  In this work, we provide a detailed analysis of a dual-hop fixed gain (FG)
amplify-and-forward relaying system, consisting of a hybrid radio frequency
(RF) and free-space optical (FSO) channels. We introduce an impairment model
which is the soft envelope limiter (SEL). Additionally, we propose the partial
relay selection (PRS) protocol with outdated channel state information (CSI)
based on the knowledge of the RF channels in order to select one relay for the
communication. Moreover, the RF channels of the first hop experience Rayleigh
fading while we propose a unified fading model for the FSO channels, called the
unified Gamma Gamma (GG), taking into account the atmospheric turbulence, the
path loss and the misalignment between the transmitter and the receiver
aperture also called the pointing error. Novel closed-forms of the outage
probability (OP), the bit error probability (BEP) and the average ergodic
capacity (EC) are derived in terms of Meijer-G and Fox-H functions.
Capitalizing on these metrics, we also derive the asymptotical high
signal-to-noise ratio (SNR) in order to get engineering insights into the
impacts of the hardware impairments and the system parameters as well. Finally,
using Monte Carlo simulations, we validate numerically the derived mathematical
formulations.
