Optimization of LDPC-coded power series MIMO/FSO link with hybrid-SIM based on machine learning in satellite downlink for 5G and beyond applications

This study presents a thorough evaluation of satellite downlink performance in a Free Space Optics (FSO) system with a Low-Density-Parity-Check (LDPC) based Multiple-Input-Multiple-Output (MIMO) configuration. Atmospheric turbulence is characterized using a generalized K-distribution and a negative exponential distribution, with specified parameters. Key performance metrics including Bit Error Rate (BER), outage probability, and accuracy are measured. To address pointing-errors (PEs) and atmospheric turbulence (AT), a novel decoding methodology for Non-Recursive Convolutional Polynomial Encoding (NRCPE)-based Pulse Position Modulation (PPM)-Gaussian Minimum Shift Keying (GMSK)-modulated FSO transmissions is introduced, leveraging Support Vector Machines (SVM). The study introduces a sophisticated Meijer-G function for MIMO statistical analysis and proposes a power series-based Probability Density Function (PDF) with non-recursive GMSK modulation. This PDF allows closed-form derivation of BER and Outage Probability expressions, showcasing improved MIMO link performance in the presence of PEs and AT. Simulations validate the models, offering insights into their effectiveness across varying turbulence levels. The findings assist FSO-MIMO designers in minimizing PEs,AT and achieving optimal results.Subsequently, authors perform a suppression to BER, Particularly, the optimum beam width factors for $$\left\{p\times q|1\times 2\times 2, \& 2\times 3\right\}$$ p × q | 1 × 2 × 2 , & 2 × 3 , diversity degrees by a $$\left\{p\times q|1\times 1\right\}$$ p × q | 1 × 1 , as a reference are 81.24%, 87.32%, and 89.61%, respectively, at $${\varepsilon }_{nj}=4.02$$ ε nj = 4.02 and $${I}_{o}=10\text{ dBm}$$ I o = 10 dBm .The proposed MIMO/FSO provides accuracy and an irradiances gain of 13.34dBm,i.e., $${\varepsilon }_{nj}=5.03$$ ε nj = 5.03 at BER $${10}^{-9}$$ 10 - 9 for downlink satellite transmission over SIMO and SISO FSO links. This study provides a comprehensive framework for optimizing FSO communication systems, considering atmospheric turbulence and pointing errors.