Atmospheric turbulence mitigation in adaptive MIMO hybrid RF/FSO links using MPPM/M-QAM modulation and TAS-MRC diversity under pointing errors

Ebrahim E. Elsayed; Mohamed A. Yakout; Ahmed S. Samra

doi:10.1515/joc-2025-0146

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Atmospheric turbulence mitigation in adaptive MIMO hybrid RF/FSO links using MPPM/M-QAM modulation and TAS-MRC diversity under pointing errors

Ebrahim E. Elsayed , Mohamed A. Yakout und Ahmed S. Samra

Veröffentlicht/Copyright: 16. Juni 2025

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Aus der Zeitschrift Journal of Optical Communications

Abstract

Ground-based Free-Space Optical (FSO) communication networks are gaining prominence due to their high data rates, bandwidth efficiency (BE), cost-effectiveness, and security. However, their performance is hindered by atmospheric turbulence, weather conditions, and pointing errors. This work proposes a hybrid Multiple-Input Multiple-Output (MIMO) Radio Frequency (RF)/FSO system with adaptive modulation to address these challenges. We analyze M-ary Pulse Position Modulation (MPPM) over Gamma–Gamma fading channels under varying turbulence levels and pointing errors, employing equal gain combining diversity to improve robustness. Closed-form expressions for the average bit error rate and outage probability are derived using the Meijer G-function. Furthermore, a novel hybrid MPPM/M-Quadrature Amplitude Modulation scheme is introduced to enhance BE and link reliability. The proposed system is compared with conventional methods, demonstrating superior performance via Monte Carlo simulations. Additionally, a MIMO hybrid RF/FSO system using transmit aperture selection and maximal ratio combining is analyzed to mitigate fading effects. Derived expressions for the average symbol error probability validate the gains of the hybrid modulation approach. The adaptive transmission modulation scheme significantly improves BE over nonadaptive techniques, leveraging the complementary strengths of RF and FSO channels.

Keywords: FSO systems; hybrid TAS-MRC-based MIMO-RF/FSO; adaptive modulation techniques; M-ary MPPM/M-QAM modulation schemes; gamma–gamma turbulence channel and pointing errors (PEs)

Corresponding author: Ebrahim E. Elsayed, Department of Electronics and Communications Engineering, Faculty of Engineering, Mansoura University, Mansoura, Egypt, E-mail: engebrahem16@gmail.com

Research ethics: This study did not involve human or animal subjects.
Informed consent: Not applicable.
Author contributions: Ebrahim E. Elsayed: Conceptualization; Formal Analysis; Methodology; Investigation; Coding; Software; Visualization; Writing – Original Draft & Editing; Writing – Review & Editing. Mohamed A. Yakout: Supervision; Visualization; Methodology; Project Administration; Resources; Validation. Ahmed S. Samra: Supervision; Visualization; Methodology; Project Administration; Resources; Validation.
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interest: The authors declare no competing financial interests or personal relationships that could influence the work reported in this study.
Research funding: This study was conducted without any external funding.
Data availability: All data generated or analyzed during this study are included in this published article.

Appendix A

This work derives the CDF for a hybrid RF/FSO communication system employing MRC at the receiver. By substituting Eqs. (6) and (7) into Eq. (10), we express Eq. (10) as shown in references [44], [45], [46].

(A1) F γ MRC γ = 2 α + β − 2 m m 2 π Γ α Γ β Γ m γ ‾ rf ∫ 0 ∞ γ rf m − 1 exp − m γ rf γ ‾ rf × G 3 , 7 6 , 1 α β 2 16 μ 2 γ − γ rf 1 , ξ 2 + 1 2 , ξ 2 + 2 2 2 , α 2 , α + 1 2 , β 2 , β + 1 2 , 0 d γ rf

Now, letting v = γ-γ _rf and substituting γ _rf and dγ _rf into Eq. (A1), Eq. (A1) is expressed as

(A2) F γ MRC γ = − 2 α + β − 2 m m 2 π Γ α Γ β Γ m γ ‾ f exp − m γ γ ‾ f ∫ 0 ∞ γ − v m − 1 × exp m γ ‾ f v G 3 , 7 6 , 1 α β 2 16 μ 2 v 1 , ξ 2 + 1 2 , ξ 2 + 2 2 ξ 2 2 , ξ 2 + 1 2 , α 2 , α + 1 2 , β 2 , β + 1 2 , 0 d v

Using a binomial expansion, the term (γ-v)^m−1 can be substituted into Eq. (A2) as

(A3) F γ MRC γ = − 2 α + β − 2 m m 2 π Γ α Γ β Γ m γ ‾ rf exp − m γ γ ‾ r f ∑ k = 0 m − 1 m − 1 k × − 1 k γ m − k − 1 ∫ 0 ∞ v k exp m γ ‾ r f v × G 3 , 7 6 , 1 α β 2 16 μ 2 v ξ 2 2 , ξ 2 + 1 2 , α 2 , α + 1 2 , β 2 , β + 1 2 , 0 2 d v

Finally, Eq. (11) can be obtained from Eq. (A3) using Eq. 7.813(1) from [53].

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Received: 2025-04-19

Accepted: 2025-05-25

Published Online: 2025-06-16

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https://doi.org/10.1515/joc-2025-0146

Schlagwörter für diesen Artikel

FSO systems; hybrid TAS-MRC-based MIMO-RF/FSO; adaptive modulation techniques; M-ary MPPM/M-QAM modulation schemes; gamma–gamma turbulence channel and pointing errors (PEs)