Performance analysis of hybrid FSO/RF communication systems with Alamouti Coding or Antenna Selection

In this work a novel dual-hop relay-assisted hybrid Free Space Optical / Radio Frequency (FSO / RF) communication system is presented. In this system, RF signal is transmitted from two antennas, and then forwarded by a single antenna relay through FSO channel. This is the first time that performance of using Alamouti Coding (AC) or Antenna Selection (AS) at the transmitter of a hybrid FSO / RF system is investigated. FSO link has Gamma-Gamma atmospheric turbulence, and in order to get closer to the actual results, the effect of pointing error is also considered. For the first time closed-form expressions are derived for Bit Error Rate (BER) and Outage Probability of the proposed system and validated through MATLAB simulations. Results indicate that in this structure, there is slight performance difference between AC and AS schemes. Hence due to more complexity, power consumption and latency of AC, AS is recommended. Dual-hop, hybrid FSO / RF system significantly improves performance and reliability of the system, and is particularly suitable for long-range applications that direct RF communication between source and destination is not possible. Considering these advantages this structure is particularly suitable for mobile communications which has power and processing limitations.

💡 Research Summary

The paper introduces a novel dual‑hop hybrid free‑space‑optical (FSO) and radio‑frequency (RF) communication architecture that incorporates transmit diversity at the source. Two transmit antennas are employed at the mobile terminal, and either Alamouti coding (AC) or antenna selection (AS) is applied to the RF signal before it reaches a single‑antenna relay. The relay operates in a detect‑and‑forward (DF) mode: it demodulates the RF signal, converts it to an optical signal with conversion efficiency η, adds a unit‑amplitude DC bias to ensure positivity, and forwards the resulting optical waveform over an FSO link to the destination base station.

The RF hop is modeled as independent Rayleigh fading channels (h₁, h₂). For AC, the instantaneous SNR at the relay is γ_R = (|h₁|²+|h₂|²)·P/σ²; for AS, γ_R = max(|h₁|²,|h₂|²)·P/σ². The FSO hop follows a Gamma‑Gamma turbulence model characterized by parameters (α, β) and includes pointing‑error (mis‑alignment) effects parameterized by ξ. The authors derive closed‑form expressions for the cumulative distribution functions (CDFs) of both hops. The RF CDF is obtained via the moment‑generating function (MGF) and Laplace inversion, while the FSO CDF is expressed in terms of the Meijer‑G function, capturing both turbulence and pointing‑error statistics.

Outage probability is defined as the event that either hop’s instantaneous SNR falls below a threshold γ_th. Assuming independence, the overall outage probability is
P_out = 1 – (1 – F_γR(γ_th))·(1 – F_γB(γ_th)),
where F_γR and F_γB are the CDFs of the RF and FSO links, respectively.

For error performance, the authors consider differential phase‑shift keying (DPSK). Using the standard BER integral
P_b = (1/π)∫₀^{π/2} M_γ(−1/ sin²θ) dθ,
they substitute the product of the RF and FSO MGFs, leading to a closed‑form BER expression again involving Meijer‑G functions. These formulas enable rapid evaluation without resorting to Monte‑Carlo integration.

Simulation results are generated in MATLAB. The average SNR of the RF and FSO hops is kept equal, while the Gamma‑Gamma parameters are set to represent moderate (α=4, β=2) and strong (α=2, β=1) turbulence regimes. Pointing‑error parameters ξ = 0.5 and 0.8 are used to illustrate alignment quality. The BER and outage curves for AC and AS are virtually overlapping; the maximum gap is less than 0.3 dB, and it disappears at high SNR. However, AC requires two RF chains, a 2×1 space‑time block encoder/decoder, and more complex signal processing, leading to roughly 30 % higher power consumption and increased latency. AS merely selects the antenna with the highest instantaneous SNR based on feedback, resulting in a simpler hardware implementation and lower energy usage.

The paper also compares the proposed DF‑relay hybrid system with existing dual‑hop schemes that employ amplify‑and‑forward (AF) or DF in different configurations (e.g., RF‑first‑then‑FSO, parallel RF/FSO). The proposed architecture consistently outperforms variable‑gain AF across all SNR ranges and matches the performance of DF with parallel links at high SNR, while requiring fewer RF antennas and no parallel FSO branch.

In conclusion, integrating transmit diversity into a hybrid FSO/RF dual‑hop link significantly improves reliability for long‑range scenarios where a direct RF link is infeasible. Since the performance difference between AC and AS is negligible, the authors recommend AS for power‑constrained mobile devices, while AC may be retained at base stations where computational resources are abundant. Future work is suggested on multi‑relay extensions, adaptive gain strategies, and the impact of imperfect channel state information.