Performance of Decode-and-Forward Relaying in Mixed Beaulieu-Xie and <tex-math notation='LaTeX'>$\mathcal{M}$ </tex-math> Dual-Hop Transmission Systems With Digital Coherent Detection

Performance analysis is presented for a decode-and-forward protocol based mixed radio-frequency (RF) and free-space optical (FSO) dual-hop transmission system with digital coherent detection. The RF path is modeled by Beaulieu-Xie fading, while the FSO hop is characterised by the Malaga ( $\mathcal {M}$ ) distributed turbulence with pointing errors. We first derive novel and exact analytical expressions for the cumulative distribution function (CDF), the probability density function and the moment generating function (MGF) of the overall signal-to-noise ratio by means of Meijer’s G function, followed by the accurate infinite series expressions of the performance criterions, such as the outage probability, the average bit-error rate (BER) and the ergodic capacity (average channel capacity). Asymptotic analysis for the CDF, the MGF, the outage probability, the average BER, and the ergodic capacity is also provided. Monte Carlo simulations are performed to verify these derived expressions.