# Performance Analysis of FSO-UWOC Mixed Dual-Hop Relay System with Decode-and-Forward Protocol
## 1 Introduction
The authors of [24] introduced a data collection scheme for underwater acoustic sensor networks aided by AUVs. By decomposing the optimization problem into cluster head selection, clustering algorithm design, media access control protocol development, and AUV path planning, the study devised two algorithms to optimize energy efficiency and data collection efficiency. Additionally, focusing on improving relay protocol performance, ref. [25] presented a new soft information relaying technique based on the soft decode-compress-forward relay protocol. This technique overcomes the limitations of traditional relay methods by generating soft Pulse Amplitude Modulation/Quadrature Amplitude Modulation symbols at the relay node and leveraging a soft scalar model to compute log-likelihood ratios at the destination, thereby enhancing decoding reliability and spectral efficiency. In view of the foregoing discussion, this study will comprehensively take into account the impacts of key channel fading factors on each transmission link, including the turbulence effects, pointing errors, and path loss, based on the reported experimental data. Under the DF relay protocol, we conduct a detailed performance analysis of the average OP, BER, and ergodic capacity for a mixed FSO-UWOC system, considering both the HD and IM/DD mechanisms. Corresponding asymptotic performance analyses under high signal-to-noise ratio (SNR) conditions are also presented. The main contributions of this study are outlined as follows:  
* A new composite fading channel model was proposed to comprehensively represent the fading statistics of FSO and/or UWOC transmission links. For the FSO link, in the light of the findings in [15], the channel is modeled as a hybrid-fading channel that integrates the GG atmospheric turbulence, zero-boresight pointing errors, and Beer-Lambert single-exponential path loss. For the UWOC link, leveraging the laboratory measurement data from [16; 17], along with the MC simulations and data-fitting results from [19], the channel is modeled as a hybrid-fading one, incorporating the GGD oceanic turbulence, zero-boresight pointing errors, and Elamassie underwater path loss. Based on the proposed composite fading channel model described above, the PDF and cumulative distribution function (CDF) closed-form expressions of the instantaneous SNR for both the FSO and UWOC links are derived using the advanced transcendental Meijer-G functions, in the case of HD and IM/DD receiver detection methods, respectively. * Employing the derived expressions for the PDF and CDF of the instantaneous SNR of the hybrid-fading FSO and UWOC links, the theoretical closed-form expressions for the average OP, average BER, and average channel capacity of the mixed dual-hop FSO-UWOC system are obtained by using the Meijer-G functions and the bivariate Fox-H functions. Moreover, asymptotic analyses for the average OP and average BER under high-SNR conditions are also presented. * MC numerical simulations are conducted to verify the accuracy of the theoretical expressions for the average OP, average BER, and average channel capacity of the mixed dual-hop FSO-UWOC system, along with their corresponding asymptotic expressions. Furthermore, the influence of different core system parameters on the whole system performance is also explored.