# Hybrid Rayleigh and Double-Weibull over Impaired RF/FSO System with Outdated CSI

## TL;DR

This paper analyzes a dual-hop RF/FSO system with outdated CSI, hardware impairments, and specific fading models, deriving formulas for outage probability and capacity to evaluate system performance.

## Contribution

It introduces a comprehensive analytical framework for RF/FSO systems considering outdated CSI, hardware impairments, and combined Rayleigh and Double-Weibull fading models, providing new performance metrics.

## Key findings

- Derived closed-form outage probability expressions.
- Provided asymptotic high-SNR capacity bounds.
- Validated results with Monte Carlo simulations.

## Abstract

In this work, we present a global framework of a dual-hop RF/FSO system with multiple relays operating at the mode of amplify-and-forward (AF) with fixed gain. Partial relay selection (PRS) protocol with outdated channel state information (CSI) is assumed since the channels of the first hop are time-varying. The optical irradiance of the second hop are subject to the Double-Weibull model while the RF channels of the first hop experience the Rayleigh fading. The signal reception is achieved either by heterodyne or intensity modulation and direct detection (IM/DD). In addition, we introduce an aggregate model of hardware impairments to the source (S) and the relays since they are not perfect nodes. In order to quantify the impairment impact on the system, we derive closed-form, approximate, upper bound and high signal-to-noise ratio (SNR) asymptotic of the outage probability (OP) and the ergodic capacity (EC). Finally, analytical and numerical results are in agreement using Monte Carlo simulation.