⚡ electrical engineering

Performance Analysis of RIS-Assisted Hybrid RF/FSO Communication Systems over Nakagami-m and Gamma–Gamma Channels with Decode-and-Forward Relaying

This paper presents an end-to-end performance analysis of a RIS-assisted hybrid RF/FSO system using decode-and-forward relaying, demonstrating that a central-limit-theorem approximation for the cascaded RIS channel is valid for $N \ge 20$ (with conservative accuracy for $N=10\text{--}20$ ) and that the RIS is essential for achieving significant power savings and reliability improvements over non-RIS baselines.

Original authors: Tinotenda Mzembi, Munyaradzi Rushambwa

Published 2026-07-29

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CC BY 4.0

Original authors: Tinotenda Mzembi, Munyaradzi Rushambwa

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to send a secret message across a vast, foggy valley. You have two ways to do it: you can shout (Radio Frequency, or RF), which travels well through fog but gets lost in echoes and hills, or you can use a powerful laser beam (Free-Space Optical, or FSO), which is incredibly fast and clear but gets scrambled by wind, rain, and atmospheric turbulence. Engineers have long tried to combine these two into a "hybrid" system, hoping that if one fails, the other will succeed. But there's a catch: if the signal gets blocked or distorted right at the start of its journey, the whole message is lost before it even reaches the second half of the trip. This is the core puzzle of modern wireless communication: how to get a reliable, high-speed connection to remote places where laying fiber-optic cables is too expensive and traditional towers struggle with bad weather.

To solve this, scientists are experimenting with a new kind of "smart mirror" called a Reconfigurable Intelligent Surface (RIS). Think of it not as a mirror that just reflects light, but as a giant, programmable wall made of thousands of tiny, passive tiles. Each tile can twist the incoming signal just a tiny bit, like a conductor directing an orchestra, so that all the scattered waves line up perfectly to boost the signal strength. When you combine this smart wall with the hybrid shouting-and-laser approach, you might think you've got the ultimate communication superpower. But does it actually work better than just shouting alone? And how many tiles do you actually need on the wall before it stops helping?

This paper dives deep into that question by building a mathematical model of a specific setup: a source sending a signal to a smart wall, which reflects it to a relay station, which then splits the message into both a shout and a laser beam to the final destination. The researchers wanted to know if this specific arrangement could survive the worst weather and terrain. They found that the smart wall is absolutely critical; without it, the hybrid system actually performs worse than just using a single radio link. The wall acts as a necessary bridge to get the signal strong enough to benefit from the backup laser.

The team discovered that adding this smart wall allows the system to reach the same level of reliability with about 7 to 8 decibels less power than systems without it. In the real world, this translates to a fivefold saving in transmit power, which is a massive deal for battery-powered or solar-powered relay stations in remote areas. However, they also found a "sweet spot" for the size of the wall. While adding more tiles (elements) helps at first, the benefits start to flatten out once you have between 10 and 20 tiles. Going beyond 20 tiles doesn't really make the connection much better because the bottleneck shifts to the second part of the journey (the relay to the destination), not the first part.

The researchers were very careful to prove their numbers. They didn't just guess; they used advanced math to create formulas for how often the connection might fail (outage probability), how much data it could carry (capacity), and how many errors might occur (bit error rate). They then ran millions of computer simulations to check their math. The results showed their formulas were accurate to within 4% across a wide range of signal strengths. They also proved that their mathematical shortcut for calculating the smart wall's effect is reliable as long as there are at least 20 tiles, though they noted that even with fewer tiles (down to 10), the error is so small and conservative that it's safe to use for planning.

One of the most surprising findings was that the weather on the radio side (the "shouting" part) matters much more than the atmospheric turbulence on the laser side. Even if the laser beam is dancing wildly in the wind, as long as the radio signal hitting the smart wall is clear, the whole system works well. But if the radio signal is weak or bumpy, no amount of laser power can save the connection. The study concludes that for engineers building these systems, the smart wall is not just a fancy add-on; it is the essential ingredient that makes the hybrid system work at all, and a wall with about 10 to 20 tiles is the most cost-effective size to aim for.

Technical Summary: Performance Analysis of RIS-Assisted Hybrid RF/FSO Communication Systems

Problem Statement
Delivering reliable broadband to sparsely populated regions remains a significant challenge in wireless network design. While fiber is often prohibitively expensive and conventional microwave backhaul struggles with non-line-of-sight propagation, hybrid Radio-Frequency/Free-Space-Optical (RF/FSO) systems offer a potential remedy by pairing complementary transmission media. However, existing literature lacks a comprehensive end-to-end statistical analysis of a specific, practical topology: a Reconfigurable Intelligent Surface (RIS) positioned on the source-to-relay hop to enhance the first link, followed by a Decode-and-Forward (DF) relay that transmits over parallel RF and FSO links to the destination. A critical gap exists in understanding how the cascaded channel created by an upstream RIS interacts with the diversity of the second hop, particularly regarding the statistical validity of approximations for the RIS gain and the resulting system performance metrics.

Methodology
The authors propose a system model comprising a Source (S), an N-element RIS, a DF Relay (R), and a Destination (D).

Channel Models: The first hop (S to RIS to R) involves Nakagami-m fading. The second hop consists of parallel links: an RF link (Nakagami-m fading) and an FSO link (Gamma–Gamma turbulence).
Relaying and Combining: The relay employs Decode-and-Forward (DF) to avoid amplifying noise. The destination utilizes Selection Combining (SC) to select the stronger of the two second-hop branches.
Statistical Approach: To characterize the cascaded RIS channel (a sum of products of Nakagami-m variates), the authors employ a Central Limit Theorem (CLT) approximation. They establish a validity domain for this approximation using a skewness criterion, determining that the Gaussian model is reliable for $N \ge 20$ elements.
Analytical Derivation: A closed-form expression for the end-to-end Outage Probability (OP) is derived by combining the RIS-assisted first-hop CDF with the product of the second-hop branch CDFs. Ergodic Capacity (EC) and Average Bit Error Rate (BER) are subsequently calculated using adaptive quadrature and numerical integration.
Verification: All analytical expressions are independently verified against Monte Carlo simulations in MATLAB, ensuring relative errors remain below 4% across the practical Signal-to-Noise Ratio (SNR) range.

Key Contributions

End-to-End Analysis: The paper derives the first closed-form end-to-end outage probability for the specific S–RIS–R–D topology where the RIS acts as the sole first-hop enhancement feeding a hybrid RF/FSO second hop.
Validity of Approximation: The study quantitatively establishes the validity of the CLT approximation for the RIS channel gain. It demonstrates that while the Gaussian model holds for $N \ge 20$ , the residual error in the cost-effective range of $N=10$ to $20$ is conservative (underestimating performance) and remains below 0.5% in outage probability at practical SNRs.
Comprehensive Metrics: The framework provides a unified analytical object from which Outage Probability, Ergodic Capacity, and Average BER are derived, offering a three-metric characterization of system performance.
Design Guidelines: The numerical study yields specific engineering insights regarding the optimal number of RIS elements and the comparative performance of hybrid systems with and without RIS assistance.

Results

Performance Gain: The RIS-assisted system achieves a consistent 7–8 dB SNR saving compared to both RF-only and non-RIS hybrid baselines to reach the same reliability targets. This translates to a fivefold reduction in required transmit power.
Diminishing Returns: Performance gains from increasing the number of RIS elements ( $N$ ) saturate beyond $N \approx 10$ to $20$. In this range, the system bottleneck shifts from the first hop to the second hop. Consequently, $N=10$ to $20$ is identified as the economical array size.
Necessity of RIS: A critical finding is that without the RIS, the hybrid RF/FSO system underperforms a single RF link. The unassisted first hop creates a bottleneck that prevents the destination's selection combining from providing diversity gains. Thus, the RIS is a precondition for hybrid diversity in this topology, not merely an add-on.
Dominant Factors: The RF-side fading severity (Nakagami-m parameter $m$ ) has a more significant impact on the link budget than atmospheric turbulence conditions (Gamma–Gamma parameters).
Robustness: The system capacity remains relatively invariant to changes in optical turbulence conditions, varying by less than 0.2 bits/s/Hz across weak to strong turbulence regimes.

Significance
The paper positions itself as closing a specific analytical gap in the literature regarding upstream RIS placement in hybrid relay systems. Its significance lies in providing a tractable, verified analytical framework that engineers can use to design cost-effective backhaul solutions. By quantifying the trade-offs between RIS element count and system performance, and by demonstrating that the hybrid system fails to outperform single-link RF without RIS assistance, the study offers a realistic assessment of the technology's value. The authors emphasize that their closed-form expressions, while relying on a CLT approximation, are sufficiently accurate and conservative for the economically optimal range of RIS deployments ( $N=10–20$ ), validated by rigorous simulation.

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