Abstract

We investigate the performance of a dual-hop mixed radio frequency (RF)/free space optical (FSO) system with variable-gain relaying. The RF link is modeled by the $\kappa$ - $\mu$ shadowed distribution, which unifies popular RF channel models. The FSO link is subject to atmospheric turbulence with non-zero boresight pointing errors. The atmospheric turbulence channel is modeled by the Fisher-Snedecor ${\mathcal F}$ distribution, which fits well with the measurement data under weak-to-strong turbulence conditions. The pointing error is modeled by the Beckmann distribution, which includes popular pointing error models. We propose an approximation method to approximate the $\kappa$ - $\mu$ shadowed distribution using an $\alpha$ - $\mu$ distribution, which is more accurate than that using a gamma distribution in the existing literatures. Then, we derive closed-form expressions for the probability density function (PDF) and the cumulative distribution function (CDF) for the irradiance fluctuations. Based on these expressions, we derive closed-form approximate expressions for the CDF, the PDF, the moment generating function (MGF), the average bit error rate (BER), and the ergodic capacity (EC) of the considered system in terms of the bivariate Fox’s H function. Furthermore, asymptotic expressions for the CDF and the average BER at high signal-to-noise ratio (SNR) are derived in terms of simple elementary functions. Finally, numerical results and Monte Carlo (MC) simulations are provided to verify the derived approximate expressions.

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