LCR and AFD of the Products of Nakagami-m and Nakagami-m Squared Random Variables: Application to Wireless Communications Through Relays

Caslav Stefanovic,Ivan Milovanovic,Mihajlo Stefanovic,Stefan Panic

doi:10.1007/s11277-021-09258-6

Caslav Stefanovic, Ivan Milovanovic + Show 2 more

Open Access

https://doi.org/10.1007/s11277-021-09258-6

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Abstract

The paper considers level crossing rate (LCR) and average fade duration (AFD) of the product of independent and identically distributed (i.i.d) Nakagami-m (NM) and double NM squared (also known as gamma-gamma) random variables (RVs). The derived statistics are then directly applied to the radio-frequency (RF) - free space optical (FSO), dual-hop (DH), amplify-and-forward (AF) relaying system over non turbulent-induced-fading channels (nTIFCs) and turbulent-induced-fading channels (TIFCs). The obtained results for LCR and AFD of DH-AF, RF-FSO system over TIFCs and nTIFCs are numerically evaluated and graphically presented for various system model parameters.

Highlights

Relaying wireless systems play an important role in wireless communications
The Nakagami-m (NM) random variables (RVs) can be used to model non turbulent-induced-fading channels (nTIFCs) in RF environments [26]-[28], while gamma-gamma RV is the most often used to model the fading for free space optical (FSO) communications in moderate to strong turbulent-induced-fading channels (TIFCs) environments [29]-[31]
The derived statistical measures are directly applied to dual-hop (DH) amplifyand forward (AF) relay RF-FSO communications over mixed nTIFC and TIFC

Summary

Introduction

Relaying wireless systems play an important role in wireless communications. The huge variety of technologies that includes relays are all radio-frequency (RF) relaying schemes, all free-space-optical (FSO) relaying schemes, mixed RF-FSO relaying schemes, millimeter-wave (mmW)-FSO relaying schemes given in [1]-[4], respectively. The above-mentioned works consider the first-order statistics (FOS) of mixed RF-FSO relay systems. The SOS over log-normal TIFC of multi-hop FSO system including pointing errors are addressed in [23]. The SOS of V2V of mixed RF-FSO-RF over NM nTIFC and gamma-gamma TIFC are considered in [6]. The Nakagami-m (NM) RV can be used to model nTIFC in RF environments [26]-[28], while gamma-gamma (double squared NM) RV is the most often used to model the fading for FSO communications in moderate to strong TIFC environments [29]-[31]. The derived statistical measures are directly applied to dual-hop (DH) AF relay RF-FSO communications over mixed nTIFC and TIFC. To the best of author’s knowledge there is no publications on the SOS of DH-AF mixed RF-FSO systems

System Model

Numerical results

Conclusion