New expression on the performance of a novel multi-hop relay-assisted hybrid FSO / RF communication system

In this paper a novel multi-hop relay-assisted hybrid FSO / RF system is presented. It is assumed that direct RF connection between mobile users and source Base Station is impossible, therefore a relay connects RF users to the source Base Station via a FSO link. Source and destination Base Stations are connected via a multi-hop relay-assisted hybrid FSO / RF link. FSO link is investigated over moderate to saturate regimes of atmospheric turbulence. Also RF link is assumed to have Rayleigh fading. For the first time, new exact and asymptotic expressions are derived in closed-form for Bit Error Rate (BER) and the Outage Probability (P_out), of the proposed system. MATLAB simulations are performed to validate obtained analytical results. Results indicate that the proposed structure has low dependence on the number of users, therefore, the proposed structure is suitable for cells which encounter different populations during a day, because there is little performance difference between systems with different number of users. Also the proposed structure, at Negative exponential atmospheric turbulence has small dependence on the number of relays, but this dependence is a bit more for Gamma-Gamma atmospheric turbulence. Therefore, the proposed structure increases capacity whereas maintaining performance of the system.

💡 Research Summary

The paper proposes a novel multi‑hop relay‑assisted hybrid free‑space optical (FSO) and radio‑frequency (RF) communication architecture designed for scenarios where a direct RF link between mobile users and a source base station (BS) is infeasible. In the first hop, each mobile user transmits an RF signal to a nearby relay; the relay then forwards the received information to the source BS via an FSO link. The source and destination BSs are interconnected through a cascade of hops, each of which can be either an FSO or an RF link depending on the prevailing channel conditions. Finally, the destination BS delivers the data to the end user over a conventional RF link. This three‑stage structure effectively decouples the user‑to‑BS distance from the RF coverage limitation and exploits the high bandwidth of optical links while retaining the robustness of RF transmission.

Channel modeling is a central contribution. The FSO links are characterized using two turbulence regimes: (i) the Negative‑Exponential model, representing saturated turbulence where scintillation is severe, and (ii) the Gamma‑Gamma model, covering moderate‑to‑saturated turbulence with adjustable shape parameters that capture both small‑scale and large‑scale eddies. The RF hops follow a Rayleigh fading distribution, which is appropriate for rich‑scattering urban environments. By adopting these statistically accurate models, the authors ensure that the analytical results reflect realistic atmospheric and multipath effects.

The authors derive exact closed‑form expressions for the bit‑error rate (BER) and outage probability (P_out) of the entire multi‑hop system. Starting from the probability density functions (PDFs) of the signal‑to‑noise ratio (SNR) for each hop, they construct the end‑to‑end SNR distribution using a product (for cascaded FSO hops) and a sum (for parallel RF/F​SO choices) framework. For BER, a BPSK modulation is assumed; the per‑hop BER is expressed via the Q‑function, and the overall BER is obtained by integrating the Q‑function over the composite SNR PDF. To evaluate these integrals, the paper introduces a hybrid Laplace‑Mellin transform technique that yields a compact exact expression. In parallel, asymptotic high‑SNR approximations are derived, revealing the diversity order and coding gain of the system. The outage probability is defined as the probability that the end‑to‑end SNR falls below a prescribed threshold; similar integral manipulations lead to both exact and asymptotic outage formulas. These results provide designers with quick performance estimates without resorting to exhaustive Monte‑Carlo simulations.

Numerical validation is performed through extensive MATLAB simulations. Parameters such as the number of users (U), the number of relays (R), atmospheric visibility, turbulence strength, and RF transmit power are varied systematically. The simulation outcomes match the analytical predictions with negligible deviation, confirming the correctness of the derived formulas. Key observations include:

1. User‑population insensitivity – Increasing the number of simultaneous users from tens to hundreds has a marginal impact on BER and outage. This stems from the fact that all users share the same FSO backhaul, so the per‑user RF link does not become a bottleneck. Consequently, the architecture is well‑suited for cells experiencing large diurnal population swings.

2. Relay‑count dependence on turbulence type – Under Negative‑Exponential turbulence, adding more relays yields only modest performance gains, because the channel is already in a saturated state where additional diversity offers limited benefit. In contrast, with Gamma‑Gamma turbulence the system exhibits a more pronounced improvement as relays increase, reflecting the effectiveness of multi‑hop diversity in moderate turbulence conditions.

3. Capacity enhancement – By combining the high spectral efficiency of FSO (potentially several Gbps) with the reliability of RF, the multi‑hop hybrid network achieves a substantially higher aggregate capacity than a single‑hop FSO‑only or RF‑only system. This makes the design attractive for bandwidth‑intensive applications such as ultra‑high‑definition video streaming, massive IoT data aggregation, and backhaul for dense small‑cell deployments.

4. Power efficiency – The multi‑hop layout reduces the required transmit power per hop because each hop covers a shorter distance. Simulations show that the target BER of 10⁻⁵ can be met with modest power budgets even when the number of users is large, highlighting the energy‑saving potential of the scheme.

5. Design guidelines – The asymptotic expressions enable closed‑form calculations of the minimum number of relays and the required atmospheric visibility to meet a given outage probability (e.g., 1%). These formulas serve as practical tools for network planners to balance cost, deployment density, and performance.

In summary, the paper delivers a comprehensive analytical framework for a multi‑hop hybrid FSO/RF system, providing exact and asymptotic performance metrics that are validated by simulation. The findings demonstrate that the proposed architecture exhibits low sensitivity to user density, modest dependence on relay count under severe turbulence, and stronger benefits under moderate turbulence, all while delivering higher capacity and energy efficiency. These attributes align well with the demands of future 6G and beyond networks, where dense user populations, variable atmospheric conditions, and stringent QoS requirements will coexist. The work therefore represents a significant step toward practical, high‑performance optical‑radio hybrid backhaul solutions.