://doi.org/10.1109/tvt.2019.2940226.Suche in Google Scholar

29. Safi, H, Dargahi, A, Cheng, J. Spatial beam tracking and data detection for an FSO link to a UAV in the presence of hovering fluctuations. arXiv preprint arXiv:1904.03774 2019.Suche in Google Scholar

30. Dabiri, MT, Sadough, SMS. Optimal placement of UAV-assisted free-space optical communication systems with DF relaying. IEEE Commun Lett 2019;24:155–8. https://doi.org/10.1109/lcomm.2019.2949274.Suche in Google Scholar

31. Nallagonda, VR, Krishnan, P. Performance analysis of FSO based inter-UAV communication systems. Opt Quant Electron 2021;53:1–20. https://doi.org/10.1007/s11082-021-02843-w.Suche in Google Scholar

32. Nallagonda, VR, Krishnan, P. Bit error rate analysis of polarization shift keying based free space optical link over different weather conditions for inter unmanned aerial vehicles communications. Opt Quant Electron 2021;53:538. https://doi.org/10.1007/s11082-021-03188-0.Suche in Google Scholar

33. Ratnam, NV. Performance analysis and enhancement of unmanned aerial vehicle based free space optical communication system. Surathkal: Diss. National Institute of Technology Karnataka; 2022.Suche in Google Scholar

34. Dabiri, MT, Khankalantary, S, Piran, MJ, Ansari, IS, Uysal, M, Saad, W, et al.. UAV-assisted free space optical communication system with amplify-and-forward relaying. IEEE Trans Veh Technol 2021;70:8926–36. https://doi.org/10.1109/tvt.2021.3098389.Suche in Google Scholar

35. Xu, G, Zhang, N, Xu, M, Xu, Z, Zhang, Q, Song, Z. Outage probability and average BER of UAV-assisted dual-hop FSO communication with amplify-and-forward relaying. IEEE Trans Veh Technol 2023;72:8287–302. https://doi.org/10.1109/tvt.2023.3252822.Suche in Google Scholar

36. Qu, L, Xu, G, Zeng, Z, Zhang, N, Zhang, Q. UAV-assisted RF/FSO relay system for space-air-ground integrated network: a performance analysis. IEEE Trans Wireless Commun 2022;21:6211–25. https://doi.org/10.1109/twc.2022.3147823.Suche in Google Scholar

37. Dabiri, MT, Savojbolaghchi, H, Sadough, SMS. On the ergodic capacity of ground-to-uav free-space optical communications. In: 2019 2nd West Asian Colloquium on Optical Wireless Communications (WACOWC). IEEE; 2019.10.1109/WACOWC.2019.8770206Suche in Google Scholar

38. Hayal, MR, Elsayed, EE, Kakati, D, Singh, M, Elfikky, A, Boghdady, AI, et al.. Modeling and investigation on the performance enhancement of hovering UAV-based FSO relay optical wireless communication systems under pointing errors and atmospheric turbulence effects. Opt Quant Electron 2023;55:625. https://doi.org/10.1007/s11082-023-04772-2.Suche in Google Scholar

39. Elsayed, EE. Investigations on OFDM UAV-based free-space optical transmission system with scintillation mitigation for optical wireless communication-to-ground links in atmospheric turbulence. Opt Quant Electron 2024;56:837. https://doi.org/10.1007/s11082-024-06692-1.Suche in Google Scholar

40. Elsayed, EE. Investigations on modified OOK and adaptive threshold for wavelength division multiplexing free-space optical systems impaired by interchannel crosstalk, atmospheric turbulence, and ASE noise. J Opt 2024:1–14. https://doi.org/10.1007/s12596-024-01929-4.Suche in Google Scholar

41. Elsayed, EE. Atmospheric turbulence mitigation of MIMO-RF/FSO DWDM communication systems using advanced diversity multiplexing with hybrid N-SM/OMI M-ary spatial pulse-position modulation schemes. Opt Commun 2024;562:130558. https://doi.org/10.1016/j.optcom.2024.130558.Suche in Google Scholar

42. Dabiri, MT, Safi, H, Parsaeefard, S, Saad, W. Analytical channel models for millimeter wave UAV networks under hovering fluctuations. IEEE Trans Wireless Commun 2020;19:2868–83. https://doi.org/10.1109/twc.2020.2968530.Suche in Google Scholar

43. Schulz, D, Jungnickel, V, Alexakis, C, Schlosser, M, Hilt, J, Paraskevopoulos, A, et al.. Robust optical wireless link for the backhaul and fronthaul of small radio cells. J Lightwave Technol 2016;34:1523–32. https://doi.org/10.1109/jlt.2016.2523801.Suche in Google Scholar

44. Sandalidis, HG, Tsiftsis, TA, Karagiannidis, GK. Optical wireless communications with heterodyne detection over turbulence channels with pointing errors. J Lightwave Technol 2009;24:4440–5. https://doi.org/10.1109/jlt.2009.2024169.Suche in Google Scholar

45. Andrews, LC, and MK Beason. Laser beam propagation in random media: new and advanced topics 2023.10.1117/3.2643989Suche in Google Scholar

46. Andrews, LC, Ronald, LP, Hopen, CY. Laser beam scintillation with applications. USA: SPIE press; 2001, 99.10.1117/3.412858Suche in Google Scholar

47. Grayshan, KJ, Strömqvist Vetelino, F, Young, CY. A marine atmospheric spectrum for laser propagation. Waves Random Complex Media 2008;18:173–84. https://doi.org/10.1080/17455030701541154.Suche in Google Scholar
Received: 2025-02-26
Accepted: 2025-04-22
Published Online: 2025-06-12

© 2025 Walter de Gruyter GmbH, Berlin/Boston

https://doi.org/10.1515/joc-2025-0067
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unmanned aerial vehicles; free-space optical; radio frequency; non-line-of-sight communicaiton; heterodyne detection; angle-of-arrival fluctuations
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